Given an integer N, the task is to find the maximum difference after applying the given operation two times on the given integer.
The operation is defined as follows:
- Choose any digit (0-9) from N and replace all instance of the same digit with any other digit (0-9).
- N after the operation cannot have leading zeros and also it cannot be equal to zero.
Examples:
Input : N = 777
Output : 888
Explanation: Select digit 7 and replace all it’s occurrences with 9 to get 999. similarly 111 can be obtained by replacing all occurrences of 7 with 1. Hence, the possible maximum difference is 888.Input : N = 123456
Output : 820000
The numbers after two operation can be 923456 and 103456. Hence, the required maximum difference is 820000.
Explanation: Maximum difference can be obtained by subtraction of the maximum and the minimum number that can be obtained by the given operation on N.
- The maximum number can be obtained by picking the first digit of N from the left which is not equal to ‘9’ and replace all the instances of that digit into ‘9’.
- Finding the minimum number is a little bit tricky as N cannot have any leading zeros and also it cannot be equal to zero. If the first digit of N from the left is ‘1’, then find the first digit from the left which is greater than ‘1’ and replace all instances of that digit with ‘0’.
- Otherwise, if the first digit of N from the left is not equal to ‘1’, then choose that digit and replace all instances of that digit with ‘1’.
- Finally, return the difference between the minimum and maximum number as the answer.
Below is the implementation of the above approach:
C++
// C++ program to find the// maximum difference// after two given operations// on a number#include <bits/stdc++.h>using namespace std;// Function that returns the// maximum difference// after two given operations// on a numberint minDifference(int num){ // Initialize the strings to make operations string maximum = to_string(num); string minimum = to_string(num); // Store length of the string int n = maximum.size(); // Make the maximum number using // the first operation for (int i = 0; i < n; i++) { // Find the first digit which // is not equal to '9' if (maximum[i] != '9') { // Store the digit for // the given operation char digit = maximum[i]; for (int j = i; j < n; j++) { // Replace all the selected // 'digit' with '9' if (maximum[j] == digit) maximum[j] = '9'; } // Break after the operation // is completed break; } } // Make the minimum number using // the second operation // Check if first digit is equal to '1' if (minimum[0] == '1') { for (int i = 1; i < n; i++) { // Find the first digit which // is greater than '1' if (minimum[i] - '0' > 1) { // Store the digit for // the given operation char digit = minimum[i]; for (int j = i; j < n; j++) { // Replace all the selected // 'digit' with '0' if (digit == minimum[j]) minimum[j] = '0'; } // Break after the // operation is completed break; } } } else { // Select the first digit for // the given operation char digit = minimum[0]; for (int i = 0; i < n; i++) { // Replace all the selected // 'digit' with '1' if (minimum[i] == digit) minimum[i] = '1'; } } // Return the difference after // converting into integers return (stoi(maximum) - stoi(minimum));}// Driver Codeint main(){ int N = 1101157; cout << minDifference(N); return 0;} |
Java
// Java program to find the maximum // difference after two given operations// on a numberimport java.util.*;class GFG{// Function that returns the// maximum difference// after two given operations// on a numberstatic int minDifference(int num){ // Initialize the strings to make operations StringBuilder maximum = new StringBuilder(Integer.toString(num)); StringBuilder minimum = new StringBuilder(Integer.toString(num)); // Store length of the string int n = maximum.length(); // Make the maximum number using // the first operation for(int i = 0; i < n; i++) { // Find the first digit which // is not equal to '9' if (maximum.charAt(i) != '9') { // Store the digit for // the given operation char digit = maximum.charAt(i); for(int j = i; j < n; j++) { // Replace all the selected // 'digit' with '9' if (maximum.charAt(j) == digit) maximum.setCharAt(j, '9'); } // Break after the operation // is completed break; } } // Make the minimum number // using the second operation // Check if first digit is equal to '1' if (minimum.charAt(0) == '1') { for(int i = 1; i < n; i++) { // Find the first digit which // is greater than '1' if (minimum.charAt(i) - '0' > 1) { // Store the digit for // the given operation char digit = minimum.charAt(i); for(int j = i; j < n; j++) { // Replace all the selected // 'digit' with '0' if (digit == minimum.charAt(j)) minimum.setCharAt(j, '0'); } // Break after the // operation is completed break; } } } else { // Select the first digit for // the given operation char digit = minimum.charAt(0); for(int i = 0; i < n; i++) { // Replace all the selected // 'digit' with '1' if (minimum.charAt(i) == digit) minimum.setCharAt(i, '1'); } } // Return the difference after // converting into integers return (Integer.parseInt(maximum.toString()) - Integer.parseInt(minimum.toString()));}// Driver codepublic static void main(String[] args){ int N = 1101157; System.out.println(minDifference(N));}}// This code is contributed by offbeat |
Python3
