[蓝桥杯][2017年第八届真题]小数第n位

题目链接:小数第n位



解题思路:因为求第n位开始的三位小数,那就要求到n+2,公式为: ( a / b ) ∗ 1 0 ( n + 2 ) % 1000 (a/b)*10^{(n+2)}\%1000 (a/b)10(n+2)%1000,例如1.2431的从4开始取为431等价于12431%1000=431

因为 x / d % m = x % ( d ∗ m ) / d x/d\%m=x\%(d*m)/d x/d%m=x%(dm)/d
所有 ( a / b ) ∗ 1 0 ( n + 2 ) % 1000 (a/b)*10^{(n+2)}\%1000 (a/b)10(n+2)%1000 => ( a ∗ 1 0 ( n + 2 ) ) % ( b ∗ 1000 ) / b (a *10 ^{ (n+2)})\%(b * 1000)/b (a10(n+2))%(b1000)/b

#include<bits/stdc++.h>
#define x first
#define y second
#define mem(h) memset(h,-1,sizeof h)
#define mcp(a,b) memcpy(a,b,sizeof b)
using namespace std;
typedef long long LL;
typedef unsigned long long ull; 
typedef pair<int,int>PII;
typedef pair<double,double>PDD;
namespace IO{
    
    
	inline LL read(){
    
    
		LL o=0,f=1;char c=getchar();
		while(c<'0'||c>'9'){
    
    if(c=='-')f=-1;c=getchar();}
		while(c>='0'&&c<='9'){
    
    o=o*10+c-'0';c=getchar();}
		return o*f;
	}
}using namespace IO;
//#############以上是自定义技巧(可忽略)########## 
const int N=1e2+7,M=2e5+7,INF=0x3f3f3f3f,mod=1e8+7,P=131;
LL a,b,n;
LL m;
LL Pow(LL Base,int M){
    
    
	LL res=1;
	while(M){
    
    
		if(M&1)res=res*Base%m;
		Base=Base*Base%m;
		M>>=1;
	}
	return res;
}
int main(){
    
    
	 cin>>a>>b>>n;
	 m=1000*b;
	 LL res=Pow(10,n+2);
	 LL ans=(a*res)%m/b;
	 printf("%03d\n",ans);
	return 0;
}

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转载自blog.csdn.net/weixin_43738764/article/details/109012710