# Dutch Flag Algorithm

Dec 29, 2020 · 2 min read

An introduction to the Dutch Flag Algorithm.

Dutch Flag Algorithm (DFA) is one of the most basic and important algorithms for arrays. It is used to segregate an array consisting of 3 numbers in linear time complexity.

The worst time complexity for DFA is O(n) and the space complexity for the algorithm is O(1). The problem statement is as follows:

An array consisting of 0s, 1s, and 2s is provided to you. The task is to write a function that segregates all the numbers together. The order can be anything.

Let's assume that the provided array A is
A = [1, 2, 0, 1, 2, 0, 1, 2, 0]
and the output expected is
A = [2, 2, 2, 0, 0, 0, 1, 1, 1]

To solve the problem, we need to first select the order. For this example, let's select 2,1,0.
Now we need to have 3 pointers namely start, end, and P, pointing to three different indices of the array.

The start will denote the first index of the middle element i.e 0 over here. The End will denote the last index of the middle element and pointer P will be used to traverse the array.

The loop will run while the P is not equal to End. As the P traverses, if P encounters 2, it will swap it with start and increment the start. Similarly, if P encounters 1, it will swap it with end and decrement end. The code is as follows:-

For a better understanding of the algorithm, write the stack trace on paper, and make sure you go through all the steps.

If you have any queries or you want me to cover any other algorithm, feel free to comment down the article.

Stay tuned for more such algorithms and concepts.

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