Humble Numbers

问题

dp问题

#define  _CODE_HDOJ_A1058_DP_
#ifdef _CODE_HDOJ_A1058_DP_
#include <stdio.h>
#include <iostream>
/************************************************************************
 f[1] = 1
for the factor 2, 3, 5 and 7.
1*2 = 2       1*3=3      1*5=5      1*7=7
2*2 = 4       2*3=6      2*5=10     2*7=14
3*2 = 6		  3*3=9      3*5=15     3*7=21
4*2 = 8		  4*3=12     4*5=20     4*7=28
5*2 = 10	  5*3=15     5*5=25     5*7=35
6*2 = 12	  6*3=18     6*5=30     6*7=42
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and the Humble number sequence is :
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27...
1)if f[j] is a humble number, so f[j]*2, f[j]*3, f[j]*5, f[j]*7 are humbles.
2)if f[i] is humble number, so it must be derived from f[j]*2 or f[k]*3 or
  f[l]*5 or f[m]*7,(j,k,l,m) < i.
3)f sequence is ascending order,so 

 trans function: f[i] = min{f[p2]*2, f[p3]*3, f[p5]*5, f[p7]*7}
************************************************************************/
const int N = 5842;
const int Tw = 2;
const int Tr = 3;
const int Fi = 5;
const int Se = 7;
int dp[N+1];
inline int Min2(int a, int b)
{
	return a < b ? a : b;
}
inline int Min4(int a, int b, int c, int d)
{
	return Min2(Min2(a,b), Min2(c, d));
}

void PrintOut(int n)
{
	printf("The %d", n);
	int last = n%100;
	if(last==13 || last==12 || last==11)
	{
		printf("th humble number is %d.\n", dp[n]);
		return ;
	}
	last = n%10;
	if(last == 1)
		printf("st");
	else if(last == 2)
		printf("nd");
	else if(last == 3)
		printf("rd");
	else
		printf("th");
	printf(" humble number is %d.\n", dp[n]);
}
void Calcul()
{
	int p2, p3, p5, p7;
	p2 = p3 = p5 = p7 = 1;
	dp[1] = 1;
	for (int i = 2; i <= N; ++i)
	{
		dp[i] = Min4(dp[p2] * Tw, dp[p3] * Tr, dp[p5] * Fi, dp[p7] * Se);

		//dp[i] = base * multiple 
		if(dp[i] == dp[p2] * Tw) p2++;
		if(dp[i] == dp[p3] * Tr) p3++;
		if(dp[i] == dp[p5] * Fi) p5++;
		if(dp[i] == dp[p7] * Se) p7++;
	} 
}

int main()
{
	int n;
	Calcul();
	while (scanf("%d", &n), n)
	{
		PrintOut(n);
	}
	return 0;
}
#endif