Minimize operations till a or b exceeds N by replacing a or b with their sum
Given three integers a, b, and N. The task is to find minimum addition operations between a and b, such that after applying the operations, either of a or b becomes greater than N. An addition operation is defined as replacing either of a or b with their sum and keeping another one intact.
Examples:
Input: a = 2, b = 3, N = 20
Output: 4
Explanation:
- Adding 2 and 3, 2 + 3 = 5 and replacing 2 with 5, now a = 5, b = 3
- Again add a and b 5 + 3 = 8 replace b with 8, now a = 5, b = 8
- Again add a and b 5 + 8 = 13 replace a with 13. now a = 13, b = 8
- Again add a and b 13 + 8 = 21 replace b with 21, now a = 13, b = 21 Here, (b>=n) therefore minimum operations required are 4
Input: a = 2, b = 3, N = 5
Output: 1
Explanation: After replacing 2 with 2+3, a becomes 5 and b becomes 3, therefore minimum operations required are 1
Approach: The idea is to add a and b and store their sum in the minimum of a and b, every time until any of the numbers is greater than N. Reason behind it is making the minimum element largest every time, makes their sum high and thereby reducing the number of operations required.
Below is the implementation of the above approach:
C++
// C++ program for the above approach #include <bits/stdc++.h> using namespace std; // Function to print the minimum number of operations // required int minOperations( int a, int b, int n) { // Store the count of operations int count = 0; while (1) { // If any value is greater than N return count if (n <= a or n <= b) { return count; break ; } else { int sum = a + b; if (a < b) a = sum; else b = sum; } count++; } return count; } // Driver code int main() { int p = 2, q = 3, n = 20; cout << minOperations(p, q, n) << "\n" ; return 0; } |
C
// C program for the above approach #include <stdio.h> // Function to print the minimum number of operations // required int minOperations( int a, int b, int n) { // Store the count of operations int count = 0; while (1) { // If any value is greater than N return count if (n <= a || n <= b) { return count; break ; } else { int sum = a + b; if (a < b) a = sum; else b = sum; } count++; } return count; } // Driver code int main() { int p = 2, q = 3, n = 20; printf ( "%d\n" , minOperations(p, q, n)); return 0; } // This code is contributed by Sania Kumari Gupta |
Java
// Java program for the above approach class GFG { // Function to print the minimum number // of operations required public static int minOperations( int a, int b, int n) { // Store the count of operations int count = 0 ; while ( true ) { // If any value is greater than N // return count if (n <= a || n <= b) { return count; } else { int sum = a + b; if (a < b) a = sum; else b = sum; } count++; } } // Driver code public static void main(String args[]) { int p = 2 , q = 3 , n = 20 ; System.out.println(minOperations(p, q, n)); } } // This code is contributed by saurabh_jaiswal. |
Python3
# python program for the above approach # Function to print the minimum number # of operations required def minOperations(a, b, n): # Store the count of operations count = 0 while ( 1 ): # If any value is greater than N # return count if (n < = a or n < = b): return count break else : sum = a + b if (a < b): a = sum else : b = sum count + = 1 return count # Driver code if __name__ = = "__main__" : p = 2 q = 3 n = 20 print (minOperations(p, q, n)) # This code is contributed by rakeshsahni |
Javascript
<script> // JavaScript Program to implement // the above approach // Function to print the minimum number // of operations required function minOperations(a, b, n) { // Store the count of operations let count = 0; while (1) { // If any value is greater than N // return count if (n <= a || n <= b) { return count; break ; } else { let sum = a + b; if (a < b) a = sum; else b = sum; } count++; } return count; } // Driver code let p = 2, q = 3, n = 20; document.write(minOperations(p, q, n) + "<br>" ); // This code is contributed by Potta Lokesh </script> |
C#
// C# program for the above approach using System; public class GFG { // Function to print the minimum number // of operations required public static int minOperations( int a, int b, int n) { // Store the count of operations int count = 0; while ( true ) { // If any value is greater than N // return count if (n <= a || n <= b) { return count; } else { int sum = a + b; if (a < b) a = sum; else b = sum; } count++; } } // Driver code public static void Main( string []args) { int p = 2, q = 3, n = 20; Console.WriteLine(minOperations(p, q, n)); } } // This code is contributed by AnkThon |
4
Time Complexity: O(min(log(max(a, N), log(max(b, N)))
Auxiliary Space: O(1)
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