Upload end-sem pyq for DAA, november-december 2025. Provided by Ayush Kalaskar.

Codes/C++/Code-A1 (Fibonacci).cpp

@@ -0,0 +1,64 @@
+// Code-A1 (Fibonacci)
+
+#include <iostream>
+using namespace std;
+
+int recursiveSteps = 0;
+int iterativeSteps = 0;
+
+// Recursive function for Fibonacci
+int fibRecursive(int n) {
+    recursiveSteps++;
+    if (n <= 1)
+        return n;  
+    return fibRecursive(n - 1) + fibRecursive(n - 2);
+}
+
+// Non-recursive (Iterative) Fibonacci
+void fibIterative(int n) {
+    if (n <= 0)
+        return;
+    int prev = 0, curr = 1, next;
+    cout << prev << " ";
+    if (n == 1)
+        return;
+
+    cout << curr << " ";
+    for (int i = 2; i < n; i++) {
+        next = prev + curr;
+        cout << next << " ";
+        prev = curr;
+        curr = next;
+        iterativeSteps++;
+    }
+}
+
+int main() {
+    int n;
+    cout << "Enter the number of terms: ";
+    cin >> n;
+
+    cout << "\nFibonacci Series using Recursion: ";
+    for (int i = 0; i < n; i++) {
+        cout << fibRecursive(i) << " ";
+    }
+    cout << "\nTotal Recursive Steps: " << recursiveSteps;
+
+    cout << "\n\nFibonacci Series using Iteration: ";
+    fibIterative(n);
+    cout << "\nTotal Iterative Steps: " << iterativeSteps;
+
+    cout << endl;
+    return 0;
+}
+
+// SAMPLE OUTOUT
+/*
+* Enter the number of terms: 5
+* 
+* Fibonacci Series using Recursion: 0 1 1 2 3 
+* Total Recursive Steps: 19
+* 
+* Fibonacci Series using Iteration: 0 1 1 2 3 
+* Total Iterative Steps: 3
+*/

Codes/C++/Code-A2 (Huffman Coding).cpp

@@ -0,0 +1,102 @@
+// Code-A2 (Huffman Coding)
+
+#include <iostream>
+#include <queue>
+#include <vector>
+#include <string>
+using namespace std;
+
+// A Huffman Tree node
+struct Node {
+    char ch;
+    int freq;
+    Node *left, *right;
+
+    Node(char c, int f) {
+        ch = c;
+        freq = f;
+        left = right = nullptr;
+    }
+};
+
+// Compare function for priority queue (min-heap)
+struct Compare {
+    bool operator()(Node* a, Node* b) {
+        return a->freq > b->freq; // smaller frequency => higher priority
+    }
+};
+
+// Recursive function to print Huffman Codes
+void printCodes(Node* root, string code) {
+    if (!root) return;
+
+    // Leaf node -> contains a character
+    if (!root->left && !root->right)
+        cout << root->ch << " : " << code << endl;
+
+    printCodes(root->left, code + "0");
+    printCodes(root->right, code + "1");
+}
+
+// Main function to build Huffman Tree and generate codes
+void huffmanEncoding(vector<char>& chars, vector<int>& freq) {
+    priority_queue<Node*, vector<Node*>, Compare> pq;
+
+    // Step 1: Create a leaf node for each character and add it to the queue
+    for (int i = 0; i < chars.size(); i++)
+        pq.push(new Node(chars[i], freq[i]));
+
+    // Step 2: Repeat until one node remains (the root)
+    while (pq.size() > 1) {
+        Node* left = pq.top(); pq.pop();
+        Node* right = pq.top(); pq.pop();
+
+        // Create new internal node with sum of two smallest frequencies
+        Node* newNode = new Node('-', left->freq + right->freq);
+        newNode->left = left;
+        newNode->right = right;
+
+        pq.push(newNode);
+    }
+
+    // Step 3: Print the Huffman codes
+    Node* root = pq.top();
+    cout << "\nHuffman Codes:\n";
+    printCodes(root, "");
+}
+
+int main() {
+    int n;
+    cout << "Enter number of characters: ";
+    cin >> n;
+
+    vector<char> chars(n);
+    vector<int> freq(n);
+
+    cout << "Enter characters: ";
+    for (int i = 0; i < n; i++)
+        cin >> chars[i];
+
+    cout << "Enter corresponding frequencies: ";
+    for (int i = 0; i < n; i++)
+        cin >> freq[i];
+
+    huffmanEncoding(chars, freq);
+
+    return 0;
+}
+
+// SAMPLE OUTPUT
+/*
+* $ ./a.out 
+* Enter number of characters: 5   
+* Enter characters: a f v c w 
+* Enter corresponding frequencies: 3 2 1 5 7 
+* 
+* Huffman Codes:
+* w : 0
+* c : 10
+* a : 110
+* v : 1110
+* f : 1111
+*/

