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

 1 #include <algorithm>
 2 #include <iostream>
 3 #include <cstdlib>
 4 #include <cstring>
 5 #include <cstdio>
 6 #include <vector>
 7 #include <cmath>
 8 #include <ctime>
 9 #include <list>
10 #include <set>
11 #include <map>
12 using namespace std;
13 typedef long long LL;
14 typedef pair <int, int> P;
15 const int N = 2e3 + 5;
16 int dp[N];
17 int a[N];
18
19 int main()
20 {
21     int n;
22     while(~scanf("%d", &n)) {
23         memset(dp, 0, sizeof(dp));
24         int res = 0;
25         for(int i = 1; i <= n; ++i) {
26             scanf("%d", a + i);
27             dp[i] = 1;
28             for(int j = 1; j < i; ++j) {
29                 if(a[i] > a[j])
30                     dp[i] = max(dp[i], dp[j] + 1);
31             }
32             res = max(res, dp[i]);
33         }
34         printf("%d\n", res);
35     }
36     return 0;
37 }

O(nlogn)

dp[i]表示LIS长度为i的最后一个元素

 1 //#pragma comment(linker, "/STACK:102400000, 102400000")
 2 #include <algorithm>
 3 #include <iostream>
 4 #include <cstdlib>
 5 #include <cstring>
 6 #include <cstdio>
 7 #include <vector>
 8 #include <cmath>
 9 #include <ctime>
10 #include <list>
11 #include <set>
12 #include <map>
13 using namespace std;
14 typedef long long LL;
15 typedef pair <int, int> P;
16 const int N = 1e5 + 5;
17 int dp[N], a[N], inf = 1e6;
18
19 int main()
20 {
21     int n;
22     while(~scanf("%d", &n)) {
23         for(int i = 0; i <= n + 1; ++i)
24             dp[i] = inf;
25         for(int i = 1; i <= n; ++i) {
26             scanf("%d", a + i);
27             *lower_bound(dp, dp + n, a[i]) = a[i];
28         }
29         printf("%d\n", lower_bound(dp, dp + n, inf) - dp);
30     }
31     return 0;
32 }