USACO Training>My Training>Section 1.2>Dual Palindromes

Dual Palindromes

Mario Cruz (Colombia) & Hugo Rickeboer (Argentina)

A number that reads the same from right to left as when read from left to right is called a palindrome. The number 12321 is a palindrome; the number 77778 is not. Of course, palindromes have neither leading nor trailing zeroes, so 0220 is not a palindrome.

The number 21 (base 10) is not palindrome in base 10, but the number 21 (base 10) is, in fact, a palindrome in base 2 (10101).

Write a program that reads two numbers (expressed in base 10):

  • N (1 <= N <= 15)
  • S (0 < S < 10000)
and then finds and prints (in base 10) the first N numbers strictly greater than S that are palindromic when written in two or more number bases (2 <= base <= 10).

Solutions to this problem do not require manipulating integers larger than the standard 32 bits.

PROGRAM NAME: dualpal

INPUT FORMAT
A single line with space separated integers N and S.

SAMPLE INPUT (file dualpal.in) 

3 25

OUTPUT FORMAT
N lines, each with a base 10 number that is palindromic when expressed in at least two of the bases 2..10. The numbers should be listed in order from smallest to largest.

SAMPLE OUTPUT (file dualpal.out)

26
27
28

Solution (Me)


/*
ID: sgospod1
PROG: dualpal
LANG: C++
*/
#include <stdio.h>
#include <string.h> 
#include <assert.h>
#include <iostream>
#include <fstream>

#define STANDARD_INPUT

#define MIN_NUM 0
#define MAX_NUM 10000
#define MIN_BASE 2
#define MAX_BASE 10
#define REQUIRED_PAL 2 

using namespace std;

char str[10];

char* itoa(int num, char *str, int base)
{
    int len;

    if(num == 0) {
        strcpy(str, "");
        return str;
    }

    itoa(num/base, str, base);

    len = strlen(str);
    str[len] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"[num%base];
    str[len+1] = '\0';
    return str;
}

bool IsPalindrome(int num, int base)
{
    itoa(num, str, base);
    int len = strlen(str);
    int i,j;
    for(i=0, j=len-1; i<=len/2; i++, j--)
        if(str[i]!=str[j]) break;
    i--;
    return i==len/2;
}

        

int main()
{

#ifdef STANDARD_INPUT
    std::istream &fin = cin;
    std::ostream &fout = cout;
#else
    std::ofstream fout ("dualpal.out");
    std::ifstream fin ("dualpal.in");
#endif
    assert(fin != NULL && fout != NULL);

    int N; /* 2<=N<=15 */
    int S; /* 0<= S <=10000*/

    fin >> N;
    assert(N>=2 && N<=15);
    fin >> S;
    assert(S>=0 && S<=10000);

    int ncount =0;
    int n = S+1;
    while(ncount<N)
    { 
        int pcount = 0;
        for(int b=MIN_BASE; b<=MAX_BASE; b++)
        {
            if(IsPalindrome(n,b)) pcount++;
            if(pcount>=REQUIRED_PAL) break;            
        }
        if(pcount>=REQUIRED_PAL)
        {
            fout << n <<endl;
            ncount++;
        }
        n++;
    }
    return 0;
}

All solutions

Tests
Input Output