If you want to learn how to code, you need to learn algorithms. Learning algorithms improves your problem solving skills by revealing design patterns in programming. In this tutorial, you will learn how to code the array partition algorithm in JavaScript and Python.
This article originally published at jarednielsen.com
How to Code the Array Partition Algorithm
Programming is problem solving. There are four steps we need to take to solve any programming problem:
Understand the problem
Make a plan
Execute the plan
Evaluate the plan
Understand the Problem
To understand our problem, we first need to define it. Let’s reframe the problem as acceptance criteria:
GIVEN an unsorted array and a range of indexes to partition between
WHEN I select a pivot value from the array and partition the array on the pivot
THEN I am returned the index of the pivot
That’s our general outline. We know our input conditions, an unsorted array and starting and ending values for the partition, and our output requirements, the index of the value used to partition the array, and our goal is to partition the array on a pivot with lower values on the left and higher values on the right.
Let’s make a plan!
Make a Plan
Let’s revisit our computational thinking heuristics as they will aid and guide is in making a plan. They are:
Decomposition
Pattern recognition
Abstraction
Algorithm design
The first step is decomposition, or breaking our problem down into smaller problems. What's the smallest problem we can solve?
An array with two elements:
[1, 2]
Easy!
It's already done.
What if the array was reversed?
[2, 1]
Where have we seen this or something like it before?
Swap!
Because we are pragmatic programmers, we're going to repurpose our swap algorithm and copy/pasta it right here:
FUNCTION swap(arr, left, right)
SET temp TO THE VALUE STORED IN arr[left]
SET arr[left] TO THE VALUE STORED IN arr[right]
SET arr[right] TO THE VALUE STORED IN temp
RETURN arr
If we pass our two element array to our swap function, the output will be:
[1, 2]
But! We didn't partition on a pivot. We could pivot on one of the two existing values, but let's make it more fun and add another element to our array:
[3, 2, 1]
How do we choose our pivot?
In our array above, we could simply choose the second element containing the value 2. But what if our array looked like this?
[3, 1, 2]
Or this?
[2, 1, 3]
We don't know what our array will look like, so we need to find a programmatic approach and not try to brute force it.
We could iterate through the array, get the sum of all of the values, divide by 2, floor that value, and use it as the pivot, but that adds at least one more step to finding our solution.
What if we just select a random value from the array for the pivot?
We could generate a random number, but because we don't know what the array looks like, we can just select any value.
Which element do we select?
We know we're going to need to iterate and the standard approach to iteration is starting at 0 and incrementing by 1 to n. So let's take the path of least resistance and select n, the last, or right element in the array.
We know we need to return the index, so we're going to need to declare an index variable. But how do we initialize it?
If we're starting at left, let's set our index to left.
Let's pseudocode what we identified so far...
FUNCTION partition(arr, left, right)
SET index TO left
SET pivot TO arr[right]
...
RETURN index
We want to start iterating at left and only iterate up to right. Rather than starting at 0, we need to begin our iteration with left, which may or may not be 0. Our for loop needs to look something like this:
FUNCTION partition(arr, left, right)
SET index TO left
SET pivot TO arr[right]
FOR EACH VALUE i BETWEEN left AND right
...
RETURN index
Now what?
As we iterate over the array, we need to compare the value stored in arr[i] to our pivot. What comparison are we making?
Less than?
Greater than?
Table time!
Let's map each iteration using this array:
[3, 1, 2]
This is what we know on our first iteration:
| i | arr[i] | pivot | index | arr[index] |
|---|---|---|---|---|
| 0 | 3 | 2 | 0 | 3 |
Our index variable and our iterator, i, are both indexing the value 3 in our arry. We can see that this value is greater than our pivot, 2. Let's see what happens in the next iteration:
| i | arr[i] | pivot | index | arr[index] |
|---|---|---|---|---|
| 0 | 3 | 2 | 0 | 3 |
| 1 | 1 | 2 | 0 | 3 |
Do you see a pattern? Or at least the emergence of a pattern?
Note that the value of arr[i] is now 1, but the value of arr[index] is still 3.
