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// problem 300. Longest Increasing Subsequence

class Solution {
public:
    int lengthOfLIS(vector<int>& nums) {
        // max len at each position 
        // --> need to know max len out of every position
        int keep_track[10000];
        int len = nums.size();
        for (int i = 0; i < len; i ++){
            keep_track[i] = 1;
        }
        for (int i = 1; i < len; i ++){
            for (int j = 0; j < i; j ++){
                if (nums[j] < nums[i]){
                    keep_track[i] = std::max(keep_track[j] + 1, keep_track[i]);
                }
            }
        }
        int res = 0;
        for (int i = 0; i < len; i ++){
            res = std::max(keep_track[i], res);
        }
        return res;
    }
};