problem
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:
#include
#include
#include
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 \n ");
printf(" i or I : input n to test \n");
printf(" g or G : get n to enable f(n)=n \n");
printf(" q or Q : quit \n");
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);
}
}
运行结果如下:
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