Problem Statement
The task revolves around reducing a given integer to zero using a specific set of operations. Each operation performed on the integer depends on its parity (even or odd). For even integers, you will halve the number (divide by 2), and for odd integers, you will decrement the value by one (subtract 1). The desired outcome of the challenge is to determine the total number of operations required to convert the integer to zero.
Examples
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 0.
Example 2
Input:
num = 8
Output:
4
Explanation:
Step 1) 8 is even; divide by 2 and obtain 4. Step 2) 4 is even; divide by 2 and obtain 2. Step 3) 2 is even; divide by 2 and obtain 1. Step 4) 1 is odd; subtract 1 and obtain 0.
Example 3
Input:
num = 123
Output:
12
Constraints
0 <= num <= 106
Approach and Intuition
The problem can be understood and tackled as a basic simulation of steps, following a straightforward algorithmic approach using a loop or recursion. The integer's properties (even or odd) dictate the operation, influencing the speed of reduction toward zero:
- If the number is even, dividing by two effectively reduces its magnitude more significantly than subtracting one, thus generally speeding up the process of reaching zero.
- If the number is odd, subtracting one turns it into an even number, which can then be halved in the next step.
From Examples
From the provided examples:
- Example 1 (num = 14): This sequence alternates operations (halve when even, and subtract when odd), taking a total of 6 steps to come down to zero.
- Example 2 (num = 8): This is purely division as the number remains even after every halving, taking just 4 steps to get to zero.
- Example 3 (num = 123): A mixed sequence of operations summing up to 12 steps.
Observing Constraints
Given the constraints (0 <= num <= 10^6), the approach chosen should efficiently handle larger values without a significant increase in computational steps:
- For very large numbers, a sequence of halving provides an efficient way to reduce the number quickly.
- Based on the constraints, this problem ensures that we can operate within these limits without special adjustments or optimizations.
This fine interplay between division and subtraction, controlled by the parity of the number, underpins the minimum steps required to achieve the goal.
Solutions
- C++
class Solution {
public:
int stepsToReduceToZero(int number) {
int stepCounter = 0;
while (number != 0) {
if (number % 2 == 0) {
number /= 2;
} else {
number -= 1;
}
stepCounter++;
}
return stepCounter;
}
};
This solution provides a method to calculate the number of steps required to reduce an integer to zero. The function stepsToReduceToZero implements a loop that continuously modifies the input number until it reaches zero. During each iteration of the loop:
- Determine if
numberis even or odd. - If
numberis even, divide it by two. - If
numberis odd, subtract one fromnumber.
Increment stepCounter in each iteration to keep track of the number of steps. The loop terminates when number becomes zero, and the function then returns the value of stepCounter, indicating the total number of steps taken. The approach efficiently handles the reduction using basic arithmetic operations and a loop, ensuring optimal performance for this straightforward computational problem.
- Java
class Solution {
public int stepsToReduceToZero(int number) {
int stepCounter = 0;
while (number != 0) {
if (number % 2 == 0) {
number /= 2;
} else {
number--;
}
stepCounter++;
}
return stepCounter;
}
}
The submitted Java code solves the problem of finding the number of steps required to reduce a number to zero. The method stepsToReduceToZero takes an integer number as its parameter and utilizes a while loop to continually transform the number until it reaches zero. The process involves two types of operations:
- Division by two if the number is even.
- Decrement by one if the number is odd.
For each operation performed, a stepCounter is incremented. This variable keeps track of the total number of operations performed. Once the number becomes zero, the method returns the accumulated count of steps.
This code addresses the problem efficiently by ensuring that each iteration either halves the number or slightly reduces it, thus guaranteeing that the loop progresses towards the target zero outcome. After running this method with any integer input, the expected outcome is an integer representing the total steps taken to reduce the initial number to zero.
- Python
class Solution:
def countSteps(self, number: int) -> int:
steps = 0
while number != 0:
if number % 2 == 0:
number /= 2
else:
number -= 1
steps += 1
return steps
The given Python solution focuses on counting the number of steps required to reduce a number to zero. Follow these steps:
- Initialize a counter
stepsto zero to keep track of the number of operations. - Use a
whileloop to perform operations on thenumberuntil it becomes zero. - Inside the loop, check if the
numberis even using the modulo operator (number % 2 == 0). If true, divide thenumberby 2. - If the
numberis odd, subtract 1 from it. - Increment the
stepscounter after each operation. - Return the
stepscounter once the number is reduced to zero.
This approach ensures that the number is reduced to zero using the minimum number of steps, alternating between division by 2 when the number is even and subtraction by 1 when it is odd.
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