leetcode : Maximum Subarray [动态规划入门]

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.

click to show more practice.

More practice:

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

 

解决方法： 动态规划

 

状态方程：  f[n] = max(f[n - 1] + nums[i], nums[i])

   f[n] 表示以第i个字符为结尾的最大子字符串和

 

public class Solution {
    public int maxSubArray(int[] nums) {
        if(nums == null || nums.length == 0) {
            return Integer.MIN_VALUE;
        }
        int length = nums.length;
        int[] f = new int[length];
        f[0] = nums[0];
        int max = nums[0];
        
        for(int i = 1; i < length; i++) {
            if(f[i - 1] + nums[i] > nums[i]) {
                f[i] = f[i - 1] + nums[i];
            } else {
                f[i] = nums[i];
            }
            max = Math.max(max,f[i]);
        }
        return max;
    }
}