1到n之间1的个数

Consider a function which, for a given whole number n, returns the number of ones required when writing out all numbers between 0 and n.

For example, f(13)=6. Notice that f(1)=1. What is the next largest n such that f(n)=n?

 

算法思想：

 

循环求出每个数中1的个数，累计之，若满足f(n)=n，则退出，否则继续。

代码如下：

/**//************************************************************************
* 0~n之间1的个数,如f(13)=6
* 1,2,3,4,5,6,7,8,9,10,11,12,13.1的个数为6
* 要求:输入一个正整数n,求出f(n),及求解f(n)=n
************************************************************************/

#include <stdio.h>
#include <string.h>
#include <Windows.h>

class CalculationTimes
...{
public:
    CalculationTimes()...{}
    ~CalculationTimes()...{}

    int GetTimes(int n);
};

//计算正整数n中1的个数
int CalculationTimes::GetTimes(int n)
...{
    int count=0;    
    while(n)
    ...{
        if(n%10==1)
            count++;
        n/=10;
    }
    return count;
}

//显示菜单
void show_menu()
...{
    printf("--------------------------------------------- ");
    printf("input command to test the program ");
    printf("   i or I : input n to test ");
    printf("   g or G : get n to enable f(n)=n ");
    printf("   q or Q : quit ");
    printf("--------------------------------------------- ");
    printf("$ input command >");
}

void main()
...{
    char sinput[10];
    int n;

    show_menu();

    scanf("%s",sinput);
    while(stricmp(sinput,"q")!=0)
    ...{
        int t=0,count=0;
        if(stricmp(sinput,"i")==0)
        ...{
            printf("  please input an integer:");
            scanf("%d",&n);

            count=0;
            CalculationTimes obj;
            t=GetTickCount();
            for(int i=1;i<=n;i++)
                count+=obj.GetTimes(i);
            t=GetTickCount()-t;
            printf("   count=%d    time=%d ",count,t);
        }
        else if(stricmp(sinput,"g")==0)
        ...{
            CalculationTimes obj;
            n=2;
            count=1;
            t=GetTickCount();
            while(1)
            ...{
                count+=obj.GetTimes(n);
                if(count==n)
                    break;
                n++;
            }
            t=GetTickCount()-t;
            printf("   f(n)=n=%d    time=%d ",n,t);
        }


        //输入命令
        printf("$ input command >");
        scanf("%s",sinput);
    }
}