Là một nhà phát triển, có lẽ bạn đã quen thuộc với khái niệm thuật toán. Nhưng nếu cấu trúc dữ liệu và thuật toán không phù hợp với bạn, đừng lo lắng. Trong bài viết này, chúng ta sẽ xem xét sáu thuật toán chính mà mọi nhà phát triển nên biết. Sáu thuật toán này hầu như luôn có thể giải quyết bất kỳ vấn đề nào bạn gặp phải trong quá trình phát triển của mình.
1. Thuật toán sắp xếp
Sắp xếp là quá trình sắp xếp các mục trong danh sách theo một thứ tự cụ thể. Các loại thuật toán sắp xếp phổ biến nhất bao gồm:
Sắp xếp bong bóng
Sắp xếp bong bóng là thuật toán sắp xếp cơ bản nhất. Nó hoạt động bằng cách hoán đổi liên tục các phần tử liền kề nếu chúng không đúng thứ tự.
1 2 3 4 5 6 7 8 9 10 11 12 | <span class="token keyword">function</span> <span class="token function">bubbleSort</span> <span class="token punctuation">(</span> <span class="token parameter">arr</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">for</span> <span class="token punctuation">(</span> <span class="token keyword">let</span> i <span class="token operator">=</span> <span class="token number">0</span> <span class="token punctuation">;</span> i <span class="token operator"><</span> arr <span class="token punctuation">.</span> length <span class="token punctuation">;</span> i <span class="token operator">++</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">for</span> <span class="token punctuation">(</span> <span class="token keyword">let</span> j <span class="token operator">=</span> <span class="token number">0</span> <span class="token punctuation">;</span> j <span class="token operator"><</span> arr <span class="token punctuation">.</span> length <span class="token operator">-</span> i <span class="token operator">-</span> <span class="token number">1</span> <span class="token punctuation">;</span> j <span class="token operator">++</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> arr <span class="token punctuation">[</span> j <span class="token punctuation">]</span> <span class="token operator">></span> arr <span class="token punctuation">[</span> j <span class="token operator">+</span> <span class="token number">1</span> <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token punctuation">[</span> arr <span class="token punctuation">[</span> j <span class="token punctuation">]</span> <span class="token punctuation">,</span> arr <span class="token punctuation">[</span> j <span class="token operator">+</span> <span class="token number">1</span> <span class="token punctuation">]</span> <span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">[</span> arr <span class="token punctuation">[</span> j <span class="token operator">+</span> <span class="token number">1</span> <span class="token punctuation">]</span> <span class="token punctuation">,</span> arr <span class="token punctuation">[</span> j <span class="token punctuation">]</span> <span class="token punctuation">]</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <span class="token keyword">return</span> arr <span class="token punctuation">;</span> <span class="token punctuation">}</span> console <span class="token punctuation">.</span> <span class="token function">log</span> <span class="token punctuation">(</span> <span class="token function">bubbleSort</span> <span class="token punctuation">(</span> <span class="token punctuation">[</span> <span class="token number">5</span> <span class="token punctuation">,</span> <span class="token number">3</span> <span class="token punctuation">,</span> <span class="token number">8</span> <span class="token punctuation">,</span> <span class="token number">2</span> <span class="token punctuation">,</span> <span class="token number">1</span> <span class="token punctuation">,</span> <span class="token number">4</span> <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token comment">// [1, 2, 3, 4, 5, 8]</span> |
Hợp nhất Sắp xếp
Hợp nhất sắp xếp sử dụng chiến lược “chia để trị”. Nó chia một mảng thành hai nửa, sắp xếp từng nửa, rồi hợp nhất các nửa đã sắp xếp lại với nhau.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | <span class="token keyword">function</span> <span class="token function">mergeSort</span> <span class="token punctuation">(</span> <span class="token parameter">arr</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> arr <span class="token punctuation">.</span> length <span class="token operator"><</span> <span class="token number">2</span> <span class="token punctuation">)</span> <span class="token keyword">return</span> arr <span class="token punctuation">;</span> <span class="token keyword">let</span> middle <span class="token operator">=</span> Math <span class="token punctuation">.</span> <span class="token function">floor</span> <span class="token punctuation">(</span> arr <span class="token punctuation">.</span> length <span class="token operator">/</span> <span class="token number">2</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">let</span> left <span class="token operator">=</span> arr <span class="token punctuation">.</span> <span class="token function">slice</span> <span class="token punctuation">(</span> <span class="token number">0</span> <span class="token punctuation">,</span> middle <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">let</span> right <span class="token operator">=</span> arr <span class="token punctuation">.</span> <span class="token function">slice</span> <span class="token punctuation">(</span> middle <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">return</span> <span class="token function">merge</span> <span class="token punctuation">(</span> <span class="token function">mergeSort</span> <span class="token punctuation">(</span> left <span class="token punctuation">)</span> <span class="token punctuation">,</span> <span class="token function">mergeSort</span> <span class="token punctuation">(</span> right <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">function</span> <span class="token function">merge</span> <span class="token punctuation">(</span> <span class="token parameter">left <span class="token punctuation">,</span> right</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> result <span class="token operator">=</span> <span class="token punctuation">[</span> <span class="token punctuation">]</span> <span class="token punctuation">;</span> <span class="token keyword">while</span> <span class="token punctuation">(</span> left <span class="token punctuation">.