LeetCode #2553 — EASY

Separate the Digits in an Array

Build confidence with an intuition-first walkthrough focused on array fundamentals.

The Problem

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 <= 1000
1 <= nums[i] <= 10⁵

Step 01

Brute Force Baseline

Problem summary: 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].

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array

Example 1

[13,25,83,77]

Example 2

[7,1,3,9]

Core Insight

What unlocks the optimal approach

Convert each number into a list and append that list to the answer.
You can convert the integer into a string to do that easily.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2553: Separate the Digits in an Array
class Solution {
    public int[] separateDigits(int[] nums) {
        List<Integer> res = new ArrayList<>();
        for (int x : nums) {
            List<Integer> t = new ArrayList<>();
            for (; x > 0; x /= 10) {
                t.add(x % 10);
            }
            Collections.reverse(t);
            res.addAll(t);
        }
        int[] ans = new int[res.size()];
        for (int i = 0; i < ans.length; ++i) {
            ans[i] = res.get(i);
        }
        return ans;
    }
}

// Accepted solution for LeetCode #2553: Separate the Digits in an Array
func separateDigits(nums []int) (ans []int) {
	for _, x := range nums {
		t := []int{}
		for ; x > 0; x /= 10 {
			t = append(t, x%10)
		}
		for i, j := 0, len(t)-1; i < j; i, j = i+1, j-1 {
			t[i], t[j] = t[j], t[i]
		}
		ans = append(ans, t...)
	}
	return
}

# Accepted solution for LeetCode #2553: Separate the Digits in an Array
class Solution:
    def separateDigits(self, nums: List[int]) -> List[int]:
        ans = []
        for x in nums:
            t = []
            while x:
                t.append(x % 10)
                x //= 10
            ans.extend(t[::-1])
        return ans

// Accepted solution for LeetCode #2553: Separate the Digits in an Array
impl Solution {
    pub fn separate_digits(nums: Vec<i32>) -> Vec<i32> {
        let mut ans = Vec::new();
        for &num in nums.iter() {
            let mut num = num;
            let mut t = Vec::new();
            while num != 0 {
                t.push(num % 10);
                num /= 10;
            }
            t.into_iter().rev().for_each(|v| ans.push(v));
        }
        ans
    }
}

// Accepted solution for LeetCode #2553: Separate the Digits in an Array
function separateDigits(nums: number[]): number[] {
    const ans: number[] = [];
    for (let num of nums) {
        const t: number[] = [];
        while (num) {
            t.push(num % 10);
            num = Math.floor(num / 10);
        }
        ans.push(...t.reverse());
    }
    return ans;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n × log_10 M)

Space

O(n × log_10 M)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.