Maximum Size Subarray Sum Equals k

Source

• leetcode: 325

Given an array nums and a target value k, find the maximum length of a subarray that sums to k. If there isn't one, return 0 instead.
Example 1:
Given nums = [1, -1, 5, -2, 3], k = 3,
return 4. (because the subarray [1, -1, 5, -2] sums to 3 and is the longest)
Example 2:
Given nums = [-2, -1, 2, 1], k = 1,
return 2. (because the subarray [-1, 2] sums to 1 and is the longest)
Follow Up:
Can you do it in O(n) time?

题解

The problem is equal to: find out a range from i to j, in which the sum (nums[i], ..., nums[j]) = k. What is the maximal range?

So we can first calculate the prefix sum of each number, so sum(i, j) = sum(j) - sum(i - 1) = k. Therefore, for each sum(j), we only need to check if there was a sum(i - 1) which equals to sum(j) - k. We can use a hash map to store the previous calculated sum.

Comments: Note the map.put(0, -1). We need to put this entry into the map before, because if the maximal range starts from 0, we need to calculate sum(j) - sum(i - 1).

java

public class Solution {
    public int maxSubArrayLen(int[] nums, int k) {
        if(nums == null || nums.length == 0) {
            return 0;
        }

        int maxLen = 0;
        Map<Integer, Integer> map = new HashMap<>();
        map.put(0, -1); // IMPOARTANT
        int sum = 0;

        for (int i = 0; i < nums.length; i++) {
            sum += nums[i];
            if (!map.containsKey(sum)) {
                map.put(sum, i);
            }

            if (map.containsKey(sum - k)) {
                maxLen = Math.max(maxLen, i - map.get(sum - k));
            }
        }

        return maxLen;
    }
}