![]() Merge Sort has a recursive function that splits the array recursively until the base case is reached. One item is considered to be a sorted array.Īn empty array also falls under the base case. In Merge Sort, you must keep splitting the array until you reach the base case. ![]() Merge sorted arrays B and C back into A recursively divide array C until base case is reached recursively divide array B until base case is reached copy second half of the array A to an array CĬopy A to C copy first half of the array A to an array BĬopy A to B If the array contains just one element, or if it is empty, it is already sorted Output: Array A sorted in increasing order You would have come across Merge Sort examples in the following way:Īlthough this is the big picture, it does not clearly define how the recursive calls occur. Let us see how this logic is applied in Merge Sort! The solutions of the subproblems are combined to solve the original problem. Without further ado, let’s dive in and learn all about Merge Sort! Merge Sort’s Divide and Conquer Algorithm Designĭivide and conquer is a popular algorithm design technique where a huge or cumbersome problem is broken down into simpler, solvable subproblems. In this blog, you will gain a thorough understanding of Merge Sort and try out fun activities to get hands-on with this amazing problem-solving algorithm. Given an array, it divides the array into two halves, sorts these two halves recursively, and then, it merges the two smaller sorted arrays into a larger sorted array.Īmongst popular sorting algorithms, Merge Sort stands out for a reason. If you don’t know how much data you’ll need sorted consider using another algorithm, like insertion sort, when the dataset is small enough to get the best of both worlds.Merge Sort is the perfect example of the Divide and Conquer algorithm design. While Merge sort is the best algorithm we’ve covered so far since it’s O(nlogn), it’s good to keep in mind that it works better with larger amounts of data. log ( mergeSort (unsortedArr ) ) Conclusion const merge = ( arr1, arr2 ) => Ĭonsole. So both arrays are gradually shrinking until one of them is empty with the leftovers thrown onto the end, since it’s already sorted. When that’s done, if there’s anything leftover, like when one array is larger, concatenate that onto the end. There are many different ways of doing this but I found this the most succinct.Īs long as there are items in either array, check if the first item in either array is smaller, then throw it into sorted and remove that item from the array with shift(). To simplify our problem we can start by creating a utility function that’ll merge two sorted arrays. Here’s the array of 50 unsorted items I’ll be referring to. Graphic/Animation thanks to Practice Data This is where the n in O(nlogn) comes from.Īs you can see one half of the array is completed before the second half, and the first half of each before the next half (the different colors represent different arrays). Since the amount of sub-arrays will be some multiple of the number of items in our main array, that’s what gives us the log in O(nlogn).įrom there we can start merging, since both arrays should already be sorted we can easily compare which numbers in each is smaller and put them in the right place. First, we need to take the entire array and break it into many sub-arrays by continuously splitting everything in half until everything is alone in its own array. Merge sort is built off the idea of comparing whole arrays instead of individual items. The goal being to break down our problem into sub-problems and recursively continue to break those down until we have a lot of simple problems that we can easily put back together. Similar to binary search, merge sort is a divide and conquer algorithm. We’re also going to be looking at recursion-based examples, so you can brush up on that here. Prerequisitesīeing able to think about time and space complexity via Big O Notation will be incredibly helpful. With this, we can move from the O(n^2) algorithms to a much more scalable O(nlogn) solution. Now we get can start digging into some of the more efficient big boy algorithms, like merge sort. Previously, we covered some of the beginner sorting algorithms that are able to get the job done but quickly go out of hand with larger datasets.
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