diff --git a/dynamic_programming/combinationfile.py b/dynamic_programming/combinationfile.py
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+++ b/dynamic_programming/combinationfile.py
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+"""
+The Algorithms - Python
+A comprehensive collection of algorithm implementations
+"""
+
+# ============================================================================
+# SORTING ALGORITHMS
+# ============================================================================
+
+
+def bubble_sort(arr):
+    """Bubble Sort - O(n^2)"""
+    n = len(arr)
+    for i in range(n):
+        swapped = False
+        for j in range(0, n - i - 1):
+            if arr[j] > arr[j + 1]:
+                arr[j], arr[j + 1] = arr[j + 1], arr[j]
+                swapped = True
+        if not swapped:
+            break
+    return arr
+
+
+def quick_sort(arr):
+    """Quick Sort - O(n log n) average"""
+    if len(arr) <= 1:
+        return arr
+    pivot = arr[len(arr) // 2]
+    left = [x for x in arr if x < pivot]
+    middle = [x for x in arr if x == pivot]
+    right = [x for x in arr if x > pivot]
+    return quick_sort(left) + middle + quick_sort(right)
+
+
+def merge_sort(arr):
+    """Merge Sort - O(n log n)"""
+    if len(arr) <= 1:
+        return arr
+
+    mid = len(arr) // 2
+    left = merge_sort(arr[:mid])
+    right = merge_sort(arr[mid:])
+
+    return merge(left, right)
+
+
+def merge(left, right):
+    """Helper function for merge sort"""
+    result = []
+    i = j = 0
+
+    while i < len(left) and j < len(right):
+        if left[i] <= right[j]:
+            result.append(left[i])
+            i += 1
+        else:
+            result.append(right[j])
+            j += 1
+
+    result.extend(left[i:])
+    result.extend(right[j:])
+    return result
+
+
+def insertion_sort(arr):
+    """Insertion Sort - O(n^2)"""
+    for i in range(1, len(arr)):
+        key = arr[i]
+        j = i - 1
+        while j >= 0 and arr[j] > key:
+            arr[j + 1] = arr[j]
+            j -= 1
+        arr[j + 1] = key
+    return arr
+
+
+# ============================================================================
+# SEARCHING ALGORITHMS
+# ============================================================================
+
+
+def binary_search(arr, target):
+    """Binary Search - O(log n) - requires sorted array"""
+    left, right = 0, len(arr) - 1
+
+    while left <= right:
+        mid = (left + right) // 2
+        if arr[mid] == target:
+            return mid
+        elif arr[mid] < target:
+            left = mid + 1
+        else:
+            right = mid - 1
+
+    return -1
+
+
+def linear_search(arr, target):
+    """Linear Search - O(n)"""
+    for i, val in enumerate(arr):
+        if val == target:
+            return i
+    return -1
+
+
+def jump_search(arr, target):
+    """Jump Search - O(√n) - requires sorted array"""
+    import math
+
+    n = len(arr)
+    step = int(math.sqrt(n))
+    prev = 0
+
+    while arr[min(step, n) - 1] < target:
+        prev = step
+        step += int(math.sqrt(n))
+        if prev >= n:
+            return -1
+
+    while arr[prev] < target:
+        prev += 1
+        if prev == min(step, n):
+            return -1
+
+    if arr[prev] == target:
+        return prev
+
+    return -1
+
+
+# ============================================================================
+# GRAPH ALGORITHMS
+# ============================================================================
+
+
+def bfs(graph, start):
+    """Breadth-First Search"""
+    visited = set()
+    queue = [start]
+    result = []
+
+    while queue:
+        vertex = queue.pop(0)
+        if vertex not in visited:
+            visited.add(vertex)
+            result.append(vertex)
