Maximum Subarray (53)

时间 2019-12-07

标签 maximum subarray 繁體版

原文原文链接

Maximum Subarray

Find the contiguous subarray within an array (containing at least one number) which has the largest sum.数组

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.code

思路：subarray sum 这种问题就考虑用前n项和。因此先获得前n项和数组，而后求他们能存在的最大差值。就变成了Best Time to Buy and Sell Stock(121)同样的问题。从左向右扫描，更新差值使其保持最大，而后更新min。it

时间复杂度： O(N)
空间复杂度： O(N)io

public class Solution {
    public int maxSubArray(int[] nums) {
        // 找到subarray sum 的最大差
        if (nums.length == 0 || nums == null) {
            return 0;
        }
        if (nums.length == 1) {
            return nums[0];
        }
        int[] sum = new int[nums.length + 1];
        sum[0] = 0;
        for (int i = 1; i <= nums.length; i++) {
            sum[i] = sum[i - 1] + nums[i - 1];
        }
        int min = Integer.MAX_VALUE;
        int largest = Integer.MIN_VALUE;
        for (int i = 0; i <= nums.length; i++) {
            largest = sum[i] - min > largest ? sum[i] - min: largest;
            min = sum[i] < min? sum[i] : min;
        }
        return largest;
    }
}