Maximum Subarray (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.

思路：subarray sum 這種問題就考慮用前n項和。 因此先獲得前n項和數組，而後求他們能存在的最大差值。就變成了Best Time to Buy and Sell Stock(121)同樣的問題。 從左向右掃描， 更新差值使其保持最大， 而後更新min。

時間複雜度： O(N)
空間複雜度： O(N)

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;
    }
}