poj 3307 Smart Sister（数论 打表）

题目：http://poj.org/problem?id=3307

Smart Sister

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 2248		Accepted: 924

Description

Yesterday, Kamran was working on a report, which he must submit to his boss next Saturday. He became tired and went out of his working room to take a nap. After some minutes, her sister, Kamelia, who is a first year university student, came to the room and
found the report. She thought, "How many large positive integers in a document. I hate these large numbers, they make me see nightmares! I should represent them in a more compact way". At first, she devised an ambiguous way to represent a number. She computed
the product of digits of a number to find a new number and repeated this process again and again until she reached a one digit number (For example, 972 was transformed to 126 and then to 12 and finally to 2).

But she simply understood that this process is not reversible and tried to find another way (Since she loves Kamran too much, she did not want to destroy his efforts!). Suddenly, she noticed an interesting property in all the numbers of the report and called
it productivity property in her mind. By her definition, a number with productivity property is a number that can be obtained by multiplying the digits of some other number (for instance, 126, 12, and 2 has productivity property, because they can be obtained
from 972, 126, and 12 respectively). She thought, "Wow, I found it. If a number
x in the report is the ith number in the increasing sequence of positive integers having productivity property, I will replace it byi". She replaced all numbers of the report, put a note for Kamran describing what she did with the numbers
of his report and went to her friend's home in a blink of an eye!!!

It is not hard to imagine, how loudly Kamran screamed when he saw the report and the note from

Kamelia! In addition, he wondered how she did this! He thought "Again this naughty smart sister". Now, Kamran needs your help to find his original report numbers.

Input

Input begins with a number T showing the number of test cases and then,T test cases follow. Each test case includes a positive integer
i which is the number written by Kamran's sister in the report. Please note than input includes thousands of test cases.

Output

For each test case, your program must output the original number x that was converted to the giveni.

Please note that it is guaranteed that the output number is less than 1018.

Sample Input

4
10
1
40
11

Sample Output

10
1
80
12

具体分析见下：

/*
问题本质就是给出i，求出第i个数。在1--10中素因子有2 3 5 7.用他们来研究数字的增长即可
*/
#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;
typedef long long LL;
const LL maxn=1e18;
LL allmin(LL a,LL b,LL c,LL d){
    return min(min(a,b),min(c,d));
}
LL a[70005],top=0;
int main()
{
    //freopen("cin.txt","r",stdin);
    LL p2,p3,p5,p7,q=1;
    a[++top]=1;
    p2=p3=p5=p7=1;
    while(q<maxn&&q>0){
        q=allmin(a[p2]*2,a[p3]*3,a[p5]*5,a[p7]*7);
        a[++top]=q;
        if(q==a[p2]*2) p2++;
        if(q==a[p3]*3) p3++;  //不是else if,因为有可能多个数字相同
        if(q==a[p5]*5) p5++;
        if(q==a[p7]*7) p7++;
    }
    //cout<<a[top-1]<<endl;
    LL ca,i;
    cin>>ca;
    while(ca--){
        scanf("%lld",&i);
        printf("%lld\n",a[i]);
    }
    return 0;
}