Codes/C++/Code-A3 (Fractical Knapsack).cpp

@@ -0,0 +1,72 @@
+// Code-A3 (Fractical Knapsack)
+
+#include <iostream>
+#include <vector>
+#include <algorithm>
+using namespace std;
+
+// Structure for an item
+struct Item {
+    int weight;
+    int value;
+};
+
+// Comparison function to sort items by value/weight ratio
+bool compare(Item a, Item b) {
+    double r1 = (double)a.value / a.weight;
+    double r2 = (double)b.value / b.weight;
+    return r1 > r2; // Sort in descending order
+}
+
+double fractionalKnapsack(int W, vector<Item>& items) {
+    // Sort items by value-to-weight ratio
+    sort(items.begin(), items.end(), compare);
+
+    double totalValue = 0.0; // Total value in knapsack
+    for (auto &i : items) {
+        if (W == 0) break; // Knapsack is full
+
+        // If item can be fully taken
+        if (i.weight <= W) {
+            W -= i.weight;
+            totalValue += i.value;
+        } else {
+            // Take fraction of item
+            totalValue += i.value * ((double)W / i.weight);
+            W = 0;
+        }
+    }
+    return totalValue;
+}
+
+int main() {
+    int n, W;
+    cout << "Enter number of items: ";
+    cin >> n;
+
+    vector<Item> items(n);
+    cout << "Enter value and weight of each item:\n";
+    for (int i = 0; i < n; i++)
+        cin >> items[i].value >> items[i].weight;
+
+    cout << "Enter capacity of knapsack: ";
+    cin >> W;
+
+    double maxValue = fractionalKnapsack(W, items);
+    cout << "\nMaximum value in knapsack = " << maxValue << endl;
+
+    return 0;
+}
+
+// SAMPLE OUTPUT
+/*
+* $ ./a.out 
+* Enter number of items: 3
+* Enter value and weight of each item:
+* 12 32
+* 56 67
+* 23 87
+* Enter capacity of knapsack: 45
+* 
+* Maximum value in knapsack = 37.6119
+*/

Codes/C++/Code-A4 (0-1 Knapsack).cpp

@@ -0,0 +1,60 @@
+// Code-A4 (0-1 Knapsack)
+
+#include <iostream>
+#include <vector>
+using namespace std;
+
+int knapsack(int W, vector<int>& wt, vector<int>& val, int n) {
+    // dp[i][w] = max value for first i items with weight limit w
+    vector<vector<int>> dp(n + 1, vector<int>(W + 1, 0));
+
+    // Build the table dp[][] bottom-up
+    for (int i = 1; i <= n; i++) {
+        for (int w = 1; w <= W; w++) {
+            if (wt[i - 1] <= w)
+                dp[i][w] = max(val[i - 1] + dp[i - 1][w - wt[i - 1]], dp[i - 1][w]);
+            else
+                dp[i][w] = dp[i - 1][w];
+        }
+    }
+
+    return dp[n][W]; // The bottom-right cell gives the result
+}
+
+int main() {
+    int n, W;
+    cout << "Enter number of items: ";
+    cin >> n;
+
+    vector<int> val(n), wt(n);
+    cout << "Enter values of items:\n";
+    for (int i = 0; i < n; i++) cin >> val[i];
+
+    cout << "Enter weights of items:\n";
+    for (int i = 0; i < n; i++) cin >> wt[i];
+
+    cout << "Enter capacity of knapsack: ";
+    cin >> W;
+
+    int maxValue = knapsack(W, wt, val, n);
+    cout << "\nMaximum value in knapsack = " << maxValue << endl;
+
+    return 0;
+}
+
+// SAMPLE OUTPUT
+/*
+* $ ./a.out 
+* Enter number of items: 3
+* Enter values of items:
+* 12
+* 32
+* 14
+* Enter weights of items:
+* 45
+* 34
+* 65
+* Enter capacity of knapsack: 60
+* 
+* Maximum value in knapsack = 32
+*/

