Codves 1044 拦截导弹 ---1999年NOIP全国联赛提高组 dp（n2 || nlogn）

Codves 1044 拦截导弹 —1999年NOIP全国联赛提高组

一遍最长不上升子序列， 一遍严格上升子序列。

n方代码：

#include <cstdio>
#include <cstring>
#include <iostream>
#include <cstdlib>
using namespace std;

#define MAXN (20+2)
int a[MAXN], dp[MAXN];

int main()
{
    int n = 1;
    while(scanf("%d", &a[n]) != EOF)
        n ++;
    n --;

    for(int i = 1; i <= n; i ++) dp[i] = 1;

    for(int i = 1; i <= n; i ++)
        for(int j = i+1; j <= n; j ++)
            if(a[j] < a[i])
                dp[j] = max(dp[j], dp[i]+1);

    int ans = 0;
    for(int i = 1; i <= n; i ++)
        ans = max(ans, dp[i]);
    cout << ans << endl;

    memset(dp,0,sizeof(dp));
    for(int i = 1; i <= n; i ++) dp[i] = 1;

    for(int i = 1; i <= n; i ++)
        for(int j = i+1; j <= n; j ++)
            if(a[j] > a[i])
                dp[j] = max(dp[j], dp[i]+1);

    ans = 0;
    for(int i = 1; i <= n; i ++)
        ans = max(ans, dp[i]);
    cout << ans << endl;
    return 0;
}

nlogn ：
翻转序列

#include <iostream>
#include <cstdio>
#include <queue>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace std;

#define MAXN (20+2)
int a[MAXN], dp[MAXN], Za[MAXN];

#define INF (1e9)

int main()
{
    int n = 1;
    while(scanf("%d", &a[n]) != EOF)
        n ++;
    n --;

    for(int i = 1; i <= n; i ++)
        Za[n-i+1] = a[i];

    fill(dp+1, dp+n+1, INF);

    for(int i = 1; i <= n; i ++)
        dp[upper_bound(dp+1, dp+n+1, Za[i])-dp] = Za[i];

    cout << (lower_bound(dp+1, dp+n+1, INF)-dp-1) << endl;

    fill(dp+1, dp+n+1, INF);

    for(int i = 1; i <= n; i ++)
        dp[lower_bound(dp+1, dp+n+1, a[i])-dp] = a[i];

    cout << (lower_bound(dp+1, dp+n+1, INF)-dp-1) << endl;

    return 0;
}