[DP]最长递增子序列

#include <iostream>
#include <limits.h>
#include <vector>
#include <algorithm>

using namespace std;

//获取最长递增子序列的递增数组
vector<int> getdp1(vector<int> arr) {
    vector<int> dp(arr.size());
    for (int i = 0; i < int(arr.size()); i ++) {
        dp[i] = 1;
        for (int j = 0; j < i; j ++) {
            if (arr[i] > arr[j])
                dp[i] = max(dp[i], dp[j] + 1);
        }
    }
    return dp;
}

vector<int> getdp2(vector<int> arr) {
    int right = 0;
    int arr_len = int(arr.size());
    int ends[arr_len];
    int dp[arr_len];
    ends[0] = arr[0];
    dp[0] = 1;
    for (int i = 1; i < arr_len; i ++) {
        //二分查找ends
        int l = 0;
        int r = right;
        while (l <= r) {
            int mid = (l + r) >> 1;
            if (arr[i] > ends[mid])
                l = mid + 1;
            else
                r = mid - 1;
        }
    }
}

// 从dp数组中逆序还原出决策路径
vector<int> generateLIS(vector<int> dp, vector<int> arr) {
    vector<int>::iterator  maxPosition = max_element(dp.begin(), dp.end()); //algorithm中求vector最大值的函数
    int maxIndex = maxPosition - dp.begin();
    int maxNum = *maxPosition;
    vector<int> res;
    res.push_back(arr[maxIndex]);
    int tmpNum = maxNum;
    for (int i = maxIndex - 1; i >= 0; i --) {
        if (dp[i] == tmpNum - 1) {
            res.push_back(arr[i]);
            tmpNum -= 1;
        } else continue;
    }
    reverse(res.begin(), res.end());
    return res;
}

int main()
{
    vector<int> test = {2, 1, 5, 3, 6, 4, 8, 9, 7};
    vector<int> dp =  getdp1(test);
    vector<int> lis = generateLIS(dp, test);
//    cout<<"LIS"<<lis.size()<<endl;
    for (auto c: lis)
        cout<<c<<endl;

    return 0;
}