最大子数组的递归求法模板

将最大子数组分三种情况讨论，一定在left段，right段，已经过mid两侧

　　mid = (low+high)/2

1. low«i«j«mid
2. low«i«mid«high
3. mid+1«i«j

#include <iostream>
#include <cstdlib>
#define inf 0x3f3f3f
using namespace std;

int findCrossingMaxSubarray(int a[],int low,int mid,int high,int &cros_left,int &cros_right){
    int left_sum=-inf;
    int sum=0;
    //find the cros_left
    for(int i=mid;i>=low;i--){
        sum += a[i];
        if(left_sum<sum){
            left_sum = sum;
            cros_left = i;
        }
    }
    sum = 0;
    int right_sum = -inf;
    //find the cros_right
    for(int i=mid+1;i<=high;i++){
        sum += a[i];
        if(right_sum<sum){
            right_sum = sum;
            cros_right = i;
        }
    }
    return left_sum+right_sum;
}

int findMaxSubarray(int a[],int low,int high,int &left,int &right){
    if(low==high){
        left = low;
        right = high;
        return a[low];
    }

    int mid = (low+high)/2;
    //find the left max subarray
    int left_left,left_right;
    int left_sum;
    left_sum =  findMaxSubarray(a,low,mid,left_left,left_right);

    int right_left,right_right;
    int right_sum;
    right_sum = findMaxSubarray(a,mid+1,high,right_left,right_right);

    //find the crossing mx subarray
    int crossing_left,crossing_right;
    int crossing_sum;
    crossing_sum = findCrossingMaxSubarray(a,low,mid,high,crossing_left,crossing_right);

    //the first or the last
    if(left_sum>=right_sum&&left_sum>crossing_sum){
        left = left_left;
        right = left_right;
        return left_sum;
    }
    else if(right_sum>=left_sum&&right_sum>crossing_sum){
        left = right_left;
        right = right_right;
        return right_sum;
    }
    else{
        left = crossing_left;
        right = crossing_right;
        return crossing_sum;
    }
}

int main()
{
    int n;
    cin>>n;
    int *a = (int*)malloc(sizeof(int)*n);

    for(int i=0;i<n;i++)
        cin>>a[i];

    int left,right,sum;
    sum = findMaxSubarray(a,0,n-1,left,right);
    cout<<"left:"<<left<<" "<<"right:"<<right<<" "<<"sum:"<<" "<<sum;
    free(a);
    //cout << "Hello world!" << endl;
    return 0;
}

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 hd1003