CodeForces 17D Notepad(同餘定理)
Nick is attracted by everything unconventional. He doesn't like decimal number system any more, and he decided to study other number systems. A number system with base b caught
his attention. Before he starts studying it, he wants to write in his notepad all the numbers of length n without leading zeros in
this number system. Each page in Nick's notepad has enough space for c
Would you help Nick find out how many numbers will be written on the last page.
Input
The only input line contains three space-separated integers b
In the only line output the amount of numbers written on the same page as the last number.
2 3 3output
1input
2 3 4output
4
題目的意思就是求 ((b-1)* b ^(n-1))%c
如果用java高精度加快速冪來求,肯定會爆炸,因為有一百萬位。
這道題目完全可以不用快速冪,利用同餘定理就可以了,當然用了快速冪會更快一些
#include <iostream>
#include <string.h>
#include <stdlib.h>
#include <algorithm>
#include <math.h>
#include <stdio.h>
#include <queue>
using namespace std;
#define MAX 1000000
char b[MAX+5];
char n[MAX+5];
long long int c;
int main()
{
while(scanf("%s%s%lld",b,n,&c)!=EOF)
{
long long int num=0;//b
long long int num2=0;//b-1
int len=strlen(b);
//b
for(int i=0;i<len;i++)
num=(b[i]-'0'+num*10)%c;
//b-1
for(int i=len-1;i>=0;i--)
if(b[i]!='0'){b[i]--;break;}
else b[i]='9';
for(int i=0;i<len;i++)
num2=(b[i]-'0'+num2*10)%c;
int len2=strlen(n);
long long int ans=0;
long long int num3=num;
//n-1
for(int i=len2-1;i>=0;i--)
if(n[i]!='0'){n[i]--;break;}
else n[i]='9';
for(int j=0;j<len2;j++)
{
if(n[j]!='0')
{
if(j!=0)
{
long long int num4=num;
for(int k=1;k<=9;k++)
num=((num%c)*num4)%c;
}
int x=n[j]-'0';
if(j==0)
x--;
for(int p=1;p<=x;p++)
num=((num%c)*num3)%c;
}
else
{
if(j!=0)
{
long long int num4=num;
for(int k=1;k<=9;k++)
num=((num%c)*num4)%c;
}
else
num=1;
}
}
num=((num%c)*(num2%c))%c;
if(num==0)
num=c;
printf("%lld\n",num);
}
return 0;
}