Merge pull request #3489 from sjain1909/t2

Adding Huffman Code in DSA folder

Author: ajay-dhangar

dsa/Advance/huffman-coding.md

@@ -0,0 +1,148 @@
+---
+id: huffman-coding
+title: Huffman Coding Solution
+sidebar_label: 0003 - Huffman Coding
+tags: [Huffman Coding, Data Compression, Algorithm, C++, Problem Solving]
+description: This is a solution to the Huffman Coding problem.
+---
+
+## Problem Statement 
+
+### Problem Description
+
+Huffman Coding assigns variable-length codes to input characters, with shorter codes assigned to more frequent characters, resulting in efficient compression. Given a set of characters and their frequencies, the goal is to build a Huffman Tree and determine the Huffman codes for each character.
+
+### Examples
+
+**Example 1:**
+
+```plaintext
+Input: Characters = {a, b, c, d, e, f}, Frequencies = {5, 9, 12, 13, 16, 45}
+Output: 
+a: 1100
+b: 1101
+c: 100
+d: 101
+e: 111
+f: 0
+```
+
+### Constraints
+The input should be a set of characters and their respective frequencies.
+
+## Solution of Given Problem
+
+### Intuition and Approach
+
+The Huffman Coding algorithm follows these steps:
+
+1. Create a leaf node for each character and build a min heap of all leaf nodes.
+2. Extract two nodes with the smallest frequency from the min heap.
+3. Create a new internal node with a frequency equal to the sum of the two nodes' frequencies.
+4. Add the new node to the min heap.
+5. Repeat steps 2-4 until the heap contains only one node, which becomes the root of the Huffman Tree.
+6. Assign binary codes to each character based on their position in the Huffman Tree.
+
+### Approaches
+
+#### Codes in Different Languages
+
+<Tabs>
+  <TabItem value="cpp" label="C++" default>
+  <SolutionAuthor name="sjain1909"/>
+   ```cpp
+    #include <bits/stdc++.h>
+    using namespace std;
+    struct MinHeapNode {
+        char data;
+        int freq;
+        MinHeapNode *left, *right;
+
+        MinHeapNode(char data, int freq) {
+            left = right = nullptr;
+            this->data = data;
+            this->freq = freq;
+        }
+    };
+
+    struct compare {
+        bool operator()(MinHeapNode* left, MinHeapNode* right) {
+            return (left->freq > right->freq);
+        }
+    };
+    void printCodes(struct MinHeapNode* root, string str) {
+        if (!root)
+            return;
+
+        if (root->data != '$')
+            cout << root->data << ": " << str << "\n";
+
+        printCodes(root->left, str + "0");
+        printCodes(root->right, str + "1");
+    }
+
+    void HuffmanCodes(char data[], int freq[], int size) {
+        struct MinHeapNode *left, *right, *top;
+        priority_queue<MinHeapNode*, vector<MinHeapNode*>, compare> minHeap;
+
+        for (int i = 0; i < size; ++i)
+            minHeap.push(new MinHeapNode(data[i], freq[i]));
+
+        while (minHeap.size() != 1) {
+            left = minHeap.top();
+            minHeap.pop();
+
+            right = minHeap.top();
+            minHeap.pop();
+
+            top = new MinHeapNode('$', left->freq + right->freq);
+
+            top->left = left;
+            top->right = right;
+
+            minHeap.push(top);
+        }
+        printCodes(minHeap.top(), "");
+    }
+
+    int main() {
+        char arr[] = {'a', 'b', 'c', 'd', 'e', 'f'};
+        int freq[] = {5, 9, 12, 13, 16, 45};
+        int size = sizeof(arr) / sizeof(arr[0]);
+
+        HuffmanCodes(arr, freq, size);
+
+        return 0;
+    }
+   ```
+
+  </TabItem>
+</Tabs>
+
+### Complexity Analysis
+
+- Time Complexity: $O(n \log n)$
+- Space Complexity: $O(n)$
+- Where `n` is the number of characters.
+- The time complexity is dominated by the operations on the min heap.
+- The space complexity is linear due to the storage of the Huffman Tree.
+
+## Video Explanation of Given Problem
+
+    <LiteYouTubeEmbed
+      id="uDS8AkTAcIU"
+      params="autoplay=1&autohide=1&showinfo=0&rel=0"
+      title="Problem Explanation | Solution | Approach"
+      poster="maxresdefault"
+      webp 
+    />
+
+---
+
+<h2>Authors:</h2>
+
+<div style={{display: 'flex', flexWrap: 'wrap', justifyContent: 'space-between', gap: '10px'}}>
+{['sjain1909'].map(username => (
+ <Author key={username} username={username} />
+))}
+</div>