</span> length <span class="token operator">&&</span> right <span class="token punctuation">.</span> length <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> left <span class="token punctuation">[</span> <span class="token number">0</span> <span class="token punctuation">]</span> <span class="token operator"><=</span> right <span class="token punctuation">[</span> <span class="token number">0</span> <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> result <span class="token punctuation">.</span> <span class="token function">push</span> <span class="token punctuation">(</span> left <span class="token punctuation">.</span> <span class="token function">shift</span> <span class="token punctuation">(</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">else</span> <span class="token punctuation">{</span> result <span class="token punctuation">.</span> <span class="token function">push</span> <span class="token punctuation">(</span> right <span class="token punctuation">.</span> <span class="token function">shift</span> <span class="token punctuation">(</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <span class="token keyword">while</span> <span class="token punctuation">(</span> left <span class="token punctuation">.</span> length <span class="token punctuation">)</span> result <span class="token punctuation">.</span> <span class="token function">push</span> <span class="token punctuation">(</span> left <span class="token punctuation">.</span> <span class="token function">shift</span> <span class="token punctuation">(</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">while</span> <span class="token punctuation">(</span> right <span class="token punctuation">.</span> length <span class="token punctuation">)</span> result <span class="token punctuation">.</span> <span class="token function">push</span> <span class="token punctuation">(</span> right <span class="token punctuation">.</span> <span class="token function">shift</span> <span class="token punctuation">(</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">return</span> result <span class="token punctuation">;</span> <span class="token punctuation">}</span> console <span class="token punctuation">.</span> <span class="token function">log</span> <span class="token punctuation">(</span> <span class="token function">mergeSort</span> <span class="token punctuation">(</span> <span class="token punctuation">[</span> <span class="token number">5</span> <span class="token punctuation">,</span> <span class="token number">3</span> <span class="token punctuation">,</span> <span class="token number">8</span> <span class="token punctuation">,</span> <span class="token number">2</span> <span class="token punctuation">,</span> <span class="token number">1</span> <span class="token punctuation">,</span> <span class="token number">4</span> <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token comment">// [1, 2, 3, 4, 5, 8]</span> |
Sắp xếp nhanh chóng
Quicksort là một thuật toán sắp xếp phổ biến, trung bình thực hiện phép so sánh n log n khi sắp xếp một mảng gồm n phần tử. Nó là một thuật toán sắp xếp hiệu quả hơn và nhanh hơn.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | <span class="token keyword">function</span> <span class="token function">quickSort</span> <span class="token punctuation">(</span> <span class="token parameter">arr</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> arr <span class="token punctuation">.</span> length <span class="token operator"><</span> <span class="token number">2</span> <span class="token punctuation">)</span> <span class="token keyword">return</span> arr <span class="token punctuation">;</span> <span class="token keyword">let</span> pivot <span class="token operator">=</span> arr <span class="token punctuation">[</span> arr <span class="token punctuation">.</span> length <span class="token operator">-</span> <span class="token number">1</span> <span class="token punctuation">]</span> <span class="token punctuation">;</span> <span class="token keyword">let</span> left <span class="token operator">=</span> <span class="token punctuation">[</span> <span class="token punctuation">]</span> <span class="token punctuation">;</span> <span class="token keyword">let</span> right <span class="token operator">=</span> <span class="token punctuation">[</span> <span class="token punctuation">]</span> <span class="token punctuation">;</span> <span class="token keyword">for</span> <span class="token punctuation">(</span> <span class="token keyword">let</span> i <span class="token operator">=</span> <span class="token number">0</span> <span class="token punctuation">;</span> i <span class="token operator"><</span> arr <span class="token punctuation">.</span> length <span class="token operator">-</span> <span class="token number">1</span> <span class="token punctuation">;</span> i <span class="token operator">++</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> arr <span class="token punctuation">[</span> i <span class="token punctuation">]</span> <span class="token operator"><</span> pivot <span class="token punctuation">)</span> <span class="token punctuation">{</span> left <span class="token punctuation">.</span> <span class="token function">push</span> <span class="token punctuation">(</span> arr <span class="token punctuation">[</span> i <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">else</span> <span class="token punctuation">{</span> right <span class="token punctuation">.</span> <span class="token function">push</span> <span class="token punctuation">(</span> arr <span class="token punctuation">[</span> i <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <span class="token keyword">return</span> <span class="token function">quickSort</span> <span class="token punctuation">(</span> left <span class="token punctuation">)</span> <span class="token punctuation">.</span> <span class="token function">concat</span> <span class="token punctuation">(</span> pivot <span class="token punctuation">,</span> <span class="token function">quickSort</span> <span class="token punctuation">(</span> right <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> console <span class="token punctuation">.</span> <span class="token function">log</span> <span class="token punctuation">(</span> <span class="token function">quickSort</span> <span class="token punctuation">(</span> <span class="token punctuation">[</span> <span class="token number">5</span> <span class="token punctuation">,</span> <span class="token number">3</span> <span class="token punctuation">,</span> <span class="token number">8</span> <span class="token punctuation">,</span> <span class="token number">2</span> <span class="token punctuation">,</span> <span class="token number">1</span> <span class="token punctuation">,</span> <span class="token number">4</span> <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token comment">// [1, 2, 3, 4, 5, 8]</span> |
