题目

[longest-increasing-subsequence](https://leetcode.com/problems/longest-increasing-subsequence/）

2. 算法

* DP

* 二分

* 二分优化

* stl-1

* stl-2

3. 代码

* dp

class Solution {
public:
    int lengthOfLIS(vector<int>& nums) {
        vector<int> dp(nums.size(), 1);
        int res = 0;
        for (int i = 0; i < nums.size(); ++i) {
            for (int j = 0; j < i; ++j) {
                if (nums[i] > nums[j]) {
                    dp[i] = max(dp[i], dp[j] + 1);
                }
            }
            res = max(res, dp[i]);
        }
        return res;
    }
};

* 二分

class Solution {
public:
    int lengthOfLIS(vector<int>& nums) {
        if (nums.empty()) return 0;
        vector<int> ends{nums[0]};
        for (auto a : nums) {
            if (a < ends[0]) ends[0] = a;
            else if (a > ends.back()) ends.push_back(a);
            else {
                int left = 0, right = ends.size();
                while (left < right) {
                    int mid = left + (right - left) / 2;
                    if (ends[mid] < a) left = mid + 1;
                    else right = mid;
                }
                ends[right] = a;
            }
        }
        return ends.size();
    }
};

* 二分优化

class Solution {
public:
    int lengthOfLIS(vector<int>& nums) {
        vector<int> dp;
        for (int i = 0; i < nums.size(); ++i) {
            int left = 0, right = dp.size();
            while (left < right) {
                int mid = left + (right - left) / 2;
                if (dp[mid] < nums[i]) left = mid + 1;
                else right = mid;
            }
            if (right >= dp.size()) dp.push_back(nums[i]);
            else dp[right] = nums[i];
        }
        return dp.size();
    }
};

* stl-1

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

* stl-2

class Solution {
public:
    int lengthOfLIS(vector<int>& nums) {
        vector<int> v;
        for (auto a : nums) {
            if (find(v.begin(), v.end(), a) != v.end()) continue;
            auto it = upper_bound(v.begin(), v.end(), a);
            if (it == v.end()) v.push_back(a);
            else *it = a;
        }
        return v.size();
    }
};