BZOJ4985 评分 二分答案、DP

传送门

题意：自己去看

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答案满足单调性，所以考虑二分答案。

二分答案很好想，但是check并不是很好想。

考虑DP：设$f_i$表示队列中第$i$个人的分数$\geq \, mid$的代价，最开始$N$个人的代价显然是：如果当前位置上没有人为$1$，如果当前的人分数$\geq mid$为$0$，否则为$INF$。$N+1$到$ans$的转移就是当前队伍的前$3$个人中至少有两个人$\geq \, mid$的代价的最小值，用队列模拟DP过程即可。

 1 //This code is written by Itst
 2 #define INF 0x3f3f3f3f
 3 #include<bits/stdc++.h>
 4 using namespace std;
 5  
 6 inline int read(){
 7     int a = 0;
 8     bool f = 0;
 9     char c = getchar();
10     while(c != EOF && !isdigit(c)){
11         if(c == '-')
12             f = 1;
13         c = getchar();
14     }
15     while(c != EOF && isdigit(c)){
16         a = (a << 3) + (a << 1) + (c ^ '0');
17         c = getchar();
18     }
19     return f ? -a : a;
20 }
21  
22 const int MAXN = 100000;
23 int pri[MAXN] , notin[MAXN] , N , M;
24 queue < int > q;
25  
26 bool check(int mid){
27     for(int i = 1 ; i <= N ; i++)
28         if(!pri[i])
29             q.push(1);
30         else
31             q.push(pri[i] >= mid ? 0 : INF);
32     int num = N - M + 1 - (lower_bound(notin + 1 , notin + N - M + 1 , mid) - notin);
33     while(1){
34         int t = q.front();
35         q.pop();
36         if(q.empty())
37             return t <= num;
38         long long p = q.front();
39         q.pop();
40         long long r = q.front();
41         q.pop();
42         if(p + r + t >= (INF << 1))
43             q.push(INF);
44         else
45             q.push(min(t + p , min(p + r , t + r)));
46     }
47 } 
48  
49 int main(){
50 #ifdef BZ
51     freopen("4985.in" , "r" , stdin);
52     //freopen("4985.out" , "w" , stdout);
53 #endif
54     N = read();
55     M = read();
56     for(int i = 1 ; i <= M ; i++){
57         int a = read() , b = read();
58         pri[b] = a;
59     }
60     for(int i = 1 ; i <= N - M ; i++)
61         notin[i] = read();
62     sort(notin + 1 , notin + N - M + 1);
63     int L = 0 , R = 1e9;
64     while(L < R){
65         int mid = L + R + 1 >> 1;
66         check(mid) ? L = mid : R = mid - 1;
67     }
68     cout << L;
69     return 0;
70 }
71