Find the Maximum Length of Valid Subsequence II

Description

You are given an integer array nums and a positive integer k.

A subsequence

sub of nums with length x is called valid if it satisfies:

• (sub[0] + sub[1]) % k == (sub[1] + sub[2]) % k == ... == (sub[x - 2] + sub[x - 1]) % k.

Return the length of the longest valid subsequence of nums.

Example 1:

Input: nums = [1,2,3,4,5], k = 2

Output: 5

Explanation:

The longest valid subsequence is [1, 2, 3, 4, 5].

Example 2:

Input: nums = [1,4,2,3,1,4], k = 3

Output: 4

Explanation:

The longest valid subsequence is [1, 4, 1, 4].

Constraints:

• 2 <= nums.length <= 103
• 1 <= nums[i] <= 107
• 1 <= k <= 103

Code

generalization of Find the Maximum Length of Valid Subsequence I.

Time Complexity: $O(NK)$, Space Complexity: $O(K^2)$

class Solution {
public:
    int maximumLength(vector<int>& nums, int k) {
        if(nums.size() == 2)
            return 2;
        vector<vector<int>> dp(k, vector<int>(k, 0));
        int res = -1;
        for(int i = 0; i < nums.size(); i++) {
            int current_mod = nums[i] % k;
            for(int mod = 0; mod < k; mod++) {
                int prev_mod = (mod - current_mod + k) % k;
                dp[current_mod][mod] = max(dp[current_mod][mod], dp[prev_mod][mod] + 1);
                res = max(res, dp[current_mod][mod]);
            }
        }
        return res;
    }
};

Source

• Find the Maximum Length of Valid Subsequence II - LeetCode