hdoj 1058 Humble Numbers

最新推荐文章于 2018-01-21 08:21:43 发布

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本博客介绍了一个算法，用于找到给定序列中指定位置的谦数。该序列由仅包含2、3、5或7作为质因数的数字组成。通过提供输入整数n，读者可以找到序列中的第n个谦数，并了解如何实现这一过程。

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Humble Numbers

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 19019 Accepted Submission(s): 8302

Problem Description

A number whose only prime factors are 2,3,5 or 7 is called a humble number. The sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, ... shows the first 20 humble numbers.

Write a program to find and print the nth element in this sequence

Input

The input consists of one or more test cases. Each test case consists of one integer n with 1 <= n <= 5842. Input is terminated by a value of zero (0) for n.

Output

For each test case, print one line saying "The nth humble number is number.". Depending on the value of n, the correct suffix "st", "nd", "rd", or "th" for the ordinal number nth has to be used like it is shown in the sample output.

Sample Input

Sample Output

The 1st humble number is 1.
The 2nd humble number is 2.
The 3rd humble number is 3.
The 4th humble number is 4.
The 11th humble number is 12.
The 12th humble number is 14.
The 13th humble number is 15.
The 21st humble number is 28.
The 22nd humble number is 30.
The 23rd humble number is 32.
The 100th humble number is 450.
The 1000th humble number is 385875.
The 5842nd humble number is 2000000000.

打表：

#include<stdio.h>
#include<string.h>
#define max 5843
int humble[max];
int min(int x,int y)
{
	return x<y?x:y;
}
int main()
{
	int n,i,j,k;
	int a2,a3,a5,a7;
	int p2,p3,p5,p7;
	humble[1]=1;p2=p3=p5=p7=1;
	for(i=2;i<max;i++)
	{
		a2=humble[p2]*2;
		a3=humble[p3]*3;
		a5=humble[p5]*5;
		a7=humble[p7]*7;
		humble[i]=min(min(a2,a3),min(a5,a7));
		if(humble[i]==a2)
		{
			p2++;
		}
		if(humble[i]==a3)
		{
			p3++;
		}
		if(humble[i]==a5)
		{
			p5++;
		}
		if(humble[i]==a7)
		{
			p7++;
		}
	}
	while(scanf("%d",&n)&&(n!=0))
	{
		k=n%100;//最后两位 
		if(k>=10&&k<=20)
		{
			printf("The %dth humble number is %d.\n",n,humble[n]);
			continue;
		}
		k=n%10;
		printf("The %d",n);
		if(k==1)
		printf("st ");
		else if(k==2)
		printf("nd ");
		else if(k==3)
		printf("rd ");
		else
		printf("th ");
		printf("humble number is %d.\n",humble[n]);
	}
	return 0;
}