C++ Coding Test Course, Making an Integer Equal to 1

Hello, everyone. In this lecture, we will discuss the algorithm problem “Making an Integer Equal to 1,” which can be implemented in C++. This problem is one of the types frequently encountered in coding tests for job preparation and requires various ways of thinking. Therefore, while solving this problem, you can enhance your basic algorithm design and trimming skills, as well as improve your C++ programming abilities.

Problem Description

Given an integer x, we want to make this integer equal to 1 using the following two operations:

• If x is even, divide x by 2.
• If x is odd, subtract 1 from x.

Only one operation can be performed at a time, and the goal is to find the minimum number of times to make x equal to 1 by repeating the above operations. The range of x is from 1 to 10⁶.

Input

x = 10

Output

result = 5

Approach to the Problem

To solve this problem, we need to calculate the minimum number of operations while transforming x to 1, either through a recursive approach or a loop. The following steps can be considered to implement the algorithm.

1. Basic Algorithm Design

Initially, determine whether x is odd or even and apply the appropriate operation based on that condition. Continue this process and increment the count until x becomes 1. While recursion can be used, a for loop might be simpler.

2. Time Complexity Analysis

The time complexity of this algorithm depends on the value of x. Since x can be up to 10^6, the operations will be performed fewer than 20 times at most. This is a very efficient method.

C++ Code Implementation

Now let’s implement the above algorithm in C++. The code below calculates the minimum number of operations required to make the given integer equal to 1.

#include 
using namespace std;

int makeOne(int x) {
    int count = 0; // Variable to count the number of operations
    while (x > 1) { // Continue looping while x is greater than 1
        if (x % 2 == 0) { // If x is even
            x /= 2; // Divide x by 2
        } else { // If x is odd
            x -= 1; // Subtract 1 from x
        }
        count++; // Increase operation count
    }
    return count; // Return the final operation count
}

int main() {
    int x;
    cout << "Enter an integer: ";
    cin >> x; // Get an integer input from the user
    int result = makeOne(x); // Call the makeOne function
    cout << "Minimum number of operations to make the integer equal to 1: " << result << endl; // Output the result
    return 0;
}

Code Explanation

The code above defines a function makeOne that takes the given integer x as an argument and calculates the minimum number of operations needed to make that integer equal to 1. Using a while loop, the operations are continuously performed while x is greater than 1, and the operation count is recorded at each iteration. As a result, it ultimately returns the total number of operations required to make x equal to 1.

Testing and Validation

Now, let's verify if the code works correctly with several test cases.

Enter an integer: 10
Minimum number of operations to make the integer equal to 1: 5

Enter an integer: 15
Minimum number of operations to make the integer equal to 1: 8

Enter an integer: 1
Minimum number of operations to make the integer equal to 1: 0

Conclusion

In this lecture, we have solved the algorithm problem "Making an Integer Equal to 1." Through this problem, we covered the basics of C++ syntax, algorithm design, and code implementation methods. It is essential to constantly think about various situations encountered during the process of solving algorithm problems and the ways to overcome them. I encourage you to solve various problems to enhance your problem-solving skills. I will return with beneficial content in the next lecture. Thank you!