HDU 1058 Humble Numbers（DP,數）

標籤：acm   hdu   動態規劃   dp   

題意  所有只能被2，3，5，7這4個素數整除的數稱為Humble Number  輸入n  輸出第n個Humble Number

1是第一個humble number  對於一個Humble Number  a  有2*a,3*a,5*a,7*a都是Humble Number  可以以1為基數  依次展開即可得到一定範圍內的Humble Number 用i,j,k,l分別記錄 2，3，5，7分別乘到了第幾個Humble Number  當前在計算第cnt個Humble Number  那麼有  hum[cnt] = min ( hum[i] * 2, hum[j] * 3, hum[k] * 5, hum[l] * 7)   然後對應min的i或j或k或l就加1  當cnt到達了n  結果就出來了

#include<cstdio>#include<algorithm>using namespace std;const int N = 5843;int hum[N], cnt, n;int main(){    int i = 1, j = 1, k = 1, l = hum[1] = 1;    for (cnt = 2; cnt < N; ++cnt)    {        hum[cnt] = min ( min(hum[i] * 2, hum[j] * 3), min (hum[k] * 5, hum[l] * 7));        if (hum[cnt] == hum[i] * 2) ++i;        if (hum[cnt] == hum[j] * 3) ++j;        if (hum[cnt] == hum[k] * 5) ++k;        if (hum[cnt] == hum[l] * 7) ++l;    }    while (scanf ("%d", &n), n)    {        printf ("The %d", n);        if (n % 100 != 11 && n % 10 == 1) printf ("st ");        else if (n % 100 != 12 && n % 10 == 2) printf ("nd ");        else if (n % 100 != 13 && n % 10 == 3) printf ("rd ");        else printf ("th ");        printf ("humble number is %d.\n", hum[n]);    }    return 0;}

Humble NumbersProblem DescriptionA 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
 
InputThe 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.
 
OutputFor 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.