From 2f6c2535c7ab40de46822c659703ebba5ba62cdc Mon Sep 17 00:00:00 2001
From: Dipanita45 <132455672+Dipanita45@users.noreply.github.com>
Date: Sun, 10 Nov 2024 20:59:12 +0530
Subject: [PATCH] Merge K sorted array

---
 .../Merge k sorted lists.c                    | 87 +++++++++++++++++++
 .../Merge_k_Sorted_Lists/Readme.md            | 25 ++++++
 2 files changed, 112 insertions(+)
 create mode 100644 Sorting Algorithms/Merge_k_Sorted_Lists/Merge k sorted lists.c
 create mode 100644 Sorting Algorithms/Merge_k_Sorted_Lists/Readme.md

diff --git a/Sorting Algorithms/Merge_k_Sorted_Lists/Merge k sorted lists.c b/Sorting Algorithms/Merge_k_Sorted_Lists/Merge k sorted lists.c
new file mode 100644
index 00000000..4d7ea611
--- /dev/null
+++ b/Sorting Algorithms/Merge_k_Sorted_Lists/Merge k sorted lists.c	
@@ -0,0 +1,87 @@
+#include <stdio.h>
+#include <stdlib.h>
+
+// Definition for singly-linked list.
+struct ListNode {
+    int val;
+    struct ListNode *next;
+};
+
+// Min-Heap Node
+struct MinHeapNode {
+    struct ListNode *listNode;
+};
+
+// MinHeap
+struct MinHeap {
+    int size;
+    struct MinHeapNode **array;
+};
+
+// Function to create a new MinHeap Node
+struct MinHeapNode* newMinHeapNode(struct ListNode *listNode) {
+    struct MinHeapNode* minHeapNode = (struct MinHeapNode*)malloc(sizeof(struct MinHeapNode));
+    minHeapNode->listNode = listNode;
+    return minHeapNode;
+}
+
+// Function to create a MinHeap
+struct MinHeap* createMinHeap(int capacity) {
+    struct MinHeap* minHeap = (struct MinHeap*)malloc(sizeof(struct MinHeap));
+    minHeap->size = 0;
+    minHeap->array= (struct MinHeapNode*)malloc(capacity * sizeof(struct MinHeapNode));
+    return minHeap;
+}
+
+// Function to swap two MinHeap Nodes
+void swapMinHeapNode(struct MinHeapNode** a, struct MinHeapNode** b) {
+    struct MinHeapNode* t = *a;
+    *a = *b;
+    *b = t;
+}
+
+// Function to min-heapify at a given index
+void minHeapify(struct MinHeap* minHeap, int idx) {
+    int smallest = idx;
+    int left = 2 * idx + 1;
+    int right = 2 * idx + 2;
+
+    if (left < minHeap->size && minHeap->array[left]->listNode->val < minHeap->array[smallest]->listNode->val)
+        smallest = left;
+
+    if (right < minHeap->size && minHeap->array[right]->listNode->val < minHeap->array[smallest]->listNode->val)
+        smallest = right;
+
+    if (smallest != idx) {
+        swapMinHeapNode(&minHeap->array[smallest], &minHeap->array[idx]);
+        minHeapify(minHeap, smallest);
+    }
+}
+
+// Function to extract the minimum node from the heap
+struct ListNode* extractMin(struct MinHeap* minHeap) {
+    if (minHeap->size == 0)
+        return NULL;
+
+    struct ListNode* root = minHeap->array[0]->listNode;
+
+    if (minHeap->size > 1) {
+        minHeap->array[0] = minHeap->array[minHeap->size - 1];
+        minHeapify(minHeap, 0);
+    }
+    minHeap->size--;
+    return root;
+}
+
+// Function to insert a new node into the heap
+void insertMinHeap(struct MinHeap* minHeap, struct MinHeapNode* minHeapNode) {
+    minHeap->size++;
+    int i = minHeap->size - 1;
+    while (i && minHeapNode->listNode->val < minHeap->array[(i - 1) / 2]->listNode->val) {
+        minHeap->array[i] = minHeap->array[(i - 1) / 2];
+        i = (i - 1) / 2;
+    }
+    minHeap->array[i] = minHeapNode;
+}
+
+// Function to merge k sorted linked
\ No newline at end of file
diff --git a/Sorting Algorithms/Merge_k_Sorted_Lists/Readme.md b/Sorting Algorithms/Merge_k_Sorted_Lists/Readme.md
new file mode 100644
index 00000000..d23c5cbf
--- /dev/null
+++ b/Sorting Algorithms/Merge_k_Sorted_Lists/Readme.md	
@@ -0,0 +1,25 @@
+## Merge k Sorted Lists
+
+# Problem Description
+The problem of merging k sorted linked lists involves taking k linked lists, each sorted in ascending order, and merging them into a single sorted linked list. The challenge is to do this efficiently, both in terms of time and space.
+
+# Example
+Given the following k sorted linked lists:
+
+List 1: 1 -> 4 -> 5
+List 2: 1 -> 3 -> 4
+List 3: 2 -> 6
+The merged sorted linked list should be:
+
+1 -> 1 -> 2 -> 3 -> 4 -> 4 -> 5 -> 6
+
+# Solution Approach
+Min-Heap (Priority Queue):
+
+Use a min-heap (or priority queue) to efficiently retrieve the smallest element among the heads of the k lists.
+Push the head of each linked list into the min-heap.
+Repeatedly extract the minimum element from the heap, adding it to the merged list, and push the next element from the same linked list into the heap.
+Continue this process until all elements from all lists have been processed.
+Iterative Merging:
+
+Alternatively, you could merge the lists iteratively, but this is less efficient than using a min-heap.
\ No newline at end of file