Codes/C++/Code-A5 (N-Queen).cpp

@@ -0,0 +1,86 @@
+// Code-A5 (N-Queen)
+
+#include <iostream>
+#include <vector>
+using namespace std;
+
+// Function to print the board
+void printBoard(vector<vector<int>>& board, int n) {
+    for (int i = 0; i < n; i++) {
+        for (int j = 0; j < n; j++)
+            cout << board[i][j] << " ";
+        cout << endl;
+    }
+    cout << endl;
+}
+
+// Function to check if placing a queen is safe
+bool isSafe(vector<vector<int>>& board, int row, int col, int n) {
+    // Check column
+    for (int i = 0; i < row; i++)
+        if (board[i][col]) return false;
+
+    // Check upper left diagonal
+    for (int i = row - 1, j = col - 1; i >= 0 && j >= 0; i--, j--)
+        if (board[i][j]) return false;
+
+    // Check upper right diagonal
+    for (int i = row - 1, j = col + 1; i >= 0 && j < n; i--, j++)
+        if (board[i][j]) return false;
+
+    return true;
+}
+
+// Backtracking function
+bool solveNQueens(vector<vector<int>>& board, int row, int n) {
+    if (row == n) {
+        printBoard(board, n); // Print one valid arrangement
+        return true;
+    }
+
+    for (int col = 0; col < n; col++) {
+        if (isSafe(board, row, col, n)) {
+            board[row][col] = 1; // Place queen
+            solveNQueens(board, row + 1, n);
+            board[row][col] = 0; // Backtrack
+        }
+    }
+    return false;
+}
+
+int main() {
+    int n, firstRow, firstCol;
+    cout << "Enter size of board (N): ";
+    cin >> n;
+
+    vector<vector<int>> board(n, vector<int>(n, 0));
+
+    cout << "Enter position of first queen (row and column index starting from 0): ";
+    cin >> firstRow >> firstCol;
+
+    // Place first queen
+    board[firstRow][firstCol] = 1;
+
+    cout << "\nAll possible solutions:\n";
+    solveNQueens(board, 0, n); // Start solving from row 0
+
+    return 0;
+}
+
+// SAMPLE OUTPUT
+/*
+* $ ./a.out 
+* Enter size of board (N): 4
+* Enter position of first queen (row and column index starting from 0): 0 0
+* 
+* All possible solutions:
+* 0 1 0 0 
+* 0 0 0 1 
+* 1 0 0 0 
+* 0 0 1 0 
+* 
+* 0 0 1 0 
+* 1 0 0 0 
+* 0 0 0 1 
+* 0 1 0 0 
+*/

Codes/Code-A1.py

@@ -1,33 +1,50 @@
+# Code-A1 (Fibonacci)
 # Problem Statement: Write a program non-recursive and recursive program to calculate Fibonacci numbers and analyze their time and space complexity.
 
-# Non-recursion
-def fibonacci(n):
-    fib_series = []
-    a = 0
-    b = 1
+# Initalize global variables
+iteration_counter = 0
+recursion_counter = 0
 
-    for i in range(n):
-        fib_series.append(a)
-        a, b = b, a + b
+# Iteration
+def fibonacci_iteration(n):
+  fib_series = []           # For storing Fibonacci series
+  previous = 0              # Previous
+  current = 1               # Next
+  global iteration_counter  # Global iteration counter
+  iteration_counter = 0     # Initialize global iteration counter to 0
 
-    return fib_series
+  for i in range(n):
+    fib_series.append(previous)
+    previous, current = current, previous + current
+    iteration_counter += 1
+
+  return fib_series
 
