hdu 1058 Humble Numbers (DP)

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

1234111213212223100100058420

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.

我们先找一下数学规律：

2         3            4             5             6           7           8            9             10              12             14               15

2         3           2*2           5             2*3          7          2*2*2*2      3*3            2*5            2*2*3           2*7              3*5

2=min(1*2,1*3,1*5,1*7)

3=min(2*2,1*3,1*5,1*7)

4=min(2*2,2*3,1*5,1*7)

5=min(3*2,2*3,1*5,1*7)

6=min(3*2,2*3,2*5,1*7)

7=min(4*2,3*3,2*5,1*7)

8=min(4*2,3*3,2*5,2*7)

分析：若一个数是humble数，那么它的2,3,5,7倍还是humble数。

设a[i]是第i个humble数，则

a[i]=min(2*a[num[0]],3*a[num[1]],5*a[num[2]],7*a[num[3]]),num[i]在被选中后，向后移

代码：

#include<stdio.h>#include<string.h>int dp[6000],num[6];int min(int a,int b){       if(a<b)            return a;       return b;}int main(){       int i,j,n;       for(i=0;i<4;i++)          num[i]=1;       dp[1]=1;       for(i=2;i<=5843;i++)       {              dp[i]=min(dp[num[0]]*2,min(dp[num[1]]*3,min(dp[num[2]]*5,dp[num[3]]*7)));              if(dp[i]==dp[num[0]]*2)                  num[0]++;              if(dp[i]==dp[num[1]]*3)                  num[1]++;              if(dp[i]==dp[num[2]]*5)                  num[2]++;              if(dp[i]==dp[num[3]]*7)                  num[3]++;       }       while(scanf("%d",&n),n)       {              if(n % 10 == 1 && n % 100 != 11)                    printf("The %dst humble number is %d.\n",n,dp[n]);              else if(n % 10 == 2 && n % 100 != 12)                    printf("The %dnd humble number is %d.\n",n,dp[n]);              else if(n % 10 == 3 && n % 100 != 13)                    printf("The %drd humble number is %d.\n",n,dp[n]);              else                    printf("The %dth humble number is %d.\n",n,dp[n]);       }       return 0;}