(多校)hdu 6050 Funny Function

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原创最新推荐文章于 2026-07-18 13:34:19 发布 1.5k 阅读 AI 写同款· GEO 优化 ›

PFC中pb模型实战：从胶结参数设置到破坏模拟全流程解析本文详细解析了PFC软件中平行胶结模型（PB模型）的实战应用全流程。从胶结参数（pb_kn, pb_ks, pb_ten等）的物理意义与精准赋值入手，深入探讨了模型构建、胶结施加以避免初始损伤的技巧，并系统介绍了破坏过程的监测、阈值判定方法以及高级可视化与常见问题诊断。旨在帮助岩土工程与颗粒材料研究者掌握从参数调试到破坏模拟的核心操作，提升数值模拟的准确性与效率。阅读详情

Funny Function

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 142 Accepted Submission(s): 53

Problem Description
Function Fx,ysatisfies:
这里写图片描述
For given integers N and M,calculate Fm,1 modulo 1e9+7.

Input
There is one integer T in the first line.
The next T lines,each line includes two integers N and M .
1<=T<=10000,1<=N,M<2^63.

Output
For each given N and M,print the answer in a single line.

Sample Input
2
2 2
3 3

Sample Output
2
33

2333 比赛的时候推了一个通项 F(m,1)=(2*k1^(m-1)+(1+(-1)^(n+1))/2)/3 其中k1=(2^n-1); 然后快速幂搞一搞就过了。。

#include <iostream>
#include <iostream>
#include <algorithm>
#include <stdio.h>
using namespace std;
const long long mod = 1e9+7;
long long f(long long x,long long k)
{
    if (k==0) return 1;
    if (k&1) 
    {
        return f(x,k-1)*x%mod;
    }else {
      long long t=f(x,k/2);
      return t*t%mod;
    } 
}
void exgcd(long long a,long long b,long long &x,long long &y)
{
    if (!b) {
        x=1;y=0;
        return;
    }
    exgcd(b,a%b,y,x);
    y-=x*(a/b);
}
long long x,y;
int main()
{
    int T;
    exgcd(3,mod,x,y);
    x=(x+mod)%mod;
    long long n3=x;
    scanf("%d",&T);
    while (T--)
    {
        long long  n,m;
        scanf("%I64d%I64d",&n,&m);
        long long k1=(f(2,n)-1+mod)%mod;
        long long tmp1=2*f(k1,m-1)%mod;
        if (n&1)
        {
            printf("%I64d\n",(tmp1+1+mod)%mod*n3%mod);
        }else printf("%I64d\n",tmp1*n3%mod);
    }
}