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.

遞歸方程;

dp[i] = dp[i-1]+nums[i] ,dp[i-1]>0

dp[i] = nums[i] ,else

 1 class
 
 Solution {
 2     public int maxSubArray(int[] nums) {
 3         int dp[] = new int[nums.length+1];
 4         int max = nums[0];
 5         dp[0] = nums[0];
 6         for(int i =1;i<nums.length;i++){
 7             if(dp[i-1]<=0)
 8                 dp[i] = nums[i];
 9             else
10                 dp[i] = dp[i-1]+nums[i];
 
11             max = Math.max(dp[i],max);
12         }
13         return max;
14     }
15 }

53. Maximum Subarray(動態規劃 求最大子數組)