為什么我的合並排序不適用於數組長度10的原因

Question

我正在設置合並排序來對我的數組進行排序。 目標是對任意長度的數組進行排序。

我嘗試查看mergesort函數，但沒有看到任何錯誤。 該排序適用於某些數組長度，無論是奇數還是偶數，但對於數組長度（例如10），我得到了一個超限異常。

import java.util.Arrays;

class MergeSort
{
 // Merge two sorted sub-arrays A[from .. mid] and A[mid + 1 .. to]
 public static void merge(int[] A, int[] temp, int from, int mid, int to)
 {
  int k = from, i = from, j = mid + 1;

  // loop till there are elements in the left and right runs
  while (i <= mid && j <= to) {
   if (A[i] < A[j]) {
    temp[k++] = A[i++];
   } else {
    temp[k++] = A[j++];
   }
  }

  // Copy remaining elements
  while (i <= mid) {
   temp[k++] = A[i++];
  }

  // Don't need to copy second half

  // copy back to the original array to reflect sorted order
  for (i = from; i <= to; i++) {
   A[i] = temp[i];
  }
 }

 // Iteratively sort array A[low..high] using temporary array
 public static void mergesort(int[] A)
 {
  int low = 0;
  int high = A.length - 1;

  // sort array A[] using temporary array temp
  int[] temp = Arrays.copyOf(A, A.length);

  // divide the array into blocks of size m
  // m = [1, 2, 4, 8, 16...]
  for (int m = 1; m <= high - low; m = 2*m)
  {
   // for m = 1, i = 0, 2, 4, 6, 8...
   // for m = 2, i = 0, 4, 8, 12...
   // for m = 4, i = 0, 8, 16...
   // ...
   for (int i = low; i < high; i += 2*m)
   {
    int from = i;
    int mid = i + m - 1;
    int to = Integer.min(i + 2 * m - 1, high);

    merge(A, temp, from, mid, to);
   }
  }
 }

 // Iterative Implementation of Mergesort algorithm
 public static void main(String[] args)
 {
  int[] A = { 5, 7, -9, 3, -4, 2, 8, 8, 10, 11 };

  System.out.println("Original Array : " + Arrays.toString(A));
  mergesort(A);
  System.out.println("Modified Array : " + Arrays.toString(A));
 }
}

Answer 1

您的中間計算錯誤。 有時您將其設置在區域范圍之外。

下面的更改通過防止中點超出范圍來修復算法，類似於您對防止中點超出范圍所做的操作。

更改int mid = i + m - 1; 到int mid = Math.min(i + m - 1, A.length - 1);

說明：如您的評論中所述，您正在檢查的區域切片正在增大。 所以這是數組的排序方式，何時發生越界錯誤，以及為什么在以2的冪為單位的大小上未發生此錯誤：

             [ -9,  5,  7,  3, -4,  2,  8,  8, 10, 11 ]           Array size
 First pass:   []  []  []  []  []  []  []  []  []  []             1
     Second:   [    ]  [    ]  [    ]  [    ]  [    ]             2
      Third:   [            ]  [            ]  [       ERROR]     4

Answer 2

這是您的解決方法：

為您的中部添加了一個if語句，使其不會越過數組邊界

if(mid<high) {
            merge(A, temp, from, mid, to);
        }

完整的代碼：

// Merge two sorted sub-arrays A[from .. mid] and A[mid + 1 .. to]
public static void merge(int[] A, int[] temp, int from, int mid, int to)
{
    int k = from, i = from, j = mid + 1;

    // loop till there are elements in the left and right runs
    while (i <= mid && j <= to) {
        if (A[i] < A[j]) {
            temp[k++] = A[i++];
        } else {
            temp[k++] = A[j++];
        }
    }

    // Copy remaining elements
    while (i <= mid) {
        temp[k++] = A[i++];
    }

    // Don't need to copy second half

    // copy back to the original array to reflect sorted order
    for (i = from; i <= to; i++) {
        A[i] = temp[i];
    }
}

// Iteratively sort array A[low..high] using temporary array
public static void mergesort(int[] A)
{
    int low = 0;
    int high = A.length - 1;

    // sort array A[] using temporary array temp
    int[] temp = Arrays.copyOf(A, A.length);
    //System.out.println("temp Array : " + Arrays.toString(temp));

    // divide the array into blocks of size m
    // m = [1, 2, 4, 8, 16...]
    for (int m = 1; m <= high - low; m = 2*m)
    {
        // for m = 1, i = 0, 2, 4, 6, 8...
        // for m = 2, i = 0, 4, 8, 12...
        // for m = 4, i = 0, 8, 16...
        // ...
        for (int i = low; i < high; i += 2*m)
        {
            int from = i;
            int mid = i + m - 1;
            int to = Integer.min(i + 2 * m - 1, high);

            if(mid<high) {
                merge(A, temp, from, mid, to);
            }

        }
    }
}

// Iterative Implementation of Mergesort algorithm
public static void main(String[] args)
{
    int[] A = { 5, 7, -9, 3, -4, 2, 8, 8, 10, 11 };

    System.out.println("Original Array : " + Arrays.toString(A));
    mergesort(A);
    System.out.println("Modified Array : " + Arrays.toString(A));
}