# Python3 program to find the # maximum difference after # two given operations # on a number # Function that returns the # maximum difference after # two given operations # on a number def minDifference(num): # Initialize the strings to # make operations maximum = list(str(num)); minimum = list(str(num)); # Store length of the string n = len(maximum); # Make the maximum number using # the first operation for i in range(n): # Find the first digit which # is not equal to '9' if (maximum[i] != '9'): # Store the digit for # the given operation digit = maximum[i]; for j in range(i, n): # Replace all the selected # 'digit' with '9' if (maximum[j] == digit): maximum[j] = '9'; # Break after the operation # is completed break; # Make the minimum number using # the second operation # Check if first digit is equal to '1' if (minimum[0] == '1'): for i in range(1, n): # Find the first digit which # is greater than '1' if (ord(minimum[i]) - ord('0') > 1): # Store the digit for # the given operation digit = minimum[i]; for j in range(i, n): # Replace all the selected # 'digit' with '0' if (digit == minimum[j]): minimum[j] = '0'; # Break after the # operation is completed break; else : # Select the first digit # for the given operation digit = minimum[0]; for i in range(n): # Replace all the selected # 'digit' with '1' if (minimum[i] == digit): minimum[i] = '1'; maximum = "".join(maximum) minimum = "".join(minimum) # Return the difference after # converting into integers return (int(maximum) - int(minimum)); # Driver Code if __name__ == "__main__": N = 1101157; print(minDifference(N)); # This code is contributed by AnkitRai01 |
C#
// C# program to find the maximum// difference after two given // operations on a number using System;using System.Collections.Generic; class GFG{ // Function that returns the // maximum difference after // two given operations on a // number static int minDifference(int num) { // Initialize the strings to make operations char[] maximum = (num.ToString()).ToCharArray(); char[] minimum = (num.ToString()).ToCharArray(); // Store length of the string int n = maximum.Length; // Make the maximum number using // the first operation for(int i = 0; i < n; i++) { // Find the first digit which // is not equal to '9' if (maximum[i] != '9') { // Store the digit for // the given operation char digit = maximum[i]; for(int j = i; j < n; j++) { // Replace all the selected // 'digit' with '9' if (maximum[j] == digit) maximum[j] = '9'; } // Break after the operation // is completed break; } } // Make the minimum number using // the second operation // Check if first digit is equal to '1' if (minimum[0] == '1') { for(int i = 1; i < n; i++) { // Find the first digit which // is greater than '1' if (minimum[i] - '0' > 1) { // Store the digit for // the given operation char digit = minimum[i]; for(int j = i; j < n; j++) { // Replace all the selected // 'digit' with '0' if (digit == minimum[j]) minimum[j] = '0'; } // Break after the // operation is completed break; } } } else { // Select the first digit for // the given operation char digit = minimum[0]; for(int i = 0; i < n; i++) { // Replace all the selected // 'digit' with '1' if (minimum[i] == digit) minimum[i] = '1'; } } // Return the difference after // converting into integers return Convert.ToInt32(string.Join("", maximum)) - Convert.ToInt32(string.Join("", minimum));} // Driver Codestatic void Main(){ int N = 1101157; Console.Write(minDifference(N)); }}// This code is contributed by divyesh072019 |
Javascript
<script>// Javascript program to find the maximum// difference after two given// operations on a number// Function that returns the// maximum difference after// two given operations on a// numberfunction minDifference(num){ // Initialize the strings to make operations let maximum = (num.toString()).split(''); let minimum = (num.toString()).split(''); // Store length of the string let n = maximum.length; // Make the maximum number using // the first operation for(let i = 0; i < n; i++) { // Find the first digit which // is not equal to '9' if (maximum[i] != '9') { // Store the digit for // the given operation let digit = maximum[i]; for(let j = i; j < n; j++) { // Replace all the selected // 'digit' with '9' if (maximum[j] == digit) maximum[j] = '9'; } // Break after the operation // is completed break; } } // Make the minimum number using // the second operation // Check if first digit is equal to '1' if (minimum[0] == '1') { for(let i = 1; i < n; i++) { // Find the first digit which // is greater than '1' if (minimum[i].charCodeAt() - '0'.charCodeAt() > 1) { // Store the digit for // the given operation let digit = minimum[i]; for(let j = i; j < n; j++) { // Replace all the selected // 'digit' with '0' if (digit == minimum[j]) minimum[j] = '0'; } // Break after the // operation is completed break; } } } else { // Select the first digit for // the given operation let digit = minimum[0]; for(let i = 0; i < n; i++) { // Replace all the selected // 'digit' with '1' if (minimum[i] == digit) minimum[i] = '1'; } } // Return the difference after // converting into integers return parseInt(maximum.join("")) - parseInt(minimum.join(""));}// Driver codelet N = 1101157; document.write(minDifference(N));// This code is contributed by suresh07</script> |
Output:
8808850
Time complexity: O((LogN)2), where N is the input number.
Space complexity: O(LogN)
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