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：

 1 public class Solution {

 2     public int maxSubArray(int[] A) {

 3         int sum=A[0],tmp=A[0];

 4         for(int i=1;i<A.length;i++){

 5             if(tmp>0){

 6                 tmp+=A[i];

 7             }

 8             else{

 9                 tmp=A[i];

10             }

11             if(tmp>sum){

12                 sum=tmp;

13             }

14         }

15         return sum;

16     }

17 }

python代码如下：

 1 class Solution:

 2     # @param A, a list of integers

 3     # @return an integer

 4     def maxSubArray(self, A):

 5         # kadane's dynamic programming algorithm

 6         maxSum = -1 * (1 << 30)

 7         currSum = maxSum

 8         for a in A:

 9             currSum = max(a, a + currSum)

10             maxSum = max(maxSum, currSum)

11         return maxSum