HDU3706Second My Problem First(单调队列)

Second My Problem First

Time Limit: 12000/4000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1928    Accepted Submission(s): 731

Problem Description

Give you three integers n, A and B. 
Then we define S_i = Aⁱ mod B and T_i = Min{ S_k | i-A <= k <= i, k >= 1}
Your task is to calculate the product of T_i (1 <= i <= n) mod B.

 

Input

Each line will contain three integers n(1 <= n <= 10⁷),A and B(1 <= A, B <= 2³¹-1). 
Process to end of file.

 

Output

For each case, output the answer in a single line.

 

Sample Input

1 2 32 3 43 4 54 5 65 6 7

 

Sample Output

23456

思路：

单调队列的应用，维护一个递增的单调队列

#include<bits/stdc++.h>using namespace std;typedef long long ll;ll n, a, b;deque<pair<int, ll> > q;int main(){    int n;    while(cin >> n >> a >> b)    {        q.clear();        ll ans = 1, tmp = 1;        for(int i = 1; i <= n; i++)        {            tmp = tmp * a % b;            while(!q.empty() && q.back().second >= tmp) q.pop_back();            q.push_back(make_pair(i, tmp));            while(!q.empty() && i - q.front().first > a) q.pop_front();            ans = ans * q.front().second % b;        }        cout << ans << endl;    }    return 0;}