Sắp xếp đống
Sắp xếp đống hoạt động bằng cách trực quan hóa các phần tử mảng dưới dạng một loại cây nhị phân hoàn chỉnh đặc biệt được gọi là đống. Quá trình đống hóa một mảng được lặp lại cho đến khi mảng được sắp xếp.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | <span class="token keyword">function</span> <span class="token function">heapSort</span> <span class="token punctuation">(</span> <span class="token parameter">arr</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> n <span class="token operator">=</span> arr <span class="token punctuation">.</span> length <span class="token punctuation">;</span> <span class="token keyword">for</span> <span class="token punctuation">(</span> <span class="token keyword">let</span> i <span class="token operator">=</span> n <span class="token operator">/</span> <span class="token number">2</span> <span class="token operator">-</span> <span class="token number">1</span> <span class="token punctuation">;</span> i <span class="token operator">>=</span> <span class="token number">0</span> <span class="token punctuation">;</span> i <span class="token operator">--</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token function">heapify</span> <span class="token punctuation">(</span> arr <span class="token punctuation">,</span> n <span class="token punctuation">,</span> i <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">for</span> <span class="token punctuation">(</span> <span class="token keyword">let</span> i <span class="token operator">=</span> n <span class="token operator">-</span> <span class="token number">1</span> <span class="token punctuation">;</span> i <span class="token operator">>=</span> <span class="token number">0</span> <span class="token punctuation">;</span> i <span class="token operator">--</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token punctuation">[</span> arr <span class="token punctuation">[</span> <span class="token number">0</span> <span class="token punctuation">]</span> <span class="token punctuation">,</span> arr <span class="token punctuation">[</span> i <span class="token punctuation">]</span> <span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">[</span> arr <span class="token punctuation">[</span> i <span class="token punctuation">]</span> <span class="token punctuation">,</span> arr <span class="token punctuation">[</span> <span class="token number">0</span> <span class="token punctuation">]</span> <span class="token punctuation">]</span> <span class="token punctuation">;</span> <span class="token function">heapify</span> <span class="token punctuation">(</span> arr <span class="token punctuation">,</span> i <span class="token punctuation">,</span> <span class="token number">0</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">return</span> arr <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">function</span> <span class="token function">heapify</span> <span class="token punctuation">(</span> <span class="token parameter">arr <span class="token punctuation">,</span> n <span class="token punctuation">,</span> i</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> largest <span class="token operator">=</span> i <span class="token punctuation">;</span> <span class="token keyword">let</span> l <span class="token operator">=</span> <span class="token number">2</span> <span class="token operator">*</span> i <span class="token operator">+</span> <span class="token number">1</span> <span class="token punctuation">;</span> <span class="token keyword">let</span> r <span class="token operator">=</span> <span class="token number">2</span> <span class="token operator">*</span> i <span class="token operator">+</span> <span class="token number">2</span> <span class="token punctuation">;</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> l <span class="token operator"><</span> n <span class="token operator">&&</span> arr <span class="token punctuation">[</span> l <span class="token punctuation">]</span> <span class="token operator">></span> arr <span class="token punctuation">[</span> largest <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> largest <span class="token operator">=</span> l <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> r <span class="token operator"><</span> n <span class="token operator">&&</span> arr <span class="token punctuation">[</span> r <span class="token punctuation">]</span> <span class="token operator">></span> arr <span class="token punctuation">[</span> largest <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> largest <span class="token operator">=</span> r <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> largest <span class="token operator">!==</span> i <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token punctuation">[</span> arr <span class="token punctuation">[</span> i <span class="token punctuation">]</span> <span class="token punctuation">,</span> arr <span class="token punctuation">[</span> largest <span class="token punctuation">]</span> <span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">[</span> arr <span class="token punctuation">[</span> largest <span class="token punctuation">]</span> <span class="token punctuation">,</span> arr <span class="token punctuation">[</span> i <span class="token punctuation">]</span> <span class="token punctuation">]</span> <span class="token punctuation">;</span> <span class="token function">heapify</span> <span class="token punctuation">(</span> arr <span class="token punctuation">,</span> n <span class="token punctuation">,</span> largest <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> console <span class="token punctuation">.</span> <span class="token function">log</span> <span class="token punctuation">(</span> <span class="token function">heapSort</span> <span class="token punctuation">(</span> <span class="token punctuation">[</span> <span class="token number">5</span> <span class="token punctuation">,</span> <span class="token number">3</span> <span class="token punctuation">,</span> <span class="token number">8</span> <span class="token punctuation">,</span> <span class="token number">2</span> <span class="token punctuation">,</span> <span class="token number">1</span> <span class="token punctuation">,</span> <span class="token number">4</span> <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token comment">// [1, 2, 3, 4, 5, 8]</span> |
