【LeetCode】53. Maximum Subarray

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53. Maximum Subarray

Description:

Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.

Example:

Input: [-2,1,-3,4,-1,2,1,-5,4],

Output: 6

Explanation: [4,-1,2,1] has the largest sum = 6.

Follow up:

If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

 解题思路：

（1）举例分析数组的规律

已经AC的代码：

public class solutionMaxSubArray {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		int[] arr = {-2, 1, -3, 4, -1, 2, 1, -5, 4};
		System.out.println(maxSubArray(arr));
	}
	
    public static int maxSubArray(int[] nums) {
       int  sum = Integer.MIN_VALUE;
       int currentSum = 0;
       for(int i=0; i<nums.length; i++) {
    	   currentSum += nums[i];
    	   if(currentSum < nums[i]) {
    		   currentSum = nums[i];
    	   }
    	   if(currentSum > sum) {
    		   sum = currentSum;
    	   }
       }
       return sum;
    }

}

（2）动态规划的解法

public class solutionMaxSubArray {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		int[] arr = {-2, 1, -3, 4, -1, 2, 1, -5, 4};
		System.out.println(maxSubArray(arr));
	}
	
    public static int maxSubArray(int[] nums) {
    	int sum = Integer.MIN_VALUE;
    	int currentSum = 0;
    	for(int i=0; i<nums.length; i++) {
    		if(currentSum <= 0)
    			currentSum = nums[i];
    		else
    			currentSum += nums[i];
    		if(currentSum > sum)
    			sum = currentSum;
    	}
		return sum;
    }
}

Python已经AC的代码：

class Solution:
	def maxSubArray(self, nums):
		nums_len = len(nums)
		result = [0 for i in range(nums_len)]
		maxSum = result[0] = nums[0]
		for i in range(1, nums_len):
			if nums[i] >= result[i-1] + nums[i]:
				result[i] = nums[i]
			else:
				result[i] = result[i-1] + nums[i]

			if maxSum <= result[i]:
				maxSum = result[i]
		return maxSum


if __name__ == '__main__':
	nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
	sol = Solution()
	print(sol.maxSubArray(nums))