300.longest-increasing-subsequence.cpp

/*
 * @lc app=leetcode id=300 lang=cpp
 *
 * [300] Longest Increasing Subsequence
 *
 * https://leetcode.com/problems/longest-increasing-subsequence/description/
 *
 * algorithms
 * Medium (39.69%)
 * Total Accepted:    175.4K
 * Total Submissions: 441.9K
 * Testcase Example:  '[10,9,2,5,3,7,101,18]'
 *
 * Given an unsorted array of integers, find the length of longest increasing
 * subsequence.
 *
 * Example:
 *
 *
 * Input: [10,9,2,5,3,7,101,18]
 * Output: 4
 * Explanation: The longest increasing subsequence is [2,3,7,101], therefore
 * the length is 4.
 *
 * Note:
 *
 *
 * There may be more than one LIS combination, it is only necessary for you to
 * return the length.
 * Your algorithm should run in O(n2) complexity.
 *
 *
 * Follow up: Could you improve it to O(n log n) time complexity?
 *
 */
class Solution {
public:
  int lis(vector<int>& nums, int k, int memo[]){
    if(memo[k] != -1)
      return memo[k];
    memo[k] = 1;
    for(int i=0; i<k; i++){
      if(nums[i] < nums[k])
        memo[k] = max(memo[k], lis(nums, i, memo) + 1);
    }
    return memo[k];
  }
    int lengthOfLIS(vector<int>& nums) {
        int maxx = 0;
        int N = (int)nums.size();
        if(N == 0)
          return 0;
        int memo[N];
        fill_n(memo, N, -1);
        for(int i=0;i<N; i++)
          maxx = max(maxx, lis(nums, i, memo));
        return maxx;
    }
};