2. Thuật toán tìm kiếm
Tìm kiếm là quá trình tìm kiếm một phần tử trong tập dữ liệu. Các loại thuật toán tìm kiếm phổ biến bao gồm:
Tìm kiếm nhị phân
Tìm kiếm nhị phân sử dụng chiến lược “chia để trị”. Nó chia một danh sách đã sắp xếp thành hai nửa và so sánh giá trị đích với phần tử ở giữa. Nếu tìm thấy kết quả khớp, vị trí của phần tử ở giữa sẽ được trả về.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | <span class="token keyword">function</span> <span class="token function">binarySearch</span> <span class="token punctuation">(</span> <span class="token parameter">arr <span class="token punctuation">,</span> x</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> left <span class="token operator">=</span> <span class="token number">0</span> <span class="token punctuation">;</span> <span class="token keyword">let</span> right <span class="token operator">=</span> arr <span class="token punctuation">.</span> length <span class="token operator">-</span> <span class="token number">1</span> <span class="token punctuation">;</span> <span class="token keyword">while</span> <span class="token punctuation">(</span> left <span class="token operator"><=</span> right <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> middle <span class="token operator">=</span> Math <span class="token punctuation">.</span> <span class="token function">floor</span> <span class="token punctuation">(</span> <span class="token punctuation">(</span> left <span class="token operator">+</span> right <span class="token punctuation">)</span> <span class="token operator">/</span> <span class="token number">2</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> arr <span class="token punctuation">[</span> middle <span class="token punctuation">]</span> <span class="token operator">===</span> x <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">return</span> middle <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">else</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> arr <span class="token punctuation">[</span> middle <span class="token punctuation">]</span> <span class="token operator"><</span> x <span class="token punctuation">)</span> <span class="token punctuation">{</span> left <span class="token operator">=</span> middle <span class="token operator">+</span> <span class="token number">1</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">else</span> <span class="token punctuation">{</span> right <span class="token operator">=</span> middle <span class="token operator">-</span> <span class="token number">1</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <span class="token keyword">return</span> <span class="token operator">-</span> <span class="token number">1</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> console <span class="token punctuation">.</span> <span class="token function">log</span> <span class="token punctuation">(</span> <span class="token function">binarySearch</span> <span class="token punctuation">(</span> <span class="token punctuation">[</span> <span class="token number">1</span> <span class="token punctuation">,</span> <span class="token number">2</span> <span class="token punctuation">,</span> <span class="token number">3</span> <span class="token punctuation">,</span> <span class="token number">4</span> <span class="token punctuation">,</span> <span class="token number">5</span> <span class="token punctuation">,</span> <span class="token number">8</span> <span class="token punctuation">]</span> <span class="token punctuation">,</span> <span class="token number">4</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token comment">// 3</span> |
Tìm kiếm theo chiều rộng đầu tiên (BFS)
Tìm kiếm theo chiều rộng là thuật toán duyệt đồ thị bắt đầu từ nút gốc và khám phá tất cả các nút lân cận.
1 2 3 4 5 6 7 8 9 10 | <span class="token keyword">function</span> <span class="token function">breadthFirstSearch</span> <span class="token punctuation">(</span> <span class="token parameter">root <span class="token punctuation">,</span> target</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> queue <span class="token operator">=</span> <span class="token punctuation">[</span> root <span class="token punctuation">]</span> <span class="token punctuation">;</span> <span class="token keyword">while</span> <span class="token punctuation">(</span> queue <span class="token punctuation">.</span> length <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> node <span class="token operator">=</span> queue <span class="token punctuation">.</span> <span class="token function">shift</span> <span class="token punctuation">(</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> node <span class="token punctuation">.</span> value <span class="token operator">===</span> target <span class="token punctuation">)</span> <span class="token keyword">return</span> node <span class="token punctuation">;</span> queue <span class="token punctuation">.</span> <span class="token function">push</span> <span class="token punctuation">(</span> <span class="token operator">...</span> node <span class="token punctuation">.</span> children <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">return</span> <span class="token keyword">null</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> |
Tìm kiếm theo chiều sâu (DFS)
Tìm kiếm theo chiều sâu là thuật toán duyệt đồ thị bắt đầu từ nút đầu tiên của đồ thị và ngày càng đi sâu hơn cho đến khi tìm thấy nút mục tiêu hoặc nút không có nút con.
