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
0
Explanation:
From 10 to 13 only 11 is the palindrome number
From 12 to 21 there is no palindromic numberInput: Q = 4, arr[][] = { { 10, 10 }, { 258, 785 }, {45, 245 }, { 1, 1000} }
Output:
0
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.
- Initialise the prefix array pref[].
- 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[].
- For Q queries the sum of all palindromic numbers for range [L, R] can be found as follows:
sum = pref[R] - pref[L - 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 <bits/stdc++.h> using namespace std; // pref[] array to precompute // the sum of all palindromic // number long long pref[100001]; // Function that return number // num if num is palindromic // else return 0 int 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 100000 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 query void 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 code int 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 range import java.util.*; class GFG{ // pref[] array to precompute // the sum of all palindromic // number static int []pref = new int [ 100001 ]; // Function that return number // num if num is palindromic // else return 0 static 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 100000 static 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 query static 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 code public 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 # number pref = [ 0 ] * 100001 # Function that return number # num if num is palindromic # else return 0 def 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 100000 def 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 query def 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 # Queries Q = 2 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 shivanisinghss2110 |
C#
// C# program to find the sum // of all palindrome numbers // in the given range using System; class GFG{ // pref[] array to precompute // the sum of all palindromic // number static int []pref = new int [100001]; // Function that return number // num if num is palindromic // else return 0 static 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 100000 static 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 query static 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 code public 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 |
11 0
Time Complexity: O(N)
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