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Sum of all odd length palindromic numbers within the range [L, R]
  • Difficulty Level : Hard
  • Last Updated : 14 Oct, 2019

Given two integers L and R, the task is to find the sum of all the palindromic numbers within the range [L, R] which are of odd length.

Examples:

Input: L = 10, R = 130
Output: 333
101 + 111 + 121 = 333

Input: L = 110, R = 1130
Output: 49399

Approach: Iterate from L to R and for every number check whether it is a palindrome and of odd length. If yes then add it to the sum. Finally print the value of the sum in the end.



Below is the implementation of the above approach:

C




// C program to find the sum of all odd length
// palindromic numbers within the given range
#include <stdbool.h>
#include <stdio.h>
  
// Function that returns true if
// the given number is a palindrome
bool isPalindrome(int num)
{
    int reverse_num = 0, remainder, temp;
  
    /* Here we are generating a new number (reverse_num)
     * by reversing the digits of original input number
     */
    temp = num;
    while (temp != 0) {
        remainder = temp % 10;
        reverse_num = reverse_num * 10 + remainder;
        temp /= 10;
    }
  
    /* If the original input number (num) is equal to
     * to its reverse (reverse_num) then its palindrome
     * else it is not.
     */
    if (reverse_num == num) {
        return true;
    }
  
    return false;
}
  
// Function that returns true if the
// given number is of odd length
bool isOddLength(int num)
{
    int count = 0;
    while (num > 0) {
        num /= 10;
        count++;
    }
    if (count % 2 != 0) {
        return true;
    }
    return false;
}
  
// Function to return the sum of all odd length
// palindromic numbers within the given range
long sumOfAllPalindrome(int L, int R)
{
    long sum = 0;
    if (L <= R)
        for (int i = L; i <= R; i++) {
  
            // if number is palindrome and of odd length
            if (isPalindrome(i) && isOddLength(i)) {
                sum += i;
            }
        }
    return sum;
}
  
// Driver code
int main()
{
    int L = 110, R = 1130;
    printf("%ld", sumOfAllPalindrome(L, R));
}

Java




// Java program to find the sum of all odd length
// palindromic numbers within the given range
  
class GFG {
  
    // Function that returns true if
    // the given number is a palindrome
    static boolean isPalindrome(int num)
    {
        int reverse_num = 0, remainder, temp;
  
        /* Here we are generating a new number (reverse_num)
    * by reversing the digits of original input number
         */
        temp = num;
        while (temp != 0) {
            remainder = temp % 10;
            reverse_num = reverse_num * 10 + remainder;
            temp /= 10;
        }
  
        /* If the original input number (num) is equal to
    * to its reverse (reverse_num) then its palindrome
    * else it is not.
         */
        if (reverse_num == num) {
            return true;
        }
  
        return false;
    }
  
    // Function that returns true if the
    // given number is of odd length
    static boolean isOddLength(int num)
    {
        int count = 0;
        while (num > 0) {
            num /= 10;
            count++;
        }
        if (count % 2 != 0) {
            return true;
        }
        return false;
    }
  
    // Function to return the sum of all odd length
    // palindromic numbers within the given range
    static long sumOfAllPalindrome(int L, int R)
    {
        long sum = 0;
        if (L <= R)
            for (int i = L; i <= R; i++) {
  
                // if number is palindrome and of odd length
                if (isPalindrome(i) && isOddLength(i)) {
                    sum += i;
                }
            }
        return sum;
    }
  
    // Driver code
    public static void main(String[] args)
    {
        int L = 110, R = 1130;
        System.out.println(sumOfAllPalindrome(L, R));
    }
}

Python3




# Python 3 program to find the sum of 
# all odd length palindromic numbers
# within the given range
  
# Function that returns true if
# the given number is a palindrome
def isPalindrome(num):
    reverse_num = 0
      
    # Here we are generating a new number 
    # (reverse_num) by reversing the digits 
    # of original input number
    temp = num
    while (temp != 0):
        remainder = temp % 10
        reverse_num = reverse_num * 10 + remainder
        temp = int(temp/10)
  