1 2 3 4 5 6 7 8 9 | <span class="token keyword">function</span> <span class="token function">depthFirstSearch</span> <span class="token punctuation">(</span> <span class="token parameter">node <span class="token punctuation">,</span> target</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> node <span class="token punctuation">.</span> value <span class="token operator">===</span> target <span class="token punctuation">)</span> <span class="token keyword">return</span> node <span class="token punctuation">;</span> <span class="token keyword">for</span> <span class="token punctuation">(</span> <span class="token keyword">let</span> child <span class="token keyword">of</span> node <span class="token punctuation">.</span> children <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> found <span class="token operator">=</span> <span class="token function">depthFirstSearch</span> <span class="token punctuation">(</span> child <span class="token punctuation">,</span> target <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> found <span class="token punctuation">)</span> <span class="token keyword">return</span> found <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">return</span> <span class="token keyword">null</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> |
3. Lập trình động
Lập trình động (DP) là một kỹ thuật thuật toán giải quyết vấn đề tối ưu hóa bằng cách chia nhỏ nó thành các vấn đề con đơn giản hơn và lợi dụng thực tế là giải pháp tối ưu cho vấn đề tổng thể phụ thuộc vào giải pháp tối ưu cho các vấn đề con của nó. Một ví dụ phổ biến là bài toán tính số Fibonacci thứ n.
1 2 3 4 5 6 7 8 9 10 11 | <span class="token keyword">function</span> <span class="token function">fibonacci</span> <span class="token punctuation">(</span> <span class="token parameter">n</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> dp <span class="token operator">=</span> <span class="token punctuation">[</span> <span class="token punctuation">]</span> <span class="token punctuation">;</span> dp <span class="token punctuation">[</span> <span class="token number">0</span> <span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token number">0</span> <span class="token punctuation">;</span> dp <span class="token punctuation">[</span> <span class="token number">1</span> <span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token number">1</span> <span class="token punctuation">;</span> <span class="token keyword">for</span> <span class="token punctuation">(</span> <span class="token keyword">let</span> i <span class="token operator">=</span> <span class="token number">2</span> <span class="token punctuation">;</span> i <span class="token operator"><=</span> n <span class="token punctuation">;</span> i <span class="token operator">++</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> dp <span class="token punctuation">[</span> i <span class="token punctuation">]</span> <span class="token operator">=</span> dp <span class="token punctuation">[</span> i <span class="token operator">-</span> <span class="token number">1</span> <span class="token punctuation">]</span> <span class="token operator">+</span> dp <span class="token punctuation">[</span> i <span class="token operator">-</span> <span class="token number">2</span> <span class="token punctuation">]</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">return</span> dp <span class="token punctuation">[</span> n <span class="token punctuation">]</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> console <span class="token punctuation">.</span> <span class="token function">log</span> <span class="token punctuation">(</span> <span class="token function">fibonacci</span> <span class="token punctuation">(</span> <span class="token number">5</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token comment">// 5</span> |
Trong ví dụ này, chúng tôi sử dụng một mảng dp để lưu trữ các kết quả trung gian của từng bài toán con (các số Fibonacci cho đến số thứ n). Điều này cho phép chúng tôi tránh tính toán dư thừa, giảm đáng kể độ phức tạp về thời gian của thuật toán.
4. Thuật toán đệ quy
Đệ quy là một kỹ thuật giải quyết vấn đề trong đó giải pháp phụ thuộc vào các giải pháp cho các trường hợp nhỏ hơn của cùng một vấn đề. Một ví dụ kinh điển về đệ quy là tính toán giai thừa.
