You’re in a coding interview. The interviewer says: “Sort an array of 0s, 1s, and 2s in place without using a library sort.” The two-pass counting sort is obvious — but the one everyone remembers is the Dutch National Flag algorithm: a single-pass, O(1) space solution using three pointers.

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The Problem

Given an array nums with objects colored red (0), white (1), or blue (2), sort them in place so same-colored objects are adjacent, in order 0, 1, 2.

Example

Input: nums = [2, 0, 2, 1, 1, 0] Output: [0, 0, 1, 1, 2, 2]

Already comfortable with the solution? Practice it in a mock interview →

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What Interviewers Are Actually Testing

Skill	What Interviewers Observe
Dutch National Flag	Do you know the three-pointer algorithm?
Pointer invariants	Can you state what each pointer represents?
Loop termination	Do you use mid <= high (not < high)?
One-pass vs. two-pass	Can you optimize from counting sort to DNF?

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Step 1: The Key Insight

Three pointers maintain three regions: low marks the 0-boundary, high marks the 2-boundary, mid scans. When nums[mid] is 0, swap to low and advance both. When 2, swap to high and retreat high only (don’t advance mid — the swapped value is unseen). When 1, advance mid.

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Python Implementation

def sortColors(nums: list[int]) -> None:
    low, mid, high = 0, 0, len(nums) - 1

    while mid <= high:
        if nums[mid] == 0:
            nums[low], nums[mid] = nums[mid], nums[low]
            low += 1
            mid += 1
        elif nums[mid] == 1:
            mid += 1
        else:
            nums[mid], nums[high] = nums[high], nums[mid]
            high -= 1
            # Don't increment mid — swapped value needs examination

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Time & Space Complexity

Aspect	Complexity
Time	O(n) — single pass
Space	O(1) — in place

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Common Interview Mistakes

1. Incrementing mid after swapping with high. The value from high is unseen — don’t skip it.
2. Using mid < high instead of mid <= high. When equal, nums[mid] is still unsorted.
3. Proposing a general sort. Use the constrained value set — that’s the point.

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What a Strong Candidate Sounds Like

“I’ll use the Dutch National Flag algorithm. Three pointers: low, mid, high. Everything left of low is 0, between low and mid is 1, right of high is 2. When I see a 0, swap to left and advance both. When 2, swap to right and retreat high only. One pass, O(1) space.”

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Related Problems to Practice

• Two Sum — Array manipulation fundamentals.
• Container With Most Water — Two-pointer pattern.
• 3Sum — Multi-pointer array traversal.

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Practice This in a Mock Interview

Start a mock interview for Sort Colors on Intervu.

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Further reading:

• How to Prepare for a Coding Interview in 2026, the complete roadmap
• Why LeetCode alone isn’t enough, and what to practice instead
• Practice any LeetCode problem as a live mock interview
• The Grind 75 Pathway, a structured study plan with AI practice links
• Browse all walkthroughs on GitHub