[leetcode]Maximum Subarray

问题描写叙述：

Find the contiguous subarray within an array (containing at least one number) which has the largest sum.

For example, given the array [−2,1,−3,4,−1,2,1,−5,4],
the contiguous subarray [4,−1,2,1] has the largest sum = 6.

基本思路：

遍历并记录最大的subarray值。O(n)时间算法

代码：

int maxSubArray(int A[], int n) {  //C++
        int max = A[0];
        int tmp = 0;
        for(int i = 0; i < n; i++)
        {
            tmp += A[i];
            if(tmp > max)
                max = tmp;    
            if(tmp < 0){
                tmp = 0;
            }
        }
        return max;
    }

分治法

int divideConquer(int A[], int low, int high){  //C++
        if(low == high)
            return A[low];
        
        int mid = (low + high)/2;
        int sum1 = divideConquer(A, low , mid);
        int sum2 = divideConquer(A, mid+1, high);
        int sum3 = findMidMax(A,low,high,mid);
        
        int max;
        max = (sum1 > sum2)? sum1:sum2;
        max = (max > sum3)?
 max: sum3;
        // cout << low << high  << mid <<max;
        return max;
        
    }
    int findMidMax(int A[] , int low , int high, int mid){
        int max = A[mid],tmp = 0,sum = 0;
        int i =  mid;
        while(i >= low ) 
        {
            tmp +=A[i];
            if(tmp > max)
                max = tmp;
            i--;
        }
        sum = max;
        
        max = 0 , tmp = 0; 
        int j = mid+1;
        while(j <= high) 
        {
            tmp +=A[j];
            if(tmp > max)
                max = tmp;
            j++;
        }
        sum += max;
        return sum;
    }
    int maxSubArray(int A[], int n) {
        return divideConquer(A,0,n-1);
    }