1 2 3 4 5 6 | <span class="token keyword">function</span> <span class="token function">factorial</span> <span class="token punctuation">(</span> <span class="token parameter">n</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> n <span class="token operator">===</span> <span class="token number">0</span> <span class="token punctuation">)</span> <span class="token keyword">return</span> <span class="token number">1</span> <span class="token punctuation">;</span> <span class="token keyword">return</span> n <span class="token operator">*</span> <span class="token function">factorial</span> <span class="token punctuation">(</span> n <span class="token operator">-</span> <span class="token number">1</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> console <span class="token punctuation">.</span> <span class="token function">log</span> <span class="token punctuation">(</span> <span class="token function">factorial</span> <span class="token punctuation">(</span> <span class="token number">5</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token comment">// 120</span> |
5. Chia để trị
Chia để trị là một chiến lược thuật toán chung liên quan đến việc chia một vấn đề thành các vấn đề con nhỏ hơn và giải quyết từng vấn đề con một cách độc lập. Một ví dụ về thuật toán chia để trị là bài toán tìm cặp điểm gần nhau nhất trong một tập hợp các điểm trong không gian 2 chiều.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <span class="token keyword">function</span> <span class="token function">closestPair</span> <span class="token punctuation">(</span> <span class="token parameter">points</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> minDistance <span class="token operator">=</span> Number <span class="token punctuation">.</span> <span class="token constant">MAX_SAFE_INTEGER</span> <span class="token punctuation">;</span> <span class="token keyword">let</span> closestPair <span class="token operator">=</span> <span class="token punctuation">[</span> <span class="token punctuation">]</span> <span class="token punctuation">;</span> points <span class="token punctuation">.</span> <span class="token function">sort</span> <span class="token punctuation">(</span> <span class="token punctuation">(</span> <span class="token parameter">a <span class="token punctuation">,</span> b</span> <span class="token punctuation">)</span> <span class="token operator">=></span> a <span class="token punctuation">.</span> x <span class="token operator">-</span> b <span class="token punctuation">.</span> x <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">for</span> <span class="token punctuation">(</span> <span class="token keyword">let</span> i <span class="token operator">=</span> <span class="token number">0</span> <span class="token punctuation">;</span> i <span class="token operator"><</span> points <span class="token punctuation">.</span> length <span class="token operator">-</span> <span class="token number">1</span> <span class="token punctuation">;</span> i <span class="token operator">++</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">for</span> <span class="token punctuation">(</span> <span class="token keyword">let</span> j <span class="token operator">=</span> i <span class="token operator">+</span> <span class="token number">1</span> <span class="token punctuation">;</span> j <span class="token operator"><</span> points <span class="token punctuation">.</span> length <span class="token punctuation">;</span> j <span class="token operator">++</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> distance <span class="token operator">=</span> Math <span class="token punctuation">.</span> <span class="token function">sqrt</span> <span class="token punctuation">(</span> <span class="token punctuation">(</span> points <span class="token punctuation">[</span> i <span class="token punctuation">]</span> <span class="token punctuation">.</span> x <span class="token operator">-</span> points <span class="token punctuation">[</span> j <span class="token punctuation">]</span> <span class="token punctuation">.</span> x <span class="token punctuation">)</span> <span class="token operator">**</span> <span class="token number">2</span> <span class="token operator">+</span> <span class="token punctuation">(</span> points <span class="token punctuation">[</span> i <span class="token punctuation">]</span> <span class="token punctuation">.</span> y <span class="token operator">-</span> points <span class="token punctuation">[</span> j <span class="token punctuation">]</span> <span class="token punctuation">.</span> y <span class="token punctuation">)</span> <span class="token operator">**</span> <span class="token number">2</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> distance <span class="token operator"><</span> minDistance <span class="token punctuation">)</span> <span class="token punctuation">{</span> minDistance <span class="token operator">=</span> distance <span class="token punctuation">;</span> closestPair <span class="token operator">=</span> <span class="token punctuation">[</span> points <span class="token punctuation">[</span> i <span class="token punctuation">]</span> <span class="token punctuation">,</span> points <span class="token punctuation">[</span> j <span class="token punctuation">]</span> <span class="token punctuation">]</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <span class="token keyword">return</span> closestPair <span class="token punctuation">;</span> <span class="token punctuation">}</span> console <span class="token punctuation">.</span> <span class="token function">log</span> <span class="token punctuation">(</span> <span class="token function">closestPair</span> <span class="token punctuation">(</span> <span class="token punctuation">[</span> <span class="token punctuation">{</span> x <span class="token operator">:</span> <span class="token number">0</span> <span class="token punctuation">,</span> y <span class="token operator">:</span> <span class="token number">0</span> <span class="token punctuation">}</span> <span class="token punctuation">,</span> <span class="token punctuation">{</span> x <span class="token operator">:</span> <span class="token number">3</span> <span class="token punctuation">,</span> y <span class="token operator">:</span> <span class="token number">4</span> <span class="token punctuation">}</span> <span class="token punctuation">,</span> <span class="token punctuation">{</span> x <span class="token operator">:</span> <span class="token number">1</span> <span class="token punctuation">,</span> y <span class="token operator">:</span> <span class="token number">1</span> <span class="token punctuation">}</span> <span class="token punctuation">,</span> <span class="token punctuation">{</span> x <span class="token operator">:</span> <span class="token number">2</span> <span class="token punctuation">,</span> y <span class="token operator">:</span> <span class="token number">2</span> <span class="token punctuation">}</span> <span class="token punctuation">,</span> <span class="token punctuation">{</span> x <span class="token operator">:</span> <span class="token number">5</span> <span class="token punctuation">,</span> y <span class="token operator">:</span> <span class="token number">6</span> <span class="token punctuation">}</span> <span class="token punctuation">,</span> <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> |
Trong ví dụ này, đầu tiên thuật toán sắp xếp các điểm theo tọa độ x của chúng. Sau đó, đối với mỗi điểm, nó so sánh khoảng cách của nó với tất cả các điểm đứng sau nó trong mảng đã sắp xếp, cập nhật khoảng cách tối thiểu và cặp gần nhất nếu tìm thấy cặp gần hơn.
