LIS (最长上升子序列)

LIS两种写法

O(n^2)

dp[i]表示以a[i]结尾的为LIS长度

 #include <algorithm>
 #include <iostream>
 #include <cstdlib>
 #include <cstring>
 #include <cstdio>
 #include <vector>
 #include <cmath>
 #include <ctime>
 #include <list>
 #include <set>
 #include <map>
 using namespace std;
 typedef long long LL;
 typedef pair <int, int> P;
 const int N = 2e3 + ;
 int dp[N];
 int a[N];

 int main()
 {
     int n;
     while(~scanf("%d", &n)) {
         memset(dp, , sizeof(dp));
         int res = ;
         for(int i = ; i <= n; ++i) {
             scanf("%d", a + i);
             dp[i] = ;
             for(int j = ; j < i; ++j) {
                 if(a[i] > a[j])
                     dp[i] = max(dp[i], dp[j] + );
             }
             res = max(res, dp[i]);
         }
         printf("%d\n", res);
     }
     return ;
 }

O(nlogn)

dp[i]表示LIS长度为i的最后一个元素

 //#pragma comment(linker, "/STACK:102400000, 102400000")
 #include <algorithm>
 #include <iostream>
 #include <cstdlib>
 #include <cstring>
 #include <cstdio>
 #include <vector>
 #include <cmath>
 #include <ctime>
 #include <list>
 #include <set>
 #include <map>
 using namespace std;
 typedef long long LL;
 typedef pair <int, int> P;
 const int N = 1e5 + ;
 int dp[N], a[N], inf = 1e6;

 int main()
 {
     int n;
     while(~scanf("%d", &n)) {
         for(int i = ; i <= n + ; ++i)
             dp[i] = inf;
         for(int i = ; i <= n; ++i) {
             scanf("%d", a + i);
             *lower_bound(dp, dp + n, a[i]) = a[i];
         }
         printf("%d\n", lower_bound(dp, dp + n, inf) - dp);
     }
     return ;
 }