Sum of all palindromic numbers lying in the range [L, R] for Q queries
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; } |
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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 |
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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 = 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 |
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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 |
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Output:
11 0
Time Complexity: O(N)
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