JXOI2018 守卫

Posted 2021-01-26 akoasm

题目大概是给一些折线，问安排多少个保安才能监控全部折点。

预处理出能否看到进行区间dp即可，转移用前缀和优化

#include <cstdio>
#include <algorithm>
#include <iostream>
using namespace std;
#define db double
const int INF = 0x3f3f3f3f;
const int maxn = 5010;
int f[maxn][maxn];
int ok[maxn][maxn];
int H[maxn];
int n;
inline db slope(int a,int b) {
    return (db)(H[a] - H[b])/(a-b);
}
int mx;
int l,r;
int ans;
int main () {
    scanf("%d",&n);
    mx = INF;
    for(int i = 1;i <= n; ++i) {
        scanf("%d",&H[i]);
        ok[i][i] = ok[i][i - 1] = 1;
        db k = slope(i - 1,i);
        for(int j = i - 2;j >= 1; --j) {
            while(j and slope(j,i) >= k) {
                ok[i][j --] = 0;
            }
            k = slope(j,i);
            ok[i][j] = 1;
        }
    }
    ans = 0;
    for(r = 1;r <= n; ++r) {
        int head = 1;
        int tail = 0;
        for(l = r;l; --l) {
            if(ok[r][l]) {
                if(!ok[r][l - 1]) tail = l - 1;
                f[l][r] = head;
            }
            else {
                f[l][r] = head + min(f[l][tail],f[l][tail + 1]);
                if (ok[r][l - 1]) {
                    head += min(f[l][tail],f[l][tail + 1]);
                }
            }
            ans ^= f[l][r];
        }
    }
    cout<<ans<<endl;
    return 0;
}