Intermediate LevelData Structures & Algorithms
Explain the K-way Merge pattern and its applications.
ā Interview Prompt: Describe the K-way merge pattern using a min-heap, its time complexity, and 3 real applications.
K-way Merge uses a min-heap to efficiently merge $K$ sorted sequences:
1
Push the first element of each sequence into the heap.
2
Pop the global minimum ā add to output.
3
Push the next element from that sequence.
4
Repeat until heap is empty.
ā¢
Time: $O(N \log K)$, Space: $O(K)$.
Applications:
1
Merge K sorted linked lists (LeetCode Hard).
2
External Sort: Merge sorted file chunks that don't fit in RAM.
3
Median from data stream: Combine results from multiple sorted partitions.
4
Smallest range covering K lists: Extended K-way merge with range tracking.
Code Implementation Example
typescript
// K-way merge returning sorted elements as array
function kWayMerge(sortedArrays: number[][]): number[] {
// Heap entry: [value, arrayIndex, elementIndex]
const heap: [number, number, number][] = [];
for (let i = 0; i < sortedArrays.length; i++) {
if (sortedArrays[i].length > 0) {
heap.push([sortedArrays[i][0], i, 0]);
}
}
heap.sort((a, b) => a[0] - b[0]); // min-heap simulation
const result: number[] = [];
while (heap.length) {
const [val, arr, idx] = heap.shift()!;
result.push(val);
if (idx + 1 < sortedArrays[arr].length) {
const next: [number, number, number] = [sortedArrays[arr][idx + 1], arr, idx + 1];
const pos = heap.findIndex(h => h[0] > next[0]);
heap.splice(pos === -1 ? heap.length : pos, 0, next);
}
}
return result;
}š”K-way merge using min-heap producing globally sorted output in O(N log K).
šÆ Interview Key Takeaway
K-way merge is a fundamental pattern in distributed systems (merge shards) and external sorting. Always use a min-heap, not repeated binary merges.
#DSA#K-way Merge#Heap#Pattern#Intermediate
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