Count numbers from a given range that can be expressed as sum of digits raised to the power of count of digits
Given an array arr[] consisting of queries of the form {L, R}, the task for each query is to count the numbers in the range [L, R] that can be expressed as the sum of its digits raised to the power of count of digits.
Examples:
Input: arr[][] = {{8, 11}}
Output: 2
Explanation:
From the given range [1, 9], the numbers that can be expressed as the sum of its digit raised to the power of count of digits are:
- 8: Sum of digits = 8, Count of digit = 1. Therefore, 81 is equal to the given number.
- 9: Sum of digits = 9, Count of digit = 1. Therefore, 91 is equal to the given number.
Therefore, the count of such numbers from the given range is 2.
Input: arr[][] = {{10, 100}, {1, 400}}
Output: 0 11
Naive Approach: The simplest approach is to iterate over the range arr[i][0] to arr[i][1] for each query and print the count of such numbers.
Time Complexity: O(Q*(R – L)*log10R), where R and L denote the limits of the longest range.
Auxiliary Space: O(1)
Efficient Approach: The above approach can be optimized by precomputing and storing all the numbers whether they can be expressed as the sum of its digit raised to the power of count of digits or not. Finally, print the count for each query efficiently.
Follow the steps below to solve the problem:
- Initialize an auxiliary array, say ans[], to store at ans[i], whether i can be expressed as the sum of its digit raised to the power of count of digits.
- Iterate over the range [1, 106] and update the array ans[] accordingly.
- Convert the array ans[] to a prefix sum array.
- Traverse the given array of queries arr[] and for each query {arr[i][0], arr[i][1]}, print the value of (ans[arr[i][1]] – ans[arr[i][1] – 1]) as the resultant count of numbers that can be expressed as the sum of its digit raised to the power of count of digits.
Below is the implementation of the above approach:
C++
// C++ program for the above approach #include <bits/stdc++.h> using namespace std; #define R 100005 int arr[R]; // Function to check if a number N can be // expressed as sum of its digits raised // to the power of the count of digits bool canExpress( int N) { int temp = N; // Stores the number of digits int n = 0; while (N != 0) { N /= 10; n++; } // Stores the resultant number N = temp; int sum = 0; while (N != 0) { sum += pow (N % 10, n); N /= 10; } // Return true if both the // numbers are same return (sum == temp); } // Function to precompute and store // for all numbers whether they can // be expressed void precompute() { // Mark all the index which // are plus perfect number for ( int i = 1; i < R; i++) { // If true, then update the // value at this index if (canExpress(i)) { arr[i] = 1; } } // Compute prefix sum of the array for ( int i = 1; i < R; i++) { arr[i] += arr[i - 1]; } } // Function to count array elements that // can be expressed as the sum of digits // raised to the power of count of digits void countNumbers( int queries[][2], int N) { // Precompute the results precompute(); // Traverse the queries for ( int i = 0; i < N; i++) { int L1 = queries[i][0]; int R1 = queries[i][1]; // Print the resultant count cout << (arr[R1] - arr[L1 - 1]) << ' ' ; } } // Driver Code int main() { int queries[][2] = { { 1, 400 }, { 1, 9 } }; int N = sizeof (queries) / sizeof (queries[0]); countNumbers(queries, N); return 0; } |
Java
// Java program for the above approach import java.util.*; import java.io.*; class GFG{ static int R = 100005 ; static int [] arr = new int [R]; // Function to check if a number N can be // expressed as sum of its digits raised // to the power of the count of digits public static boolean canExpress( int N) { int temp = N; // Stores the number of digits int n = 0 ; while (N != 0 ) { N /= 10 ; n++; } // Stores the resultant number N = temp; int sum = 0 ; while (N != 0 ) { sum += (( int )Math.pow(N % 10 , n)); N /= 10 ; } // Return true if both the // numbers are same if (sum == temp) return true ; return false ; } // Function to precompute and store // for all numbers whether they can // be expressed public static void precompute() { // Mark all the index which // are plus perfect number for ( int i = 1 ; i < R; i++) { // If true, then update the // value at this index if (canExpress(i)) { arr[i] = 1 ; } } // Compute prefix sum of the array for ( int i = 1 ; i < R; i++) { arr[i] += arr[i - 1 ]; } } // Function to count array elements that // can be expressed as the sum of digits // raised to the power of count of digits public static void countNumbers( int [][] queries, int N) { // Precompute the results precompute(); // Traverse the queries for ( int i = 0 ; i < N; i++) { int L1 = queries[i][ 0 ]; int R1 = queries[i][ 1 ]; // Print the resultant count System.out.print((arr[R1] - arr[L1 - 1 ]) + " " ); } } // Driver Code public static void main(String args[]) { int [][] queries = { { 1 , 400 }, { 1 , 9 } }; int N = queries.length; // Function call countNumbers(queries, N); } } // This code is contributed by zack_aayush |
