算法导论4.1DivideAndConquer寻找最大子数组-优快云博客

本文介绍了一种寻找一维数组中具有最大和的连续子数组的算法实现。该算法通过递归方式分解问题，并结合左右子数组的最大和来确定整个数组的最大子数组范围及其和。代码示例使用C++编写，展示了核心函数Find_MaxiMum_SubArray的具体实现。

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寻找最大子数组

// find_max_sub_array.h
#include <stdint.h>

int Find_MAX_CROSSING_SUBARRAY(int* A, int low, int mid, int high, int& max_left, int& max_right, int& max_value)
{
    int left_sum = 0xFFFFFFFF; // 不可能的最小值
    int sum = 0;

    for(int i = mid; i > low; i--)
    {
        sum = sum + A[i];
        if(sum > left_sum)
        {
            left_sum = sum;
            max_left = i;
        }
    }

    int right_sum = 0xFFFFFFFF; // 不可能的最小值
    sum = 0;

    for(int j = mid + 1; j < high; j++)
    {
        sum = sum + A[j];
        if(sum > right_sum)
        {
            right_sum = sum;
            max_right = j;
        }
    }

    max_value = left_sum + right_sum;
    return 0;
}

int Find_MaxiMum_SubArray(int* A, int low, int high, int& max_left, int& max_right, int& max_value)
{
    if(high == low)
    {
        max_left  = low;
        max_right = high;

        max_value = A[low];
    }
    else
    {
        int mid = (low + high) / 2;

        int tmp_left_low;
        int tmp_left_high;
        int tmp_left_sum;

        Find_MaxiMum_SubArray(A, low, mid, tmp_left_low, tmp_left_high, tmp_left_sum);

        int tmp_right_low;
        int tmp_right_high;
        int tmp_right_sum;

        Find_MaxiMum_SubArray(A, mid + 1, high, tmp_right_low, tmp_right_high, tmp_right_sum);

        int tmp_cross_low;
        int tmp_cross_high;
        int tmp_cross_sum;

        Find_MAX_CROSSING_SUBARRAY(A, low, mid, high, tmp_cross_low, tmp_cross_high, tmp_cross_sum);

        if ((tmp_left_sum >= tmp_right_sum) && (tmp_left_sum >= tmp_cross_sum))
        {
            max_left  = tmp_left_low;
            max_right = tmp_left_high;
            max_value = tmp_left_sum;
        }
        else if((tmp_right_sum >= tmp_left_sum) && (tmp_right_sum >= tmp_cross_sum))
        {
            max_left  = tmp_right_low;
            max_right = tmp_right_high;
            max_value = tmp_right_sum;
        }
        else
        {
            max_left  = tmp_cross_low;
            max_right = tmp_cross_high;
            max_value = tmp_cross_sum;
        }
    }
    return 0;
}

// main.cpp
#include <iostream>
#ifdef __linux
#include <stdio.h>
#endif

#include "find_max_sub_array.h"

using std::cout;
using std::endl;

int B[10] = { 1, -10, 2, 4, 6, -15, 6, 1, 9, -8 };

int main()
{
    cout<<endl;
    int max_left, max_right, max_value;
    Find_MaxiMum_SubArray(B, 0, sizeof(B)/sizeof(int) - 1 , max_left, max_right, max_value);
    cout<< max_left << "\t" << max_right << "\t" << max_value <<endl;
    cout <<endl;
    getchar();
    return 0;
}