Palindromic gapful numbers | Rosetta Code | #19

URL to the problem page: http://rosettacode.org/wiki/Palindromic_gapful_numbers


Numbers that are (evenly) divisible by the number formed by the first and last digit are known as gapful numbers.

Evenly divisible means divisible with no remainder.

All one─ and two─digit numbers have this property and are trivially excluded. Only numbers ≥ 100 will be considered for this Rosetta Code task.


      Example

1037 is a gapful number because it is evenly divisible by the number 17 which is formed by the first and last decimal digits of 1037.

A palindromic number, when the number is reversed, is the same as the original number.


Show (nine sets) the first 20 palindromic gapful numbers that end with:

• the digit 1
• the digit 2
• the digit 3
• ··· ···
• the digit 9

#include <iostream>

using namespace std;

int finddigits(int a) {

    int cnt = 1;

    while (a >= 10) {

        a /= 10;

        cnt++;

    }

    return cnt;

}

int power(int a, int b) {

    int result = 1;

    for (int i = 0; i < b; i++) {

        result *= a;

    }

    return result;

}

int main() {

    int cnt = 1, cnt2, digitnumber, divisor, numbers[9][20], a[9] = { 0 };

    for (int i = 100; cnt <= 180; i++) {

        cnt2 = 0;

        digitnumber = finddigits(i);

        int* digits = new int[digitnumber];

        for (int j = 0; j < digitnumber; j++) {

            digits[j] = (i % power(10, j + 1) / power(10, j));

        }

        divisor = (digits[digitnumber - 1] * 10) + digits[0];

        if (i % divisor == 0) {

            for (int j = 0, k = digitnumber - 1; j < (digitnumber / 2), k >= (digitnumber + 1) / 2; j++, k--) {

                if (digits[j] != digits[k]) {

                    cnt2++;

                    break;

                }

            }

            if (cnt2 == 0) {

                if (a[digits[0] - 1] < 20) {

                    numbers[digits[0] - 1][a[digits[0] - 1]] = i;

                    a[digits[0] - 1]++;

                    cnt++;

                }

            }

        }

    }

    for (int i = 0; i < 9; i++) {

        cout << "First 20 palindromic gapful numbers that end with " << i + 1 << " are:" << endl << endl;

        for (int j = 0; j < 20; j++) {

            cout << numbers[i][j] << ", ";

        }

        cout << endl << endl << endl;

    }

}

CLICK TO SEE THE OUTPUT.