最大字串和问题(Maximum Subarray)

问题描述：

ind 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.

public class MaxSubarray
{
	public int maxSubArray(int[] nums)
	{
		int sum = nums[0];
		int max = nums[0];
		for(int i = 1; i < nums.length; i ++)
		{
			if(sum < 0)
			{
				sum = 0;
			}
			sum += nums[i];
			if(max < sum)
			{
				max = sum;
			}
		}
		return max;
	}
	//穷举法O(n^3)
	public int maxSubArray1(int[] nums)
	{
		int max = 0;
		for(int i = 0; i < nums.length; i ++)
		{
			for(int j = i; j < nums.length; j ++)
			{
				int sum = 0;
				for(int k = i; k < j; k ++)
				{
					sum += nums[k];
				}
				if(sum > max)
				{
					max = sum;
				}
			}
		}
		return max;
    }
	//O(n^2)
	public int maxSubArray2(int[] nums)
	{
		int max = 0;
		for(int i = 0; i < nums.length; i ++)
		{
			int sum = 0;
			for(int j = i; j < nums.length; j ++)
			{
				sum += nums[j];
				if(sum > max)
				{
					max = sum;
				}
			}
		}
		return max;
	}
}