Solution #23 - Daniel/Edited - 18.03.2025

Heaps/#23 - Merge K Sorted Arrays - Medium/Explanation - Merge-K-Sorted-Arrays.md

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+# Merge K Sorted Arrays Solution
+
+## Overview
+
+The goal of this solution is to merge k sorted arrays into a single sorted array.
+
+## Possible Approaches
+
+### 1. Sorting
+
+- Create result array
+- Append all elements of all k lists to the array
+- Sort the array
+
+#### Time Complexity
+
+O((N*K)*log(N\*K)), K is number of arrays and N is average number of elements in the array
+
+#### Space Complexity
+
+O(N\*K)
+
+Traversing all k lists, sorting the final list
+
+### 2. Merge Sort
+
+- Create a helper function that performs merge sort on two arrays using two pointers
+
+- Call the function in pairs to effectively half the number of arrays every iteration.
+
+- Return the output array
+
+#### Time Complexity
+
+O((N*K)*log(K))
+
+Log(k) levels of recursion calls, and at each level, K arrays are traversed for merging.
+
+#### Space Complexity
+
+O((N*K)*log(K))
+
+Log(k) levels and O(N\*K) space is required to store the answer every call.
+
+### 3. Min Heap
+
+- Most straightforward approach so far and the one implemented.
+- Iterate through all of the k arrays and append to a min heap implemented by a priority queue.
+- At each pass, append a single element from each array.
+- Pop the min element and insert the next element from which the element is extracted. If empty, array is merged.
+- Traverse the priority queue to store in a vector.
+- Return the vector
+
+#### Time Complexity
+
+O((N*K)*log(k))
+
+Min-heap of size k used. For insertion and removal of elements, the time complexity is N \* Klog(K).
+
+#### Space Complexity
+
+O(N\*K)
+
+Min-heap of size K used, for arrays averaging N elements.

Heaps/#23 - Merge K Sorted Arrays - Medium/Solution - Merge-K-Sorted-Arrays.cpp

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+#include <bits/stdc++.h> 
+vector<int> mergeKSortedArrays(vector<vector<int>>&kArrays, int k)
+{
+    priority_queue<int, vector<int>, greater<int>> q;
+    vector<int> result;
+    for(int i=0; i<kArrays.size(); i++){
+        for(int j=0; j<kArrays[i].size(); j++){
+            q.push(kArrays[i][j]);
+        }
+    }
+    while(!q.empty()){
+        result.push_back(q.top());
+        q.pop();
+    }
+    return result;
+}