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
. . . .
. . . .
. . . .
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