Longest Increasing Subsequence

Desicription

Given an unsorted array of integers, find the length of longest increasing subsequence.

Example:

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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?

Solution

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class Solution {
public:
    int lengthOfLIS(vector<int>& nums) {
        vector<int> dp;
        for(const auto& num : nums) {
            auto res = lower_bound(dp.begin(), dp.end(), num);
            if(res == dp.end()) {
                dp.push_back(num);
            } else {
                *res = num;
            }
        }
        return dp.size();
    }
};