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# Sum of all palindromic numbers lying in the range [L, R] for Q queries

• Last Updated : 05 Apr, 2021

Given Q queries in the form of 2D array arr[][] whose every row consists of two numbers L and R which denotes the range [L, R], the task is to find the sum of all Palindrome Numbers lying in range [L, R].

Input: Q = 2, arr[][] = { {10, 13}, {12, 21} }
Output:
11

Explanation:
From 10 to 13 only 11 is the palindrome number
From 12 to 21 there is no palindromic number
Input: Q = 4, arr[][] = { { 10, 10 }, { 258, 785 }, {45, 245 }, { 1, 1000} }
Output:

27024
2955
50040

Approach:
The idea is to use the prefix sum array. The sum of all palindromic number till that particular index is precomputed and stored in an array pref[] so that every query can be answered in O(1) time.

1. Initialise the prefix array pref[].
2. Iterate from 1 to N and check if the number is palindromic or not:
• If the number is palindromic then, the current index of pref[] will store the sum of the number and the number at previous index of pref[].
• Else the current index of pref[] is same as the value at previous index of pref[].
3. For Q queries the sum of all palindromic numbers for range [L, R] can be found as follows:

sum = pref[R] - pref[L - 1]
1.

Below is the implementation of the above approach

## C++

 // C++ program to find the sum// of all palindrome numbers// in the given range#include using namespace std; // pref[] array to precompute// the sum of all palindromic// numberlong long pref[100001]; // Function that return number// num if num is palindromic// else return 0int checkPalindrome(int num){     // Convert num to string    string str = to_string(num);     int l = 0, r = str.length() - 1;     while (l < r) {        if (str[l] != str[r]) {            return 0;        }        l++;        r--;    }    return num;} // Function to precompute the// sum of all palindrome numbers// upto 100000void preCompute(){    for (int i = 1; i <= 100000; ++i) {         // checkPalindrome()        // return the number i        // if i is palindromic        // else return 0        pref[i] = pref[i - 1]                  + checkPalindrome(i);    }} // Function to print the sum// for each queryvoid printSum(int L, int R){    cout << pref[R] - pref[L - 1]         << endl;} // Function to print sum of all// palindromic numbers between// [L, R]void printSumPalindromic(int arr[][2],                         int Q){     // Function that pre computes    // the sum of all palindromic    // numbers    preCompute();     // Iterate over all Queries    // to print the sum    for (int i = 0; i < Q; i++) {        printSum(arr[i][0], arr[i][1]);    }} // Driver codeint main(){    // Queries    int Q = 2;    int arr[][2] = { { 10, 13 },                     { 12, 21 } };     // Function that print the    // the sum of all palindromic    // number in Range [L, R]    printSumPalindromic(arr, Q);    return 0;}

## Java

 // Java program to find the sum// of all palindrome numbers// in the given rangeimport java.util.*; class GFG{  // pref[] array to precompute// the sum of all palindromic// numberstatic int []pref = new int[100001];  // Function that return number// num if num is palindromic// else return 0static int checkPalindrome(int num){      // Convert num to String    String str = String.valueOf(num);      int l = 0, r = str.length() - 1;      while (l < r) {        if (str.charAt(l) != str.charAt(r)) {            return 0;        }        l++;        r--;    }    return num;}  // Function to precompute the// sum of all palindrome numbers// upto 100000static void preCompute(){    for (int i = 1; i <= 100000; ++i) {          // checkPalindrome()        // return the number i        // if i is palindromic        // else return 0        pref[i] = pref[i - 1]                  + checkPalindrome(i);    }}  // Function to print the sum// for each querystatic void printSum(int L, int R){    System.out.print(pref[R] - pref[L - 1]         +"\n");}  // Function to print sum of all// palindromic numbers between// [L, R]static void printSumPalindromic(int arr[][],                         int Q){      // Function that pre computes    // the sum of all palindromic    // numbers    preCompute();      // Iterate over all Queries    // to print the sum    for (int i = 0; i < Q; i++) {        printSum(arr[i][0], arr[i][1]);    }}  // Driver codepublic static void main(String[] args){    // Queries    int Q = 2;    int arr[][] = { { 10, 13 },                     { 12, 21 } };      // Function that print the    // the sum of all palindromic    // number in Range [L, R]    printSumPalindromic(arr, Q);}} // This code is contributed by 29AjayKumar

## Python3

 # Python3 program to find the sum# of all palindrome numbers# in the given range # pref[] array to precompute# the sum of all palindromic# numberpref=[0]*100001 # Function that return number# num if num is palindromic# else return 0def checkPalindrome(num):         # Convert num to string    strr = str(num)    l = 0    r = len(strr)- 1    while (l < r):        if (strr[l] != strr[r]):            return 0                     l+=1        r-=1         return num  # Function to precompute the# sum of all palindrome numbers# upto 100000def preCompute():    for i in range(1,100001):        # checkPalindrome()        # return the number i        # if i is palindromic        # else return 0        pref[i] = pref[i - 1]+ checkPalindrome(i)       # Function to print the sum# for each querydef printSum(L, R):    print(pref[R] - pref[L - 1])  # Function to prsum of all# palindromic numbers between# [L, R]def printSumPalindromic(arr,Q):         # Function that pre computes    # the sum of all palindromic    # numbers    preCompute()         # Iterate over all Queries    # to print the sum    for i in range(Q):        printSum(arr[i][0], arr[i][1])       # Driver code # QueriesQ = 2arr= [[10, 13 ],[ 12, 21 ]] # Function that print the# the sum of all palindromic# number in Range [L, R]printSumPalindromic(arr, Q) # This code is contributed by shivanisinghss2110

## C#

 // C# program to find the sum// of all palindrome numbers// in the given rangeusing System; class GFG{   // pref[] array to precompute// the sum of all palindromic// numberstatic int []pref = new int[100001];   // Function that return number// num if num is palindromic// else return 0static int checkPalindrome(int num){       // Convert num to String    String str = String.Join("",num);       int l = 0, r = str.Length - 1;       while (l < r) {        if (str[l] != str[r]) {            return 0;        }        l++;        r--;    }    return num;}   // Function to precompute the// sum of all palindrome numbers// upto 100000static void preCompute(){    for (int i = 1; i <= 100000; ++i) {           // checkPalindrome()        // return the number i        // if i is palindromic        // else return 0        pref[i] = pref[i - 1]                  + checkPalindrome(i);    }}   // Function to print the sum// for each querystatic void printSum(int L, int R){    Console.Write(pref[R] - pref[L - 1]         +"\n");}   // Function to print sum of all// palindromic numbers between// [L, R]static void printSumPalindromic(int [,]arr,                         int Q){       // Function that pre computes    // the sum of all palindromic    // numbers    preCompute();       // Iterate over all Queries    // to print the sum    for (int i = 0; i < Q; i++) {        printSum(arr[i,0], arr[i,1]);    }}   // Driver codepublic static void Main(String[] args){    // Queries    int Q = 2;    int [,]arr = { { 10, 13 },                     { 12, 21 } };       // Function that print the    // the sum of all palindromic    // number in Range [L, R]    printSumPalindromic(arr, Q);}} // This code is contributed by PrinciRaj1992

## Javascript


Output:
11
0

Time Complexity: O(N)

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