3201. Find the Maximum Length of Valid Subsequence I

You are given an integer array nums.

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

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

Return the length of the longest valid subsequence of nums.

A subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.

 Example 1:

Input: nums = [1,2,3,4]

Output: 4

Explanation:

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

Example 2:

Input: nums = [1,2,1,1,2,1,2]

Output: 6

Explanation:

The longest valid subsequence is [1, 2, 1, 2, 1, 2].

Example 3:

Input: nums = [1,3]

Output: 2

Explanation:

The longest valid subsequence is [1, 3].

 Constraints:

• 2 <= nums.length <= 2 * 105
• 1 <= nums[i] <= 107

Solution 1: Dynamic Programming

JAVA 

• class Solution {
      public int maximumLength(int[] nums) {
          int k = 2;
          int[][] f = new int[k][k];
          int ans = 0;
          for (int x : nums) {
              x %= k;
              for (int j = 0; j < k; ++j) {
                  int y = (j - x + k) % k;
                  f[x][y] = f[y][x] + 1;
                  ans = Math.max(ans, f[x][y]);
              }
          }
          return ans;
      }
  }

C++

• class Solution {
  public:
      int maximumLength(vector<int>& nums) {
          int k = 2;
          int f[k][k];
          memset(f, 0, sizeof(f));
          int ans = 0;
          for (int x : nums) {
              x %= k;
              for (int j = 0; j < k; ++j) {
                  int y = (j - x + k) % k;
                  f[x][y] = f[y][x] + 1;
                  ans = max(ans, f[x][y]);
              }
          }
          return ans;
      }
  };