Javascript 中的 HeapSort 实现

Question

我正在学习堆，我想使用 MinHeap 在 Javascript 中实现堆排序算法。问题是我一直得到一个未排序的数组。我什至试图将一个工作算法从 C++ 翻译成 Javascript。原始算法 link：https://www.geeksforgeeks.org/heap-sort-for-decreasing-order-using-min-heap/

C++:

// To heapify a subtree rooted with node i which is 
// an index in arr[]. n is size of heap 
void heapify(int arr[], int n, int i) 
{ 
    int smallest = i; // Initialize smalles as root 
    int l = 2 * i + 1; // left = 2*i + 1 
    int r = 2 * i + 2; // right = 2*i + 2 


// If left child is smaller than root 
if (l < n && arr[l] < arr[smallest]) 
    smallest = l; 

// If right child is smaller than smallest so far 
if (r < n && arr[r] < arr[smallest]) 
    smallest = r; 

// If smallest is not root 
if (smallest != i) { 
    swap(arr[i], arr[smallest]); 

    // Recursively heapify the affected sub-tree 
    heapify(arr, n, smallest); 


 } 
} 



// main function to do heap sort 
void heapSort(int arr[], int n) 
{ 
    // Build heap (rearrange array) 
    for (int i = n / 2 - 1; i >= 0; i--) 
        heapify(arr, n, i); 
  
    // One by one extract an element from heap 
    for (int i = n - 1; i >= 0; i--) { 
        // Move current root to end 
        swap(arr[0], arr[i]); 
  
        // call max heapify on the reduced heap 
        heapify(arr, i, 0); 
    } 
}

Javascipt（翻译代码）：

    function swap(arr, i, j){
    const c = arr[i];
    arr[i] = arr[j];
    arr[j] = c;
}

function heapify(arr, n, i) 
{ 
    let smallest = i; // Initialize smalles as root 
    let l = 2 * i + 1; // left = 2*i + 1 
    let r = 2 * i + 2; // right = 2*i + 2 
  
    // If left child is smaller than root 
    if (l < n && arr[l] < arr[smallest]) 
        smallest = l; 
  
    // If right child is smaller than smallest so far 
    if (r < n && arr[r] < arr[smallest]) 
        smallest = r; 
  
    // If smallest is not root 
    if (smallest != i) { 
        swap(arr[i], arr[smallest]); 
  
        // Recursively heapify the affected sub-tree 
        heapify(arr, n, smallest); 
    } 
} 
  
// main function to do heap sort 
function heapSort(arr, n) 
{ 
    // Build heap (rearrange array) 
    for (let i = n / 2 - 1; i >= 0; i--) 
        heapify(arr, n, i); 
  
    // One by one extract an element from heap 
    for (let i = n - 1; i >= 0; i--) { 
        // Move current root to end 
        swap(arr[0], arr[i]); 
  
        // call max heapify on the reduced heap 
        heapify(arr, i, 0); 
    } 
}

当我尝试使用这个数组 arr = [1,2,7,3,5] 时，heapSort 算法 returns 这个 table [ 1, 2, 7, 3, 5 ] ;

你能帮我弄清楚 JS 实现有什么问题吗？提前谢谢你！

Answer 1

这段代码应该没问题：

const heapify = (arr, length, i) => {
  let largest = i
  const left = i * 2 + 1
  const right = left + 1

  if (left < length && arr[left] > arr[largest]) {
    largest = left
  }

  if (right < length && arr[right] > arr[largest]) {
    largest = right
  }

  if (largest !== i) {
    [arr[i], arr[largest]] = [arr[largest], arr[i]]
    heapify(arr, length, largest)
  }

  return arr
}

const heapSort = arr => {
  const length = arr.length
  let i = Math.floor(length / 2 - 1)
  let k = length - 1

  while (i >= 0) {
    heapify(arr, length, i)
    i--
  }

  while (k >= 0) {
    [arr[0], arr[k]] = [arr[k], arr[0]]
    heapify(arr, k, 0)
    k--
  }

  return arr
}

const arr = [4, 6, 3, 2, 9];
sortedArr = heapSort(arr);

console.log("Sorted array is \n", sortedArr)

我从here那里拿来的。如果您对它的实现方式更感兴趣，请查看 post。解释的很好。

更新

好的，关于你的代码，我看到了 2 个问题：

您错误地使用了“交换”功能。只需将 swap(arr[i], arr[smallest] 更改为 swap(arr, i, smallest)； swap(arr[0], arr[i]) swap(arr, 0, i)。此外，如果你想使用最新的 ES6 功能，你可以交换数组中的元素而无需实现“交换”功能，就像这样：[arr[0], arr[2]] = [arr[2], arr[0]]（这会将位置 0 的元素与位置 2 的元素交换).这叫做destructuring assignment.
在“heapSort”函数的第一个 for 循环中，将 i 变量初始化为整数（注意 n / 2 可能是浮点数）。你可以这样做：let i = Math.floor(n / 2 - 1).

这里我把固定代码留给你。我自己执行了它并且有效：

function swap(arr, i, j){
  const c = arr[i];
  arr[i] = arr[j];
  arr[j] = c;
}

function heapify(arr, n, i) 
{ 
  let smallest = i; // Initialize smallest as root 
  let l = 2 * i + 1; // left = 2*i + 1 
  let r = 2 * i + 2; // right = 2*i + 2 

  // If left child is smaller than root 
  if (l < n && arr[l] < arr[smallest]) 
      smallest = l; 

  // If right child is smaller than smallest so far 
  if (r < n && arr[r] < arr[smallest]) 
      smallest = r; 

  // If smallest is not root 
  if (smallest != i) { 
      swap(arr, i, smallest); 

      // Recursively heapify the affected sub-tree 
      heapify(arr, n, smallest); 
  } 
} 

// main function to do heap sort 
function heapSort(arr, n) 
{ 
  // Build heap (rearrange array) 
  for (let i = Math.floor(n / 2 - 1); i >= 0; i--) 
      heapify(arr, n, i); 

  // One by one extract an element from heap 
  for (let i = n - 1; i >= 0; i--) { 
      // Move current root to end 
      swap(arr, 0, i); 

      // call max heapify on the reduced heap 
      heapify(arr, i, 0); 
  } 
}

const arr = [4, 6, 3, 2, 9];
heapSort(arr, arr.length);

console.log("Sorted array is \n", arr)

Javascript 中的 HeapSort 实现

HeapSort implementation in Javascript

javascript

heap

heapsort

更新