 # Recursion
-def fibonacci_recursive(n):
-    if n <= 0:
-        return []
-    elif n == 1:
-        return [0]
-    elif n == 2:
-        return [0, 1]
-    else:
-        fib_series = fibonacci_recursive(n - 1)  # Get the series up to n-1
-        fib_series.append(fib_series[-1] + fib_series[-2])  # Append the next Fibonacci number
-        return fib_series
+def fibonacci_recursion(n):
+  global recursion_counter # Global recursion counter
+  recursion_counter += 1   # Increment recursion counter for each call
+
+  if (n <= 0):    # Handle n less than or equal to 0
+    return 0
+  elif (n <= 1):  # Handle n less than or equal to 1
+    return n
+  else:           # Recursive call
+    return fibonacci_recursion(n - 1) + fibonacci_recursion(n - 2)
 
-# Non-recursion
 n = int(input("Enter total numbers to print in fibonacci series:\t"))
-print("Fibonacci Series (non-recusive):\t", fibonacci(n))
 
-# Recursion
-print("Fibonacci Series (recusive):\t\t", fibonacci_recursive(n))
+# Fibonacci using iteration
+fib_series = fibonacci_iteration(n)
+print(f"Fibonacci using iteration:\t{fib_series}")
+print(f"Iteration counter:\t{iteration_counter}| Time Complexity: O(n) (linear growth)")
+
+print("="*80)
+
+# Fibonacci using recursion
+fib_series = []
+for i in range(n):
+  fib_series.append(fibonacci_recursion(i))
+print(f"Fibonacci using recursion:\t{fib_series}")
+print(f"Recursion counter:\t{recursion_counter} | Time Complexity: O(2^n) (exponential growth)")
+

Codes/Python/Code-A1-optimized.py

@@ -0,0 +1,46 @@
+# Problem Statement: Write a program non-recursive and recursive program to calculate Fibonacci numbers and analyze their time and space complexity.
+
+## NOTE: THIS IS A HEAVILY OPTIMIZED CODE FOR FIBONACCI.
+## NUMBER OF RECURSION CALLS (IN RECURSION) ARE LOWER THAN NUMBER OF ITERATIONS (IN ITERATION FUNCTION)
+
+iteration_counter = 0
+recursion_counter = 0
+
+# Non-recursion
+def fibonacci(n):
+    global iteration_counter
+    fib_series = []
+    a = 0
+    b = 1
+
+    for i in range(n):
+        fib_series.append(a)
+        a, b = b, a + b
+        iteration_counter += 1
+
+    return fib_series
+
+# Recursion
+def fibonacci_recursive(n):
+    global recursion_counter
+    recursion_counter += 1
+    if n <= 0:
+        return []
+    elif n == 1:
+        return [0]
+    elif n == 2:
+        return [0, 1]
+    else:
+        fib_series = fibonacci_recursive(n - 1)  # Get the series up to n-1
+        fib_series.append(fib_series[-1] + fib_series[-2])  # Append the next Fibonacci number
+        return fib_series
+
+# Non-recursion
+n = int(input("Enter total numbers to print in fibonacci series:\t"))
+print("Fibonacci Series (non-recusive):\t", fibonacci(n))
+print("Iteration counter:\t", iteration_counter)
+
+# Recursion
+print("Fibonacci Series (recusive):\t\t", fibonacci_recursive(n))
+print("Recursion counter:\t", recursion_counter)
+