    # If the original input number (num) is 
    # equal to its reverse (reverse_num) then 
    # its palindrome else it is not.
    if (reverse_num == num):
        return True
  
    return False
  
# Function that returns true if the given 
# number is of odd length
def isOddLength(num):
    count = 0
    while (num > 0):
        num = int (num / 10)
        count += 1
  
    if (count % 2 != 0):
        return True
  
    return False
  
# Function to return the sum of all odd length
# palindromic numbers within the given range
def sumOfAllPalindrome(L, R):
    sum = 0
    if (L <= R):
        for i in range(L, R + 1, 1):
              
            # if number is palindrome and of 
            # odd length
            if (isPalindrome(i) and isOddLength(i)):
                sum += i
              
    return sum
  
# Driver code
if __name__ == '__main__':
    L = 110
    R = 1130
    print(sumOfAllPalindrome(L, R))
  
# This code is contributed by
# Shashank_Sharma

C#




// C# program to find the sum of all odd length
// palindromic numbers within the given range
using System;
  
public class GFG {
  
    // Function that returns true if
    // the given number is a palindrome
    static bool isPalindrome(int num)
    {
        int reverse_num = 0, remainder, temp;
  
        /* Here we are generating a new number (reverse_num)
    * by reversing the digits of original input number
        */
        temp = num;
        while (temp != 0) {
            remainder = temp % 10;
            reverse_num = reverse_num * 10 + remainder;
            temp /= 10;
        }
  
        /* If the original input number (num) is equal to
    * to its reverse (reverse_num) then its palindrome
    * else it is not.
        */
        if (reverse_num == num) {
            return true;
        }
  
        return false;
    }
  
    // Function that returns true if the
    // given number is of odd length
    static bool isOddLength(int num)
    {
        int count = 0;
        while (num > 0) {
            num /= 10;
            count++;
        }
        if (count % 2 != 0) {
            return true;
        }
        return false;
    }
  
    // Function to return the sum of all odd length
    // palindromic numbers within the given range
    static long sumOfAllPalindrome(int L, int R)
    {
        long sum = 0;
        if (L <= R)
            for (int i = L; i <= R; i++) {
  
                // if number is palindrome and of odd length
                if (isPalindrome(i) && isOddLength(i)) {
                    sum += i;
                }
            }
        return sum;
    }
  
    // Driver code
    public static void Main(String[] args)
    {
        int L = 110, R = 1130;
        Console.WriteLine(sumOfAllPalindrome(L, R));
    }
}

PHP




<?php
// PHP program to find the sum of x
// all odd length palindromic numbers 
// within the given range
  
// Function that returns true if
// the given number is a palindrome
function isPalindrome($num)
{
    $reverse_num = 0;
    $remainder;
    $temp;
  
    // Here we are generating a new number 
    // (reverse_num) by reversing the 
    // digits of original input number 
    $temp = $num;
    while ($temp != 0) 
    {
        $remainder = $temp % 10;
        $reverse_num = $reverse_num * 10 + 
                       $remainder;
        $temp = (int)($temp / 10);
    }
  
    // If the original input number (num) is
    // equal to its reverse (reverse_num) 
    // then its palindrome else it is not.
    if ($reverse_num == $num
    {
        return true;
    }
  
    return false;
}
  
// Function that returns true if the
// given number is of odd length
function isOddLength($num)
{
    $count = 0;
    while ($num > 0) 
    {
        $num = (int)($num / 10);
        $count++;
    }
    if ($count % 2 != 0) 
    {
        return true;
    }
    return false;
}
  
// Function to return the sum of 
// all odd length palindromic numbers 
// within the given range
function sumOfAllPalindrome($L, $R)
{
    $sum = 0;
    if ($L <= $R)
        for ($i = $L; $i <= $R; $i++) 
        {
  
            // if number is palindrome and 
            // of odd length
            if (isPalindrome($i) && isOddLength($i))
            {
                $sum += $i;
            }
        }
    return $sum;
}
  
// Driver code
$L = 110;
$R = 1130;
echo sumOfAllPalindrome($L, $R);
  
// This code is contributed by mits
?>
Output:
49399

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