Separate the Digits in an Array - Solution & Explanation
Problem Statement
Given an array of positive integers nums, return an array answer that consists of the digits of each integer in nums after separating them in the same order they appear in nums.
To separate the digits of an integer is to get all the digits it has in the same order.
- For example, for the integer
10921, the separation of its digits is[1,0,9,2,1].
Example 1:
Input: nums = [13,25,83,77] Output: [1,3,2,5,8,3,7,7] Explanation: - The separation of 13 is [1,3]. - The separation of 25 is [2,5]. - The separation of 83 is [8,3]. - The separation of 77 is [7,7]. answer = [1,3,2,5,8,3,7,7]. Note that answer contains the separations in the same order.
Example 2:
Input: nums = [7,1,3,9] Output: [7,1,3,9] Explanation: The separation of each integer in nums is itself. answer = [7,1,3,9].
Constraints:
1 <= nums.length <= 10001 <= nums[i] <= 105
Approach Overview
Problem Overview: You receive an array of positive integers. For every number, split it into its individual digits and append those digits to a result array while preserving the original order. For example, [13, 25] becomes [1, 3, 2, 5]. The challenge is simply extracting digits efficiently while keeping the sequence correct.
This problem falls under basic Array traversal and Simulation. You process each number one by one and simulate digit extraction.
Approach 1: String Conversion Method (O(n·k) time, O(n·k) space)
The simplest implementation converts each number into a string, then iterates over its characters. Each character represents a digit, so convert it back to an integer and append it to the result list. If n is the number of integers and k is the average number of digits per integer, the algorithm performs roughly n × k operations.
This approach is popular because it is extremely readable and avoids manual digit manipulation. Most high-level languages provide fast string iteration, so the performance is usually more than sufficient for interview constraints. The tradeoff is extra temporary memory used by the string representation, which makes the space complexity O(n·k) including the output.
Approach 2: Mathematical Division Method (O(n·k) time, O(n·k) space)
This method extracts digits using arithmetic instead of string operations. For each number, repeatedly apply num % 10 to obtain the last digit and num / 10 to remove it. Because this produces digits in reverse order, store them temporarily (for example in a stack or small list) and then append them back to the result in reverse.
The algorithm still processes every digit exactly once, so the time complexity remains O(n·k). Space complexity is also O(n·k) due to the output plus a small temporary buffer per number. This approach is useful when you want tighter control over numeric operations or when avoiding string conversions is preferred.
Recommended for interviews: Both approaches are acceptable because the complexity is identical. The string conversion solution demonstrates clean thinking and quick implementation, which interviewers appreciate for an easy problem. The mathematical division method shows deeper understanding of digit manipulation and is sometimes preferred in lower-level environments where avoiding string conversion matters.
Approach 1: String Conversion Method
This approach involves converting each integer in the array to a string, then iterating over each character in the string to convert it back to an integer. This allows us to access each digit in its original order effortlessly.
This C solution uses a character array to convert each number into a string. We iterate through each character of the string, convert it to an integer, and append it to the resulting array. Clarification of the logic is managed by utilizing snprintf for conversion and indexing through the string to build the desired output.
Complexity
Time Complexity: O(n * k) where n is the number of elements and k is the number of digits in each number (up to 5).
Space Complexity: O(n * k) mostly due to storing digits in the output array.
Approach 2: Mathematical Division Method
This approach involves using mathematical operations to extract digits from each number without converting it to a string. The core idea retains the remainder of number by using modulo operation followed by integer division to remove processed digits from the right.
This solution first reverses each number by iteratively extracting digits via modulo and shifting them via integer division. The reversal happens twice to maintain sequence, ensuring digits return in the same order as input.
Complexity
Time Complexity: O(n * k) since each digit is processed twice.
Space Complexity: O(n * k) though original number storage is minimized.
Approach 3: Simulation
Split each number in the array into digits, then put the split numbers into the answer array in order.
The time complexity is O(n times log_{10} M), and the space complexity is O(n times log_{10} M). Where n is the length of the array nums, and M is the maximum value in the array nums.
Approach 4: Default Approach
Code
Rust
Complexity Comparison
| Approach | Complexity |
|---|---|
| String Conversion Method | Time Complexity: O(n * k) where n is the number of elements and k is the number of digits in each number (up to 5). |
| Mathematical Division Method | Time Complexity: O(n * k) since each digit is processed twice. |
| Simulation | — |
| Default Approach | — |
Detailed Complexity Analysis
| Approach | Time | Space | When to Use |
|---|---|---|---|
| String Conversion Method | O(n·k) | O(n·k) | Best for readability and fast implementation in interviews |
| Mathematical Division Method | O(n·k) | O(n·k) | When avoiding string conversion or demonstrating numeric digit extraction |
Video Solution
Separate the Digits in an Array || LeetCode Biweekly Contest 97 || Explanation with Solution • Learn to Code • 1,210 views views
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