Python3
# Python 3 program for the above approach R = 100005 arr = [ 0 for i in range (R)] # Function to check if a number N can be # expressed as sum of its digits raised # to the power of the count of digits def canExpress(N): temp = N # Stores the number of digits n = 0 while (N ! = 0 ): N / / = 10 n + = 1 # Stores the resultant number N = temp sum = 0 while (N ! = 0 ): sum + = pow (N % 10 , n) N / / = 10 # Return true if both the # numbers are same return ( sum = = temp) # Function to precompute and store # for all numbers whether they can # be expressed def precompute(): # Mark all the index which # are plus perfect number for i in range ( 1 , R, 1 ): # If true, then update the # value at this index if (canExpress(i)): arr[i] = 1 # Compute prefix sum of the array for i in range ( 1 ,R, 1 ): arr[i] + = arr[i - 1 ] # Function to count array elements that # can be expressed as the sum of digits # raised to the power of count of digits def countNumbers(queries, N): # Precompute the results precompute() # Traverse the queries for i in range (N): L1 = queries[i][ 0 ] R1 = queries[i][ 1 ] # Print the resultant count print ((arr[R1] - arr[L1 - 1 ]),end = " " ) # Driver Code if __name__ = = '__main__' : queries = [[ 1 , 400 ],[ 1 , 9 ]] N = len (queries) countNumbers(queries, N) # This code is contributed by SURENDRA_GANGWAR. |
C#
// C# program for the above approach using System; class GFG{ static int R = 100005; static int [] arr = new int [R]; // Function to check if a number N can be // expressed as sum of its digits raised // to the power of the count of digits public static bool canExpress( int N) { int temp = N; // Stores the number of digits int n = 0; while (N != 0) { N /= 10; n++; } // Stores the resultant number N = temp; int sum = 0; while (N != 0) { sum += (( int )Math.Pow(N % 10, n)); N /= 10; } // Return true if both the // numbers are same if (sum == temp) return true ; return false ; } // Function to precompute and store // for all numbers whether they can // be expressed public static void precompute() { // Mark all the index which // are plus perfect number for ( int i = 1; i < R; i++) { // If true, then update the // value at this index if (canExpress(i)) { arr[i] = 1; } } // Compute prefix sum of the array for ( int i = 1; i < R; i++) { arr[i] += arr[i - 1]; } } // Function to count array elements that // can be expressed as the sum of digits // raised to the power of count of digits public static void countNumbers( int [,] queries, int N) { // Precompute the results precompute(); // Traverse the queries for ( int i = 0; i < N; i++) { int L1 = queries[i, 0]; int R1 = queries[i, 1]; // Print the resultant count Console.Write((arr[R1] - arr[L1 - 1]) + " " ); } } // Driver Code static public void Main() { int [,] queries = { { 1, 400 }, { 1, 9 } }; int N = queries.GetLength(0); // Function call countNumbers(queries, N); } } // This code is contributed by Dharanendra L V. |
Javascript
<script> // javascript program for the above approach var R = 100005; var arr = Array(R).fill(0); // Function to check if a number N can be // expressed as sum of its digits raised // to the power of the count of digits function canExpress(N) { var temp = N; // Stores the number of digits var n = 0; while (N != 0) { N = parseInt(N/10); n++; } // Stores the resultant number N = temp; var sum = 0; while (N != 0) { sum += Math.pow(N % 10, n); N = parseInt(N/10); } // Return true if both the // numbers are same return (sum == temp); } // Function to precompute and store // for all numbers whether they can // be expressed function precompute() { // Mark all the index which // are plus perfect number for ( var i = 1; i < R; i++) { // If true, then update the // value at this index if (canExpress(i)) { arr[i] = 1; } } // Compute prefix sum of the array for ( var i = 1; i < R; i++) { arr[i] += arr[i - 1]; } } // Function to count array elements that // can be expressed as the sum of digits // raised to the power of count of digits function countNumbers(queries , N) { // Precompute the results precompute(); // Traverse the queries for ( var i = 0; i < N; i++) { var L1 = queries[i][0]; var R1 = queries[i][1]; // Print the resultant count document.write((arr[R1] - arr[L1 - 1]) + " " ); } } // Driver Code var queries = [ [ 1, 400 ], [ 1, 9 ] ]; var N = queries.length; // function call countNumbers(queries, N); // This code is contributed by Princi Singh </script> |
12 9
Time Complexity: O(Q + 106)
Auxiliary Space: O(106)