Humble Numbers
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
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
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.
1 #include<cstdio> 2 #include<string> 3 #include<cstring> 4 #include<map> 5 using namespace std; 6 7 int dp[6000]; 8 int min(int x,int y,int z,int w) 9 { 10 int temp1=x<y?x:y; 11 int temp2=temp1<z?temp1:z; 12 return temp2<w?temp2:w; 13 } 14 15 int main() 16 { 17 //freopen("in.txt","r",stdin); 18 int t[8],n; 19 dp[1]=1; 20 t[7]=t[2]=t[3]=t[5]=1; 21 for(int i=2;i<=5842;i++) 22 { 23 dp[i]=min(dp[t[2]]*2,dp[t[3]]*3,dp[t[5]]*5,dp[t[7]]*7); 24 while(dp[t[2]]*2<=dp[i])t[2]++; 25 while(dp[t[3]]*3<=dp[i])t[3]++; 26 while(dp[t[5]]*5<=dp[i])t[5]++; 27 while(dp[t[7]]*7<=dp[i])t[7]++; 28 } 29 while(scanf("%d",&n),n) 30 { 31 printf("The %d",n); 32 if(n%10==1&&n%100!=11) 33 printf("st "); 34 else if(n%10==2&&n%100!=12) 35 printf("nd "); 36 else if(n%10==3&&n%100!=13) 37 printf("rd "); 38 else 39 printf("th "); 40 printf("humble number is %d. ",dp[n]); 41 } 42 return 0; 43 }