hdu 3706 Second My Problem First

Second My Problem First

Time Limit: 12000/4000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1223    Accepted Submission(s): 468

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

 

这道题目一看就知道是单调队列了，恒定的区间长度维护一个最小值，这个是单调队列最明显的性质了。

代码：

#include<cstdio>#include<iostream>#define Maxn 10000010#define ll long longusing namespace std;int p[Maxn],sq[Maxn<<1];int main(){    int n,a,b;    while(~scanf("%d%d%d",&n,&a,&b)){        p[0]=1;        for(int i=1;i<=n;i++)            p[i]=p[i-1]*(ll)a%b;        int s=0,e=-1;        int res=1;        for(int i=1;i<=n;i++){            while(s<=e&&p[sq[e]]>=p[i]) e--;            sq[++e]=i;            if(sq[s]+a-1<sq[e]) s++;            res=(ll)res*p[sq[s]]%b;        }        printf("%d\n",res);    }return 0;}