ZOJ Problem Set–1078 Palindrom Numbers

Time Limit: 2 Seconds      Memory Limit: 65536 KB

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Statement of the Problem

We say that a number is a palindrom if it is the sane when read from left to right or from right to left. For example, the number 75457 is a palindrom.

Of course, the property depends on the basis in which is number is represented. The number 17 is not a palindrom in base 10, but its representation in base 2 (10001) is a palindrom.

The objective of this problem is to verify if a set of given numbers are palindroms in any basis from 2 to 16.

Input Format

Several integer numbers comprise the input. Each number 0 < n < 50000 is given in decimal basis in a separate line. The input ends with a zero.

Output Format

Your program must print the message Number i is palindrom in basis where I is the given number, followed by the basis where the representation of the number is a palindrom. If the number is not a palindrom in any basis between 2 and 16, your program must print the message Number i is not palindrom.

Sample Input

17
19
0

Sample Output

Number 17 is palindrom in basis 2 4 16
Number 19 is not a palindrom

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Source: South America 2001

  1: #include<iostream>
  2: #include<vector>
  3: #include<set>
  4: #include<algorithm>
  5: using namespace std;
  6: vector<int>& transfor(int num, int basis)
  7: {
  8:   vector<int> *vecResult = new vector<int>();
  9:   while(num)
 10:   {
 11:     (*vecResult).push_back(num%basis);
 12:     num /= basis;
 13:   }
 14:   return *vecResult;
 15: }
 16: int main(void)
 17: {
 18:   int num;
 19:   while(cin>>num && num)
 20:   {
 21:     set<int> s;
 22:     for(int i = 2; i <= 16;i++)
 23:     {
 24:       vector<int> temp1 = transfor(num, i);
 25:       vector<int> temp2(temp1);
 26:       reverse(temp2.begin(), temp2.end());
 27:       if(temp1 == temp2)
 28:       {
 29:         s.insert(i);
 30:       }
 31:         
 32:     }
 33:     if(s.size() > 0)
 34:     {
 35:       cout<<"Number "<<num<<" is palindrom in basis";
 36:       for(set<int>::iterator it = s.begin(); it != s.end(); it++)
 37:         cout<<" "<<*it;
 38:       cout<<endl;
 39:     }
 40:     else
 41:     {
 42:       cout<<"Number "<<num<<" is not a palindrom"<<endl;
 43:     }
 44:   }
 45:   return 0;
 46: }