SGU154——Factorial （poj1401变形题——数论+二分）

154. Factorial

time limit per test: 0.5 sec.

memory limit per test: 4096 KB
input: standard input

output: standard output

You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N. For example, 5! = 120, 120 contains one zero on the trail.

Input
One number Q written in the input (0<=Q<=10^8).
Output
Write "No solution", if there is no such number N, and N otherwise.

Sample test(s)

Input

2


Output

10





题目描述：输入一个数n、求某个数的阶乘后面有n个0的数p；

会了poj1401就好办了、直接来个二分搜素。

#include<iostream>
#include<string.h>
#include<stdio.h>
#include<ctype.h>
#include<algorithm>
#include<stack>
#include<queue>
#include<set>
#include<math.h>
#include<vector>
#include<map>
#include<deque>
#include<list>
#define N 0x7fffffff
using namespace std;
int num0(int n)
{
    int count=0;
    while(n)
    {
        count+=n/5;
        n/=5;
    }
    return count;
}
void find(int w)
{
    int left=0,right=N,mid;
    while(left<=right)
    {
        mid=(left+right)>>1;//位运算速度快
//        mid=(left+right)/2;
        if(num0(mid)>=w)
        right=mid-1;
        else
        left=mid+1;
    }
    if(num0(left)==w)
    printf("%d\n",left);
    else
    puts("No solution");
}
int main()
{
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        if(n==0)
        printf("1\n");
        else
        {
            find(n);
        }
    }
    return 0;
}

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