+            queue.extend([n for n in graph[vertex] if n not in visited])
+
+    return result
+
+
+def dfs(graph, start, visited=None):
+    """Depth-First Search"""
+    if visited is None:
+        visited = set()
+
+    visited.add(start)
+    result = [start]
+
+    for neighbor in graph[start]:
+        if neighbor not in visited:
+            result.extend(dfs(graph, neighbor, visited))
+
+    return result
+
+
+def dijkstra(graph, start):
+    """Dijkstra's Shortest Path Algorithm"""
+    import heapq
+
+    distances = {node: float("inf") for node in graph}
+    distances[start] = 0
+    pq = [(0, start)]
+    visited = set()
+
+    while pq:
+        curr_dist, curr_node = heapq.heappop(pq)
+
+        if curr_node in visited:
+            continue
+
+        visited.add(curr_node)
+
+        for neighbor, weight in graph[curr_node].items():
+            distance = curr_dist + weight
+
+            if distance < distances[neighbor]:
+                distances[neighbor] = distance
+                heapq.heappush(pq, (distance, neighbor))
+
+    return distances
+
+
+# ============================================================================
+# DYNAMIC PROGRAMMING
+# ============================================================================
+
+
+def fibonacci(n, memo={}):
+    """Fibonacci with Memoization - O(n)"""
+    if n in memo:
+        return memo[n]
+    if n <= 2:
+        return 1
+
+    memo[n] = fibonacci(n - 1, memo) + fibonacci(n - 2, memo)
+    return memo[n]
+
+
+def knapsack(weights, values, capacity):
+    """0/1 Knapsack Problem"""
+    n = len(weights)
+    dp = [[0] * (capacity + 1) for _ in range(n + 1)]
+
+    for i in range(1, n + 1):
+        for w in range(1, capacity + 1):
+            if weights[i - 1] <= w:
+                dp[i][w] = max(
+                    values[i - 1] + dp[i - 1][w - weights[i - 1]], dp[i - 1][w]
+                )
+            else:
+                dp[i][w] = dp[i - 1][w]
+
+    return dp[n][capacity]
+
+
+def longest_common_subsequence(s1, s2):
+    """Longest Common Subsequence"""
+    m, n = len(s1), len(s2)
+    dp = [[0] * (n + 1) for _ in range(m + 1)]
+
+    for i in range(1, m + 1):
+        for j in range(1, n + 1):
+            if s1[i - 1] == s2[j - 1]:
+                dp[i][j] = dp[i - 1][j - 1] + 1
+            else:
+                dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
+
+    return dp[m][n]
+
+
+# ============================================================================
+# STRING ALGORITHMS
+# ============================================================================
+
+
+def kmp_search(text, pattern):
+    """Knuth-Morris-Pratt String Matching"""
+
+    def compute_lps(pattern):
+        lps = [0] * len(pattern)
+        length = 0
+        i = 1
+
+        while i < len(pattern):
+            if pattern[i] == pattern[length]:
+                length += 1
+                lps[i] = length
+                i += 1
+            else:
+                if length != 0:
+                    length = lps[length - 1]
+                else:
+                    lps[i] = 0
+                    i += 1
+        return lps
+
+    lps = compute_lps(pattern)
+    i = j = 0
+    indices = []
+
+    while i < len(text):
+        if pattern[j] == text[i]:
+            i += 1
+            j += 1
+
+        if j == len(pattern):
+            indices.append(i - j)
+            j = lps[j - 1]
+        elif i < len(text) and pattern[j] != text[i]:
+            if j != 0:
+                j = lps[j - 1]
+            else:
+                i += 1
+
+    return indices
+
+
+def is_palindrome(s):
+    """Check if string is palindrome"""
+    return s == s[::-1]
+
+
+# ============================================================================
