Data Structures and Algorithms: Partition Labels 🎯

Welcome to Partition Labels, a fascinating topic that bridges the gap between data structures and algorithms! In this tutorial, we'll learn how to find the partition labels of an array, a concept that will help you understand and solve complex problems more efficiently.

What are Partition Labels? 📝

Partition labels refer to the unique positions in an array where each position's label is the last position of the partition before it. Each partition is a contiguous subarray with all elements being the same.

Let's make this clearer with an example.

Example:

Consider the array [6, 2, 6, 2, 6, 2, 6]. Here, the partitions are:

[6]
[2]
[6, 2, 6] (note that the subarray containing the repeated 6 is a single partition)
Empty partition (no elements left)

The partition labels are [5, 1, 0, -1], where the position -1 denotes the end of the array.

Algorithm for Finding Partition Labels 💡

To find the partition labels, we'll use the following simple algorithm:

Initialize an empty list labels to store the partition labels.
Initialize a dictionary counts to store the counts of each element.
Iterate through the array and for each element:
- If its count in counts is 1, add its index to labels.
- Update the count of the element in counts.
Return the labels list.

Code Example 1: Python 📝

python

def partition_labels(arr):
    counts = {}
    labels = []

    for num in arr:
        counts[num] = counts.get(num, 0) + 1

        if counts[num] == 1:
            labels.append(arr.index(num))

    return labels

Code Example 2: JavaScript 📝

javascript

function partitionLabels(arr) {
    let counts = {};
    let labels = [];

    for (let num of arr) {
        counts[num] = counts[num] ? counts[num] + 1 : 1;

        if (counts[num] === 1) {
            labels.push(arr.indexOf(num));
        }
    }

    return labels;
}

Putting it into Practice 💡

Now that you understand the concept and the algorithm, let's practice with some examples.

Example 1:

[5, 1, 5, 8, 1, 5, 8, 1, 5, 8]

Partition labels: [7, 0, 4]

Example 2:

[1, 2, 2, 3, 3, 3, 4, 4, 4, 4]

Partition labels: [6, 3, 2, 1]

Quiz Time 💡

Congratulations on learning Partition Labels! This concept is a great stepping stone to understanding more complex data structures and algorithms. Keep practicing and soon you'll be solving problems like a pro! 💡 🎉