Number of Steps to Reduce a Number to Zero - Complete Solution Guide

Number of Steps to Reduce a Number to Zero is LeetCode problem 1342, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Given an integer num , return the number of steps to reduce it to zero . In one step, if the current number is even, you have to divide it by 2 , otherwise, you have to subtract 1 from it. Example 1: Input: num = 14 Output: 6 Explanation: Step 1) 14 is even; divide by 2 and obtain 7. Step 2) 7 is odd; subtract 1 and obtain 6. Step 3) 6 is even; divide by 2 and obtain 3. Step 4) 3 is odd; subtract 1 and obtain 2. Step 5) 2 is even; divide by 2 and obtain 1. Step 6) 1 is odd; subtract 1 and obtain

Detailed Explanation

This problem asks us to calculate the exact number of operations required to reduce a positive integer, `num`, all the way down to zero. The rules for these operations are quite specific: if the current number is even, we must divide it by 2; if it's odd, we must subtract 1 from it. We increment a step counter after each operation. The challenge lies in accurately simulating this process and returning the final step count.

Solution Approach

The provided solution takes a direct, iterative simulation approach. It maintains a `steps` counter initialized to zero and enters a loop that continues as long as `num` is greater than zero. Inside the loop, it checks the parity of `num`. If `num` is even (i.e., `num % 2 == 0`), it performs the required division (`num //= 2`). If `num` is odd, it performs the required subtraction (`num -= 1`). In either case, after an operation, the `steps` counter is incremented. This process precisely mirrors the problem description, ensuring that every valid operation is counted until `num` finally reaches zero. The elegance of this approach lies in its simplicity and direct translation of the problem statement into executable code, requiring no complex data structures or advanced algorithms.

Step-by-Step Algorithm

1. Step 1: Initialize a `steps` counter to 0.
2. Step 2: Enter a `while` loop that continues as long as `num` is greater than 0.
3. Step 3: Check if `num` is even using the modulo operator (`%`).
4. Step 4: If even, divide `num` by 2; otherwise, subtract 1 from `num`.
5. Step 5: Increment the `steps` counter.
6. Step 6: Repeat steps 3-5 until `num` becomes 0.
7. Step 7: Return the final value of `steps`.

Key Insights

• **Direct Simulation of Rules**: The most straightforward and effective approach is to directly simulate the given rules. There's no hidden trick or complex strategy; simply perform the specified operation based on `num`'s parity and increment a counter in each step.
• **Guaranteed Termination**: Since both operations (division by 2 for even numbers, subtraction by 1 for odd numbers) strictly decrease the value of `num` (as long as `num > 0`), the process is guaranteed to terminate. Eventually, `num` will reach zero, preventing infinite loops.
• **Parity as the Sole Decision Factor**: The core decision in each step is exclusively based on whether `num` is even or odd. This conditional check (`num % 2 == 0`) efficiently determines which of the two prescribed operations to apply, making the logic clean and easy to follow.

Complexity Analysis

Time Complexity: O(log(n))

Space Complexity: O(1)

Topics

This problem involves: Math, Bit Manipulation.

Companies

Asked at: Hudson River Trading.