Bản đồ băm
Hashmap là một cấu trúc dữ liệu lưu trữ các cặp khóa-giá trị và cho phép chèn, xóa và tra cứu O(1) theo thời gian không đổi. Nó hoạt động bằng cách lấy khóa và áp dụng hàm băm cho nó, hàm này trả về một chỉ mục trong một mảng, phần tử của chỉ mục đó được gọi là nhóm. Giá trị sau đó được lưu trữ trong nhóm đó.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 | <span class="token keyword">class</span> <span class="token class-name">HashMap</span> <span class="token punctuation">{</span> <span class="token function">constructor</span> <span class="token punctuation">(</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> buckets <span class="token operator">=</span> <span class="token function">Array</span> <span class="token punctuation">(</span> <span class="token number">10</span> <span class="token punctuation">)</span> <span class="token punctuation">.</span> <span class="token function">fill</span> <span class="token punctuation">(</span> <span class="token keyword">null</span> <span class="token punctuation">)</span> <span class="token punctuation">.</span> <span class="token function">map</span> <span class="token punctuation">(</span> <span class="token punctuation">(</span> <span class="token punctuation">)</span> <span class="token operator">=></span> <span class="token punctuation">[</span> <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> keys <span class="token operator">=</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> keys <span class="token operator">=</span> <span class="token punctuation">{</span> <span class="token punctuation">}</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token function">hash</span> <span class="token punctuation">(</span> <span class="token parameter">key</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> hash <span class="token operator">=</span> <span class="token number">0</span> <span class="token punctuation">;</span> <span class="token keyword">for</span> <span class="token punctuation">(</span> <span class="token keyword">let</span> i <span class="token operator">=</span> <span class="token number">0</span> <span class="token punctuation">;</span> i <span class="token operator"><</span> key <span class="token punctuation">.</span> length <span class="token punctuation">;</span> i <span class="token operator">++</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> hash <span class="token operator">+=</span> key <span class="token punctuation">.</span> <span class="token function">charCodeAt</span> <span class="token punctuation">(</span> i <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">return</span> hash <span class="token operator">%</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> buckets <span class="token punctuation">.</span> length <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token function">set</span> <span class="token punctuation">(</span> key <span class="token punctuation">,</span> value <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> index <span class="token operator">=</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> <span class="token function">hash</span> <span class="token punctuation">(</span> key <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">for</span> <span class="token punctuation">(</span> <span class="token keyword">let</span> bucket <span class="token keyword">of</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> buckets <span class="token punctuation">[</span> index <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> bucket <span class="token punctuation">[</span> <span class="token number">0</span> <span class="token punctuation">]</span> <span class="token operator">===</span> key <span class="token punctuation">)</span> <span class="token punctuation">{</span> bucket <span class="token punctuation">[</span> <span class="token number">1</span> <span class="token punctuation">]</span> <span class="token operator">=</span> value <span class="token punctuation">;</span> <span class="token keyword">return</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> buckets <span class="token punctuation">[</span> index <span class="token punctuation">]</span> <span class="token punctuation">.</span> <span class="token function">push</span> <span class="token punctuation">(</span> <span class="token punctuation">[</span> key <span class="token punctuation">,</span> value <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> keys <span class="token punctuation">[</span> key <span class="token punctuation">]</span> <span class="token operator">=</span> value <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token function">get</span> <span class="token punctuation">(</span> key <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> index <span class="token operator">=</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> <span class="token function">hash</span> <span class="token punctuation">(</span> key <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">for</span> <span class="token punctuation">(</span> <span class="token keyword">let</span> bucket <span class="token keyword">of</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> buckets <span class="token punctuation">[</span> index <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> bucket <span class="token punctuation">[</span> <span class="token number">0</span> <span class="token punctuation">]</span> <span class="token operator">===</span> key <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">return</span> bucket <span class="token punctuation">[</span> <span class="token number">1</span> <span class="token punctuation">]</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <span class="token keyword">return</span> <span class="token keyword">null</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">delete</span> <span class="token punctuation">(</span> key <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">let</span> index <span