Big O notation is a mathematical concept used in computer science to describe the complexity of algorithms. It’s an important tool for analyzing and comparing algorithms, especially as the size of data sets increases.

In this post, we’ll take a closer look at Big O notation and explain what it means. We’ll also provide some examples to help illustrate the concepts.

What is Big O Notation?

Big O notation is a way of expressing the time complexity of an algorithm. In other words, it describes how the running time of an algorithm grows as the size of the input data grows. The notation uses the letter O, followed by a function that describes the growth rate.

The function used in Big O notation represents the worst-case scenario for an algorithm. It’s used to describe the upper bound of the running time, so we can get a general idea of how efficient an algorithm is.

Examples

O(1) – Constant Time

An algorithm that takes the same amount of time to complete regardless of the size of the input data has a time complexity of O(1). A good example of this is accessing an element in an array by its index.

fun getElement(array: Array<Int>, index: Int): Int {
    return array[index]
}

In this example, the time it takes to get an element from an array is constant, regardless of the size of the array.

O(n) – Linear Time

An algorithm that takes time proportional to the size of the input data has a time complexity of O(n). A good example of this is searching for an element in an unsorted array.

fun search(array: Array<Int>, target: Int): Boolean {
    for (element in array) {
        if (element == target) {
            return true
        }
    }
    return false
}

In this example, the time it takes to search for an element in an array increases linearly with the size of the array.

O(n^2) – Quadratic Time

An algorithm that takes time proportional to the square of the size of the input data has a time complexity of O(n^2). A good example of this is sorting an array using bubble sort.

fun bubbleSort(array: Array<Int>) {
    val n = array.size
    for (i in 0 until n) {
        for (j in 0 until n-i-1) {
            if (array[j] > array[j+1]) {
                val temp = array[j]
                array[j] = array[j+1]
                array[j+1] = temp
            }
        }
    }
}

In this example, the time it takes to sort an array increases quadratically with the size of the array.

Conclusion

Big O notation is an essential tool for understanding algorithm performance. It helps us compare algorithms and determine which is the most efficient for a given task. By knowing the time complexity of an algorithm, we can make better decisions when designing and implementing our programs.