Merge sort divides a collection into smaller parts, sorts those parts and merges them in order. Understanding the merge step is essential: dividing the input alone does not sort it. Trace the process before trying to memorise an implementation.
Follow the divide-and-conquer structure
In a common top-down version, split the sequence until each part contains at most one item, then combine the parts through ordered merges. A one-item sequence is already sorted. Keep the base case explicit in recursive pseudocode so that the process stops and the logic can be followed.
Understand the merge step
Compare the next available item from each sorted part and take the smaller according to the ordering rule. Continue until one part is exhausted, then append what remains from the other. The merge depends on both input parts already being sorted; applying it to arbitrary unsorted parts does not establish the required result.
Trace a small input
For the sequence 4, 1, 3, 2, the split produces 4, 1 and 3, 2, then individual items. Merging gives 1, 4 and 2, 3, followed by 1, 2, 3, 4. Show the comparisons and returned sequences separately. A trace should explain the order of operations, not simply draw the desired sorted sequence at the bottom.
Discuss complexity with the implementation
The standard array version performs work across levels of division and has O(n log n) running time. Common implementations need additional storage for merging. State the version and assumptions being analysed; implementation details affect memory use and stability. Do not confuse a complexity class with a measured duration on one computer.
Test edge cases and justify the code
Check empty and single-item inputs, duplicates and an already sorted sequence. If stability matters, explain how equal keys are handled. Use the pseudocode convention or programming language required by your module, and attribute any adapted implementation. A correct trace and clear reasoning are more useful than code you cannot explain.
Sources and further reading
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