class="token operator">=</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> <span class="token function">hash</span> <span class="token punctuation">(</span> key <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">let</span> i <span class="token operator">=</span> <span class="token number">0</span> <span class="token punctuation">;</span> <span class="token keyword">for</span> <span class="token punctuation">(</span> <span class="token keyword">let</span> bucket <span class="token keyword">of</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> buckets <span class="token punctuation">[</span> index <span class="token punctuation">]</span> <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">if</span> <span class="token punctuation">(</span> bucket <span class="token punctuation">[</span> <span class="token number">0</span> <span class="token punctuation">]</span> <span class="token operator">===</span> key <span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> buckets <span class="token punctuation">[</span> index <span class="token punctuation">]</span> <span class="token punctuation">.</span> <span class="token function">splice</span> <span class="token punctuation">(</span> i <span class="token punctuation">,</span> <span class="token number">1</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token keyword">delete</span> <span class="token keyword">this</span> <span class="token punctuation">.</span> keys <span class="token punctuation">[</span> key <span class="token punctuation">]</span> <span class="token punctuation">;</span> <span class="token keyword">return</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> i <span class="token operator">++</span> <span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <span class="token keyword">let</span> map <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">HashMap</span> <span class="token punctuation">(</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> map <span class="token punctuation">.</span> <span class="token function">set</span> <span class="token punctuation">(</span> <span class="token string">"name"</span> <span class="token punctuation">,</span> <span class="token string">"John Smith"</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> map <span class="token punctuation">.</span> <span class="token function">set</span> <span class="token punctuation">(</span> <span class="token string">"age"</span> <span class="token punctuation">,</span> <span class="token number">30</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> console <span class="token punctuation">.</span> <span class="token function">log</span> <span class="token punctuation">(</span> map <span class="token punctuation">.</span> <span class="token function">get</span> <span class="token punctuation">(</span> <span class="token string">"name"</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token comment">// "John Smith"</span> console <span class="token punctuation">.</span> <span class="token function">log</span> <span class="token punctuation">(</span> map <span class="token punctuation">.</span> <span class="token function">get</span> <span class="token punctuation">(</span> <span class="token string">"age"</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token comment">// 30</span> map <span class="token punctuation">.</span> <span class="token function">delete</span> <span class="token punctuation">(</span> <span class="token string">"name"</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> console <span class="token punctuation">.</span> <span class="token function">log</span> <span class="token punctuation">(</span> map <span class="token punctuation">.</span> <span class="token function">get</span> <span class="token punctuation">(</span> <span class="token string">"name"</span> <span class="token punctuation">)</span> <span class="token punctuation">)</span> <span class="token punctuation">;</span> <span class="token comment">// null</span> |
Trong ví dụ này, chúng tôi đã tạo một lớp HashMap có thuộc tính buckets , keys và methods hash , set , get , delete . Phương thức hash lấy một khóa làm đầu vào, chuyển đổi nó thành một giá trị số và trả về chỉ mục của nhóm tương ứng trong mảng. Các phương thức set , get và delete sử dụng phương thức hash để tìm nhóm thích hợp, sau đó thêm, truy xuất hoặc xóa cặp khóa-giá trị nếu thích hợp.
Hashmap là một cấu trúc dữ liệu mạnh mẽ được sử dụng trong nhiều tình huống, chẳng hạn như lưu vào bộ nhớ đệm, triển khai từ điển hoặc lưu trữ lượng lớn dữ liệu. Biết cách sử dụng Hashmap sẽ hữu ích trong nhiều vấn đề mà bạn sẽ gặp phải với tư cách là nhà phát triển.
Phần kết luận
Hiểu và thành thạo sáu thuật toán chính là rất quan trọng đối với bất kỳ nhà phát triển nào.
Sáu thuật toán là:
- Thuật toán sắp xếp: sắp xếp bong bóng, sắp xếp hợp nhất, sắp xếp nhanh, sắp xếp đống
- Thuật toán tìm kiếm: tìm kiếm nhị phân, tìm kiếm theo chiều rộng, tìm kiếm theo chiều sâu
- Lập trình năng động
- đệ quy
- Phân chia và chinh phục
Các thuật toán này là các khối xây dựng cơ bản của khoa học máy tính và được sử dụng trong nhiều loại vấn đề, từ sắp xếp và tìm kiếm dữ liệu đến tối ưu hóa các vấn đề phức tạp. Hiểu và thực hành các thuật toán này sẽ cải thiện kỹ năng phát triển của bạn và giúp bạn trở thành một lập trình viên năng suất và hiệu quả hơn. Ngoài ra, việc học các thuật toán này sẽ cung cấp cho bạn nền tảng vững chắc về kiến thức khoa học máy tính sẽ hữu ích cho dù bạn đang làm việc với ngôn ngữ lập trình nào.
Hiểu và sử dụng Hashmap cũng là một kỹ năng quan trọng đối với nhà phát triển, đó là cấu trúc dữ liệu có thể giúp bạn lưu trữ, truy xuất và sửa đổi lượng lớn dữ liệu một cách hiệu quả.
Mỗi thuật toán này đi kèm với các trường hợp sử dụng, điểm mạnh và điểm yếu riêng. Nắm vững tất cả chúng sẽ giúp bạn chọn đúng thuật toán để giải quyết bất kỳ vấn đề cụ thể nào mà bạn có thể gặp phải trong sự nghiệp phát triển của mình.
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