leetcode------Maximum Subarray

标题：	Maximum Subarray
通过率：	34.5%
难度：	中等

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.

本题就是求最大字段和，算法设计的基础算法。动态规划

公式解读：B[i]为到位置i时的最大字段和，A[i]为第i个位置的元素

那么B[k]=max{a[k],B[k-1]+A[k]}

java代码如下：

public class Solution {
    public int maxSubArray(int[] A) {
        int sum=A[0],tmp=A[0];
        for(int i=1;i<A.length;i++){
            if(tmp>0){
                tmp+=A[i];
            }
            else{
                tmp=A[i];
            }
            if(tmp>sum){
                sum=tmp;
            }
        }
        return sum;
    }
}

python代码如下：

class Solution:
    # @param A, a list of integers
    # @return an integer
    def maxSubArray(self, A):
        # kadane's dynamic programming algorithm
        maxSum = -1 * (1 << 30)
        currSum = maxSum
        for a in A:
            currSum = max(a, a + currSum)
            maxSum = max(maxSum, currSum)
        return maxSum