+# MATHEMATICAL ALGORITHMS
+# ============================================================================
+
+
+def gcd(a, b):
+    """Greatest Common Divisor - Euclidean Algorithm"""
+    while b:
+        a, b = b, a % b
+    return a
+
+
+def lcm(a, b):
+    """Least Common Multiple"""
+    return abs(a * b) // gcd(a, b)
+
+
+def is_prime(n):
+    """Check if number is prime"""
+    if n < 2:
+        return False
+    if n == 2:
+        return True
+    if n % 2 == 0:
+        return False
+
+    for i in range(3, int(n**0.5) + 1, 2):
+        if n % i == 0:
+            return False
+    return True
+
+
+def sieve_of_eratosthenes(limit):
+    """Generate all primes up to limit"""
+    primes = [True] * (limit + 1)
+    primes[0] = primes[1] = False
+
+    for i in range(2, int(limit**0.5) + 1):
+        if primes[i]:
+            for j in range(i * i, limit + 1, i):
+                primes[j] = False
+
+    return [i for i in range(limit + 1) if primes[i]]
+
+
+def power(base, exp):
+    """Fast Exponentiation - O(log n)"""
+    if exp == 0:
+        return 1
+    if exp == 1:
+        return base
+
+    if exp % 2 == 0:
+        half = power(base, exp // 2)
+        return half * half
+    else:
+        return base * power(base, exp - 1)
+
+
+# ============================================================================
+# DATA STRUCTURE IMPLEMENTATIONS
+# ============================================================================
+
+
+class Stack:
+    """Stack Implementation"""
+
+    def __init__(self):
+        self.items = []
+
+    def push(self, item):
+        self.items.append(item)
+
+    def pop(self):
+        return self.items.pop() if self.items else None
+
+    def peek(self):
+        return self.items[-1] if self.items else None
+
+    def is_empty(self):
+        return len(self.items) == 0
+
+
+class Queue:
+    """Queue Implementation"""
+
+    def __init__(self):
+        self.items = []
+
+    def enqueue(self, item):
+        self.items.append(item)
+
+    def dequeue(self):
+        return self.items.pop(0) if self.items else None
+
+    def is_empty(self):
+        return len(self.items) == 0
+
+
+# ============================================================================
+# DEMONSTRATION
+# ============================================================================
+
+if __name__ == "__main__":
+    print("=" * 60)
+    print("THE ALGORITHMS - PYTHON IMPLEMENTATION")
+    print("=" * 60)
+
+    # Sorting
+    print("\n--- SORTING ALGORITHMS ---")
+    arr = [64, 34, 25, 12, 22, 11, 90]
+    print(f"Original: {arr}")
+    print(f"Quick Sort: {quick_sort(arr.copy())}")
+    print(f"Merge Sort: {merge_sort(arr.copy())}")
+
+    # Searching
+    print("\n--- SEARCHING ALGORITHMS ---")
+    sorted_arr = [1, 3, 5, 7, 9, 11, 13, 15]
+    target = 7
+    print(f"Array: {sorted_arr}, Target: {target}")
+    print(f"Binary Search: Index {binary_search(sorted_arr, target)}")
+
+    # Graph Algorithms
+    print("\n--- GRAPH ALGORITHMS ---")
+    graph = {
+        "A": ["B", "C"],
+        "B": ["A", "D", "E"],
+        "C": ["A", "F"],
+        "D": ["B"],
+        "E": ["B", "F"],
+        "F": ["C", "E"],
+    }
+    print(f"BFS from 'A': {bfs(graph, 'A')}")
+    print(f"DFS from 'A': {dfs(graph, 'A')}")
+
+    # Dynamic Programming
+    print("\n--- DYNAMIC PROGRAMMING ---")
+    print(f"Fibonacci(10): {fibonacci(10)}")
+    print(f"LCS('ABCDGH', 'AEDFHR'): {longest_common_subsequence('ABCDGH', 'AEDFHR')}")
+
+    # Mathematical
+    print("\n--- MATHEMATICAL ALGORITHMS ---")
+    print(f"GCD(48, 18): {gcd(48, 18)}")
+    print(f"Is 17 prime? {is_prime(17)}")
+    print(f"Primes up to 30: {sieve_of_eratosthenes(30)}")
+
+    print("\n" + "=" * 60)