【HDU】1058 - Humble Numbers（dp）

FishWang

发布于 2025-08-27 11:24:46

1840

点击打开题目

Humble Numbers

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 23949 Accepted Submission(s): 10478

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.

Source

University of Ulm Local Contest 1996

后面的是由前面的推出来的。

代码如下：

#include <stdio.h>
#include <cstring>
#include <algorithm>
using namespace std;
#define CLR(a,b) memset(a,b,sizeof(a))
#define INF 0x3f3f3f3f
#define LL long long
int Min(int a,int b,int c,int d)
{
	return min(min(min(a,b),c),d);
}
int main()
{
	int num[42000] = {0,1};
	int n2,n3,n5,n7;
	int t;
	n2 = n3 = n5 = n7 = 1;
	for (int i = 2 ; i <= 5842 ; i++)
	{
		t = Min(num[n2]*2 , num[n3]*3 , num[n5]*5 , num[n7]*7);
		num[i] = t;
		if (t == num[n2]*2)
			n2++;
		if (t == num[n3]*3)
			n3++;
		if (t == num[n5]*5)
			n5++;
		if (t == num[n7]*7)
			n7++;
	}
	int n;
	while (~scanf ("%d",&n) && n)
	{
		if (n % 100 == 11 || n % 100 == 12 || n % 100 == 13)
			printf ("The %dth humble number is %d.\n",n,num[n]);
		else if (n % 10 == 1)
			printf ("The %dst humble number is %d.\n",n,num[n]);
		else if (n % 10 == 2)
			printf ("The %dnd humble number is %d.\n",n,num[n]);
		else if (n % 10 == 3)
			printf ("The %drd humble number is %d.\n",n,num[n]);
		else
			printf ("The %dth humble number is %d.\n",n,num[n]);
	}
	return 0;
}

本文参与腾讯云自媒体同步曝光计划，分享自作者个人站点/博客。

原始发表：2025-08-26，如有侵权请联系 cloudcommunity@tencent.com 删除

numbers