• 归并排序(Merge sort)


    思想:分治

    方法: 分为自顶向下自低向上两种。

    1. 自顶向下递归:

    #include<stdio.h>
    #include<stdlib.h>
    /*#include<time.h>*/
    #define MAX 10
    int numbers[MAX]={0};
    int temp[MAX] = {0};
    
    void mergeSort(int[], int); /* 提á供?接ó口ú */
    void m_sort(int[], int[], int, int); /* 分?割?排?序ò */
    void merge(int[], int[], int, int, int); /* 归é并¢ */
    
    void mergeSort(int numbers[], int temp[], int array_size)
    {
        m_sort(numbers, temp, 0, array_size - 1);
    }
    void m_sort(int numbers[], int temp[], int left, int right)
    {
        int mid;
        if (right > left)
        {
            mid = (right + left) / 2;
            m_sort(numbers, temp, left, mid);
            m_sort(numbers, temp, mid+1, right);
            merge(numbers, temp, left, mid+1, right);
    
        }
    }
    void merge(int numbers[], int temp[], int left, int mid, int right) // left -> mid-1, mid -> right two sequences
    {
        int start1 = left, start2 = mid;
        for(int j = left; j <= right; ++j)
        {
            if (start1 < mid && (numbers[start1] < numbers[start2] || start2 > right)) temp[j] = numbers[start1++];
            else temp[j] = numbers[start2++];
        }
        for (int i = left; i <= right; i++)
            numbers[i] = temp[i];
    }
    void init_array()
    {
        int i;
        /*srand((unsigned) time(NULL));*/
        for(int i = 0; i < MAX; i++)
            numbers[i] = rand() % MAX;
    }
    void print_array()
    {
        int i;
        for(i = 0; i < MAX; i++)
            printf("%d	", numbers[i]);
    }
    int main()
    {
        init_array();
        mergeSort(numbers, temp, MAX);
        print_array();
        printf("
    ");
        return 0;
    }
    

    2.自底向上排序(非递归)

    #include<stdio.h>
    #include<stdlib.h>
    #include<time.h>
    #define MIN(a, b) ((a) < (b) ? (a) : (b))
    #define N 1000000
    int A[N]={0}; // data
    int T[N] = {0};  // work array
    void BottomUpMerge(int A[], int iLeft, int iRight, int iEnd, int B[]);
    
    void BottomUpSort(int A[], int T[], int n)
    {
        int width;
        for (width = 1; width < n; width = 2 * width)
        {
            int i, j;
            for (i = 0; i < n; i = i + 2 * width)
            {
                BottomUpMerge(A, i, MIN(i+width, n), MIN(i+2*width, n), T);
            }
            for(j = 0; j < n; ++j) 
                A[j] = T[j];
        }
    }
    void BottomUpMerge(int A[], int iLeft, int iRight, int iEnd, int T[])
    {
        int i0 = iLeft, i1 = iRight, j;
        for (j = iLeft; j < iEnd; j++)
        {
            if (i0 < iRight && (i1 >= iEnd || A[i0] <= A[i1]))
                T[j] = A[i0++];
            else
                T[j] = A[i1++];
        }
    }
    int main()
    {
        init_array();
        BottomUpSort(A, T, N);
        print_array();
        printf("
    ");
        return 0;
    }
    

    稳定排序。空间复杂度 O(n)。时间复杂度 O(nlgn),如图:

    shot

    精简代码

    (自顶向下)

    void merge_sort(int A[], int T[], int left, int right){ // right = n-1;
    	if (right > left){
    		int mid = (right + left) / 2;
    		merge_sort(A, T, left, mid);
    		merge_sort(A, T, mid+1, right);
    		merge(A, T, left, mid+1, right);
    	}
    }
    void merge(int A[], int T[], int s1, int s2, int last){
    	int tag1 = s1, tag2 = s2;
    	for(int j = s1; j <= last; ++j) {
    		if(s1 < tag2 && (A[s1] <= A[s2] || s2 > right)) T[j] = A[s1++];
    		else T[j] = A[s2++];
    	}
    	for (int i = tag1; i <= last; i++) A[i] = T[i];
    }
    

     (自底向上):Ο(n(logn)2) time complexity.

    void Merge(int A[], vector<int>& T, int s1, int s2, int end) {
    	int tag = s2;
    	for(int j = s1; j < end; ++j) 
    		if(s1 < tag && (A[s1] <= A[s2] || s2 >= end)) T[j] = A[s1++];
    		else T[j] = A[s2++];
    }
    void MergeSort(int A[], int n) {
    	vector<int> T(n);
    	for(int width = 1; width < n; width *= 2){
    		for(int start = 0; start < n; start += 2*width)
    			Merge(A, T, start, min(start+width, n), min(start+2*width, n));
    		for(int i = 0; i < n; ++i) A[i] = T[i];
    	}
    }
    
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  • 原文地址:https://www.cnblogs.com/liyangguang1988/p/3704027.html
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