53. Maximum Subarray.md

##53. 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.

解题思路： <br/ > Kadane's Algorithm <br/ > https://www.youtube.com/watch?v=epTQfFlhQBo <br/ > local_max: 存从开头到i的sum. 如果i之前的数为负数，到i的最大数为i. <br/ > max: 存最后的返回值，就算local_max保证了最大值，如果最大local_max之后的i位值为负，则不录入max. <br/ > 每轮比较max 和local_max的大小，大的存入max. <br/ > 最终返回 max <br/ >

public int maxSubArray(int [] nums){
		int max = Integer.MIN_VALUE;
		int local_max = 0;
		
		for (int i=0; i < nums.length; i++){
			local_max += nums[i];
			local_max = Math.max(local_max, nums[i]); 
			max = Math.max(max, local_max);
		}	
		return max;
	}