Merge Sort is a powerful divide-and-conquer sorting algorithm. It works by recursively dividing an array into smaller subarrays, sorting them, and then merging them back together. The key principle involves three steps: divide the array into halves, conquer by recursively sorting each half, and combine by merging the sorted halves. This approach guarantees O of n log n time complexity in all cases.
The recursive division process continues until we reach the base case. Starting with the original array, we split it into two halves. Each half is then recursively divided again until every subarray contains only a single element. Single element arrays are considered already sorted, which forms our base case for the recursion.
The merge process is the heart of merge sort. We take two already sorted arrays and combine them into one sorted array. The algorithm compares the first elements of both arrays, takes the smaller one, and places it in the result array. This process continues until all elements are merged, maintaining the sorted order.
Let's trace through a complete merge sort example. Starting with array 38, 27, 43, 3, we first divide it into two halves. Each half is recursively divided until we have individual elements. Then we merge them back: 27 and 38 merge to form 27, 38, while 3 and 43 merge to form 3, 43. Finally, these two sorted arrays merge to give us the final sorted result: 3, 27, 38, 43. Merge sort has O of n log n time complexity and O of n space complexity, and it's a stable sorting algorithm.
To summarize what we've learned about merge sort: It's a divide-and-conquer algorithm that recursively divides arrays into smaller pieces, sorts them, and merges them back together. This approach guarantees consistent O of n log n performance, making it one of the most reliable sorting algorithms in computer science.
The recursive division process continues until we reach the base case. Starting with the original array, we split it into two halves. Each half is then recursively divided again until every subarray contains only a single element. Single element arrays are considered already sorted, which forms our base case for the recursion.
The merge process is the heart of merge sort. We take two already sorted arrays and combine them into one sorted array. The algorithm compares the first elements of both arrays, takes the smaller one, and places it in the result array. This process continues until all elements are merged, maintaining the sorted order.
Let's trace through a complete merge sort example. Starting with array 38, 27, 43, 3, we first divide it into two halves. Each half is recursively divided until we have individual elements. Then we merge them back: 27 and 38 merge to form 27, 38, while 3 and 43 merge to form 3, 43. Finally, these two sorted arrays merge to give us the final sorted result: 3, 27, 38, 43. Merge sort has O of n log n time complexity and O of n space complexity, and it's a stable sorting algorithm.
To summarize what we've learned about merge sort: It's a divide-and-conquer algorithm that recursively divides arrays into smaller pieces, sorts them, and merges them back together. This approach guarantees consistent O of n log n performance, making it one of the most reliable sorting algorithms in computer science.