Longest Increasing Subsequence

Given a sequence of integers, find the longest increasing subsequence (LIS).

You code should return the length of the LIS.

Example

For [5, 4, 1, 2, 3], the LIS  is [1, 2, 3], return 3

For [4, 2, 4, 5, 3, 7], the LIS is [4, 4, 5, 7], return 4

Challenge

Time complexity O(n^2) or O(nlogn)

Clarification

What's the definition of longest increasing subsequence?

    * The longest increasing subsequence problem is to find a subsequence of a given sequence in which the subsequence's elements are in sorted order, lowest to highest, and in which the subsequence is as long as possible. This subsequence is not necessarily contiguous, or unique.  

    * https://en.wikipedia.org/wiki/Longest_common_subsequence_problem

// Refer to : http://en.wikipedia.org/wiki/Longest_increasing_subsequence

class Solution {
    int insert(vector<int> &A, int lastIndex, int target) {
        int i = 0, j = lastIndex;
        while(i <= j) {
            int m = (i+j)/2;
            if (A[m] > target) 
               j = m - 1;
            else 
               i = m + 1;
        }
        A[i] = target;
        return i;
    }
public:
    /**
     * @param nums: The integer array
     * @return: The length of LIS (longest increasing subsequence)
     */
    int longestIncreasingSubsequence(vector<int> nums) {
        int n = nums.size();
        if (n < 2) return n;
        
        vector<int> M(n, 0);
        int longest = 0;
        M[0] = nums[0];
        
        for(int i =1; i < n; i++) 
            longest = max(longest, insert(M, longest, nums[i]));
        
        return longest+1;
    }
};