# Generate all palindromic numbers less than n

Find all numbers less than n, which are palindromic. Numbers can be printed in any order.

Examples:

```Input : n = 12
Output : 1, 2, 3, 4, 5, 6, 7, 8, 9, 11

Input : n = 104
Output : 1, 2, 3, 4, 5, 6, 7, 8, 9, 11,
22, 33, 44, 55, 66, 77, 88, 99, 101
[Note that below program prints these numbers
in different order]
```

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

Brute Force: We check all the numbers from 1 to n whether its decimal representation is palindrome or not.

Efficient Approach: We start from 1 and create palindromes of odd digit and even digits up to n. For every number (starting from 1), we append its reverse at end if we need even length palindrome numbers. For odd length palindrome, we append reverse of all digits except last one.

## C/C++

```// A C++ program to generate palindromic numbers
// less than n.
#include <iostream>
using namespace std;

// A utility for creating palindrome
int createPalindrome(int input, int b, bool isOdd)
{
int n = input;
int palin = input;

// checks if number of digits is odd or even
// if odd then neglect the last digit of input in
// finding reverse as in case of odd number of
// digits middle element occur once
if (isOdd)
n /= b;

// Creates palindrome by just appending reverse
// of number to itself
while (n > 0)
{
palin = palin * b + (n % b);
n /= b;
}
return palin;
}

// Fruition to print decimal palindromic number
void generatePaldindromes(int n)
{
int number;

// Run two times for odd and even length palindromes
for (int j = 0; j < 2; j++)
{
// Creates palindrome numbers with first half as i.
// Value of j decided whether we need an odd length
// of even length palindrome.
int i = 1;
while ((number = createPalindrome(i, 10, j % 2)) < n)
{
cout << number << " ";
i++;
}
}
}

// Driver Program to test above function
int main()
{
int n = 104;
generatePaldindromes(n);
return 0;
}
```

## Python

```# Generate all palindromic numbers less than n
# A Python program to generate palindromic numbers
# less than n.
def createPalindrome(inp, b, isOdd):
n = inp
palin = inp

# checks if number of digits is odd or even
# if odd then neglect the last digit of input in
# finding reverse as in case of odd number of
# digits middle element occur once
if (isOdd):
n = n / b

# Creates palindrome by just appending reverse
# of number to itself
while (n > 0):
palin = palin * b + (n % b)
n = n / b
return palin

# Function to print decimal palindromic number
def generatePaldindromes(n):

# Run two times for odd and even length palindromes
for j in range(2):
# Creates palindrome numbers with first half as i.
# Value of j decided whether we need an odd length
# of even length palindrome.
i = 1
while (createPalindrome(i, 10, j % 2) < n):
print createPalindrome(i, 10, j % 2),
i = i + 1

# Driver Program to test above function
n = 104
generatePaldindromes(n)

#This code is contributed by Afzal Ansari
```

Output:

```1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 101
22, 33, 44, 55, 66, 77, 88, 99,
```

Note that the above program doesn’t print output in sorted order. To print in sorted order, we can store palindromes in a vector and store it.

# GATE CS Corner    Company Wise Coding Practice

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