We need to swap the values stored in arr[i] and arr[index], so our comparison is:
IF arr[i] IS LESS THAN pivot
swap(arr, index, i)
And before we exit the conditional, we need to increment index.
Our pseudocode now looks like this:
FUNCTION partition(arr, left, right)
SET index TO left
SET pivot TO arr[right]
FOR EACH VALUE i BETWEEN left AND THE LENGTH OF arr
IF arr[i] IS LESS THAN pivot
swap(arr, index, i)
INCREMENT index BY 1
RETURN index
And our array now looks like this:
[1, 3, 2]
But in our final iteration, our condition won't be met, so how do we make that final swap?
Let's look at that table again:
| i | arr[i] | pivot | index | arr[index] |
|---|---|---|---|---|
| 0 | 3 | 2 | 0 | 3 |
| 1 | 1 | 2 | 0 | 3 |
| 2 | 2 | 2 | 1 | 3 |
Our index value is correct, but the value stored in arr[index] is not. Where is that value? At the end, or right of the array. So let's swap 'em!
Our final pseudocode looks like this:
FUNCTION partition(arr, left, right)
SET index TO left
SET pivot TO arr[right]
FOR EACH VALUE i BETWEEN left AND THE LENGTH OF arr
IF arr[i] IS LESS THAN pivot
swap(arr, index, i)
INCREMENT index BY 1
swap(arr, index, right)
RETURN index
Let's step through this using a slightly larger array:
[5, 1, 4, 2, 3]
When we call our partition function, we'll use the default values of the first and last element for left and right, so left will be equal to 0 and right will be equal to the length of our arrary minus 1.
We then set our index to left and our pivot to the value stored in arr[right]. In this case, that's 3.
When we begin iterating, i is equal to left, which is 0.
The value stored in arr[i] is 5.
5 is not less than 3, so we leave it.
In the next iteration, i is equal to 1.
The value stored in arr[i] is now 1.
1 is less than 3, so we swap the values in arr[index] and arr[i], here that's 5 and 1.
Now our array looks like this:
[1, 5, 4, 2, 3]
We increment our index by 1, so its value is now 1.
In the next iteration, i is equal to 2.
The value stored in arr[i] is now 4.
4 is not less than 3, so we leave it.
In the next iteration, i is equal to 3.
The value stored in arr[i] is now 2.
2 is less than 3, so we swap the values in arr[index] and arr[i], here that's 5 and 2.
Now our array looks like this:
[1, 2, 4, 5, 3]
We increment our index by 1, so its value is now 2.
In the next iteration, i is equal to 4.
The value stored in arr[i] is now 3.
3 is not less than 3, so we leave it and exit our loop.
We still need to get our pivot in the right place, and we do this by swapping the value stored in arr[index] with the value stored in arr[right], which are 4 and 3 respectively.
Now our array looks like this:
[1, 2, 3, 5, 4]
Finally, we return our index, which is 2, where the value of our pivot is currently stored in the array.
Execute the Plan
Now it's simply a matter of translating our pseudocode into the syntax of our programming language.
How to Code the Array Partition Algorithm in JavaScript
Let's start with JavaScript...
const swap = (arr, left, right) => {
let temp = arr[left];
arr[left] = arr[right];
arr[right] = temp;
return arr;
}
const partition = (arr, left = 0, right = arr.length - 1) => {
let index = left;
let pivot = arr[right];
for (let i = left; i < right; i++) {
if (arr[i] < pivot) {
swap(arr, index, i);
index++;
}
}
swap(arr, index, right);
return index;
}
How to Code the Array Partition Algorithm in Python
Now let's see it in Python...
def swap(arr, left, right):
temp = arr[left]
arr[left] = arr[right]
arr[right] = temp
return arr
def partitionLomuto(arr, left = 0, right = None):
if right == None:
right = len(arr) - 1
pivot = arr[right]
index = left
for i in range(left, right):
if arr[i] < pivot:
swap(arr, index, i)
index += 1
swap(arr, index, right)
return index
Evaluate the Plan
Can we do better?
Yes!
This algorithm is using the Lomuto partition scheme. This approach is perfectly fine and perfect for beginners. There is another approach, the Hoare partition scheme, which is more efficient but slightly more complicated. It works by iterating forward and back through the array.
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