Humble Numbers 1095

#include <iostream>
using namespace std;
int a[5844];

int min(int b,int c,int d,int e)
{
    int t;
    t=b<c?b:c;
    t=t<d?t:d;
    t=t<e?t:e;
    return t;
}
int main()
{
    int i=0;
    a[i]=1;
    int x=0,y=0,z=0,m=0;
    while(i<=5843)
    {
        a[++i]=min(a[x]*2,a[y]*3,a[z]*5,a[m]*7);
        if(a[i]==a[x]*2)  x++;
        if(a[i]==a[y]*3)  y++;
        if(a[i]==a[z]*5)  z++;
        if(a[i]==a[m]*7)  m++;
    }
    int n;
    while (cin>>n,n)
    {
        cout<<"The "<<n;
        if(n%100/10==1)
       cout<<"th humble number is ";
        else if(n%10==1) 
            cout<<"st humble number is ";
        else      if(n%10==2) 
            cout<<"nd humble number is ";
        else  if(n%10==3) 
            cout<<"rd humble number is ";
        else  cout<<"th humble number is ";
        cout<<a[n-1]<<"."<<endl;
    }
    return 0;
}

 

Humble Numbers

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Time Limit: 2 Seconds      Memory Limit: 65536 KB

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A number whose only prime factors are 2,3,5 or 7 is called a humblenumber. 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 Specification

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 Specification

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

1
2
3
4
11
12
13
21
22
23
100
1000
5842
0

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.

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Source: University of Ulm Local Contest 1996

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