Codes/Python/Code-A2 (Huffman Coding).py

@@ -0,0 +1,95 @@
+# Code-A2 (Huffman Coding)
+
+import heapq
+
+# Node class for Huffman Tree
+class Node:
+    def __init__(self, char, freq):
+        self.char = char
+        self.freq = freq
+        self.left = None
+        self.right = None
+
+    # Comparison function for priority queue
+    def __lt__(self, other):
+        return self.freq < other.freq
+
+
+# Function to build Huffman Tree
+def build_huffman_tree(char_freq):
+    heap = [Node(ch, freq) for ch, freq in char_freq.items()]
+    heapq.heapify(heap)
+
+    while len(heap) > 1:
+        # Pick two smallest nodes (greedy choice)
+        left = heapq.heappop(heap)
+        right = heapq.heappop(heap)
+
+        # Merge them into a new node
+        merged = Node(None, left.freq + right.freq)
+        merged.left = left
+        merged.right = right
+
+        heapq.heappush(heap, merged)
+
+    return heap[0]
+
+
+# Function to generate Huffman codes
+def generate_codes(root, current_code="", codes={}):
+    if root is None:
+        return
+
+    if root.char is not None:
+        codes[root.char] = current_code
+
+    generate_codes(root.left, current_code + "0", codes)
+    generate_codes(root.right, current_code + "1", codes)
+    return codes
+
+
+# Main program
+text = input("Enter text to encode: ")
+
+# Step 1: Calculate frequency of each character
+freq = {}
+for ch in text:
+    freq[ch] = freq.get(ch, 0) + 1
+
+# Step 2: Build Huffman Tree using greedy approach
+root = build_huffman_tree(freq)
+
+# Step 3: Generate Huffman Codes
+codes = generate_codes(root)
+
+# Step 4: Encode the text
+encoded_text = "".join(codes[ch] for ch in text)
+
+# Step 5: Display results
+print("\nCharacter | Frequency | Huffman Code")
+print("------------------------------------")
+for ch in freq:
+    print(f"    {ch!r}     |     {freq[ch]}      |    {codes[ch]}")
+
+print("\nEncoded Text:", encoded_text)
+
+# SAMPLE OUTPUT
+"""
+Enter text to encode: lord kska git
+
+Character | Frequency | Huffman Code
+------------------------------------
+    'l'     |     1      |    1100
+    'o'     |     1      |    1101
+    'r'     |     1      |    001
+    'd'     |     1      |    1010
+    ' '     |     2      |    011
+    'k'     |     2      |    100
+    's'     |     1      |    000
+    'a'     |     1      |    010
+    'g'     |     1      |    1011
+    'i'     |     1      |    1111
+    't'     |     1      |    1110
+
+Encoded Text: 110011010011010011100000100010011101111111110
+"""

Codes/Python/Code-A5 (N-Queen).py

@@ -0,0 +1,74 @@
+# Code-A5 (N-Queen)
+
+def print_board(board, n):
+    for i in range(n):
+        for j in range(n):
+            print(board[i][j], end=" ")
+        print()
+    print()  # blank line between solutions
+
+
+def is_safe(board, row, col, n):
+    # Check column
+    for i in range(row):
+        if board[i][col] == 1:
+            return False
+
+    # Check upper-left diagonal
+    i, j = row, col
+    while i >= 0 and j >= 0:
+        if board[i][j] == 1:
+            return False
+        i -= 1
+        j -= 1
+
+    # Check upper-right diagonal
+    i, j = row, col
+    while i >= 0 and j < n:
+        if board[i][j] == 1:
+            return False
+        i -= 1
+        j += 1
+
+    return True
+
+
+def solve_n_queens(board, row, n):
+    if row == n:
+        print_board(board, n)
+        return True
+
+    res = False
+    for col in range(n):
+        if is_safe(board, row, col, n):
+            board[row][col] = 1
+            res = solve_n_queens(board, row + 1, n) or res
+            board[row][col] = 0  # backtrack
+
+    return res
+
+
+# Main program
+n = int(input("Enter number of queens: "))
+board = [[0 for _ in range(n)] for _ in range(n)]
+
+print(f"\nSolutions for {n}-Queens Problem:\n")
+if not solve_n_queens(board, 0, n):
+    print("No solution exists!")
+
+# SAMPLE OUTPUT
+"""
+Enter number of queens: 4
+
+Solutions for 4-Queens Problem:
+
+0 1 0 0 
+0 0 0 1 
+1 0 0 0 
+0 0 1 0 
+
+0 0 1 0 
+1 0 0 0 
+0 0 0 1 
+0 1 0 0 
+"""

README.md

@@ -23,6 +23,10 @@ This repository contains valuable resources for the Design and Analysis of Algor
 4. [Code-A4 - 0/1 Knapsack](Codes/Code_A4.java)
 5. [Code-A5 - N-Queen Problem](Codes/Code-A5.py)
 
+> [!NOTE]
+> C++ versions of all codes are available in the [./Codes/C++](./Codes/C++) directory.
+> Python version of some codes are available in [./Codes/Python](./Codes/Python) directory.
+
 ### Practical
 
 1. [Practical-1](Practical/Practical-1)
@@ -37,6 +41,7 @@ This repository contains valuable resources for the Design and Analysis of Algor
 - [END-SEM](Question%20Papers/END-SEM)
 
 ### [IN-SEM PYQ Answers](Notes/IN-SEM%20PYQ%20Answers)
+### [END-SEM PYQ Answers](Notes/END-SEM%20PYQ%20Answers)
 
 ---