For example, if we have a large 10,000 element array, Linear Search would require 10,000 comparisons at worst case. Since Linear Search can work on sorted arrays, if the array is small, or if we need to search the array just once, then Linear Search might be a better choice.īinary Search is a great choice if we have to make multiple searches on large arrays. The sorting step, if using an efficient algorithm, will have a time complexity of O(nlog(n)). It should be noted that Binary Search only works on sorted arrays. Performance summary tableīinary Search has much better time complexity than Linear Search, which has a Big O(n) – linear time.įrom the graph of Big O Notation below, we can see that with larger input arrays, Binary Search (yellow line) will take a lot less time to compute than Linear Search (blue line). Therefore the space complexity of Binary Search is O(1) – constant space. Space complexity of Binary Searchīinary Search requires three pointers to elements (start, middle and end), regardless of the size of the array. Image Source: JavaScript Algorithms and Data Structures Masterclass by Colt Steele Average case complexity of Binary Search So, the Big O complexity of binary search is O(log(n)) – logarithmic time complexity: log(32) = 5. See the image below: if we have an array 32 elements long and our target is 32, then the array will be divided five times until we find 32. The worst case complexity of Binary Search occurs when the target value is at the beginning or end of the array. Therefore, the best case time complexity is O(1) - constant time. This means that regardless of the size of the array, we’ll always get the result in constant time. The best case complexity of Binary Search occurs when the first comparison is correct (the target value is in the middle of the input array). Binary Search time complexity Best case complexity of Binary Search On each iteration of the while loop, we are effectively discarding half of the array, until we find our value or until we’ve exhausted the array. If the target equals the middle, return the index.If the target is less than the middle element, move the right pointer down.If the target is greater than the middle element, move the left pointer up.While the left pointer comes before the right pointer:.Create a left pointer at the first element of the array, and a right pointer at the last element of the array.The function accepts a sorted array and a target value.Now we understand the logic of Binary Search, let’s implement it in JavaScript.Ĭonsole. This tremendously decreases time complexity! Binary Search in JavaScript So, with Binary Search, the data set keeps getting divided in half until we find our target. Equal! Return the index of that element, 2.Is 5 greater than, smaller than, or equal to 5?.Greater, so 5 must be in the right half of the array.Is 5 greater than, smaller than, or equal to 2?.Start at middle (even length array, so middle – 1):.
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