Maximum Subarray

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.

click to show more practice.

More practice:If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

数据结构书上的经典题，甚至是引言中的题目。不细说。

O(N)算法

class Solution {
public:
    int maxSubArray(int A[], int n) {
        int sum = A[0];
        int biggest = A[0];
        for(int i = 1; i < n; i++){
            if(sum < 0){
                sum = A[i];
            }
            else{
                sum += A[i];
            }
            biggest = biggest < sum? sum: biggest;
        }
        return biggest;
    }
};

O（nlogn）算法

class Solution {
public:
    int maxSubArray(int A[], int n) {
        return _maxSubArray(A, 0, n);
    }
    //[left, right)
    int _maxSubArray(int A[], int left, int right){
        //base case
        if(right - left == 1){
            return A[left];
        }
        int mid = (left + right) / 2;
        int a = _maxSubArray(A, left, mid);
        int b = _maxSubArray(A, mid, right);
        int maxLeftAdjacent = 0;
        int maxRightAdjacent = 0;
        int sum = 0;
        for(int i = mid - 1; i >=left; i--){
            if(i == mid - 1) maxLeftAdjacent = A[i];
            sum += A[i];
            maxLeftAdjacent = sum > maxLeftAdjacent? sum: maxLeftAdjacent;
        }
        sum = 0;
        for(int i = mid; i < right; i++){
            if(i == mid) maxRightAdjacent = A[i];
            sum +=A[i];
            maxRightAdjacent = sum > maxRightAdjacent? sum: maxRightAdjacent;
        }
        return max(max(a,b),maxLeftAdjacent + maxRightAdjacent);
    }
};