Merge pull request #857 from siri-chandana-macha/new

Added more Problems in Dynamic programming

Algorithms_and_Data_Structures/Dynamic-Programming-Series/Basic-DP-Problems/Paint_House.py

@@ -0,0 +1,22 @@
+"""
+Problem: You are tasked with painting houses. Each house can be painted in one of k colors,
+and no two adjacent houses can have the same color. Find the minimum cost to paint all houses.
+"""
+def paint_house(costs):
+    if not costs:
+        return 0
+
+    n = len(costs)
+    k = len(costs[0])
+    dp = costs[0][:]
+
+    for i in range(1, n):
+        prev_dp = dp[:]
+        for j in range(k):
+            dp[j] = costs[i][j] + min(prev_dp[m] for m in range(k) if m != j)
+
+    return min(dp)
+
+# Example usage
+costs = [[17, 2, 17], [16, 16, 5], [14, 3, 19]]
+print(f"Minimum cost to paint all houses: {paint_house(costs)}")  # Output: Minimum cost to paint all houses: 10

Algorithms_and_Data_Structures/Dynamic-Programming-Series/Basic-DP-Problems/SubSet_Sum.py

@@ -0,0 +1,17 @@
+# Problem: Given a set of integers, find if there is a subset with sum equal to a given number.
+
+
+def subset_sum(nums, target):
+    dp = [False] * (target + 1)
+    dp[0] = True
+
+    for num in nums:
+        for i in range(target, num - 1, -1):
+            dp[i] = dp[i] or dp[i - num]
+
+    return dp[target]
+
+# Example usage
+nums = [3, 34, 4, 12, 5, 2]
+target = 9
+print(f"Is there a subset with sum {target}? {'Yes' if subset_sum(nums, target) else 'No'}")  # Output: Yes

Algorithms_and_Data_Structures/Dynamic-Programming-Series/Basic-DP-Problems/nth_tribonacci_num.py

@@ -0,0 +1,23 @@
+"""
+Problem: Similar to the Fibonacci sequence, the Tribonacci sequence is defined as:
+dp[n] = dp[n-1] + dp[n-2] + dp[n-3].
+Given n, find the N-th Tribonacci number.
+"""
+
+def tribonacci(n):
+    if n == 0:
+        return 0
+    elif n == 1 or n == 2:
+        return 1
+
+    dp = [0] * (n + 1)
+    dp[0], dp[1], dp[2] = 0, 1, 1
+
+    for i in range(3, n + 1):
+        dp[i] = dp[i - 1] + dp[i - 2] + dp[i - 3]
+
+    return dp[n]
+
+# Example usage
+n = 10
+print(f"The {n}-th Tribonacci number is: {tribonacci(n)}")  # Output: The 10-th Tribonacci number is: 149

Algorithms_and_Data_Structures/Dynamic-Programming-Series/Basic-DP-Problems/zero_one_knapsack.py

@@ -0,0 +1,25 @@
+# 0/1 Knapsack Problem Solution
+
+# Problem: Given n items with weight and value, find the maximum value you can carry in a knapsack of capacity W.
+
+def knapsack(weights, values, W):
+    n = len(weights)
+    # Create a 2D array to store maximum values
+    dp = [[0] * (W + 1) for _ in range(n + 1)]
+
+    # Fill the dp array
+    for i in range(1, n + 1):
+        for w in range(W + 1):
+            if weights[i - 1] <= w:
+                # Maximize value for the current item
+                dp[i][w] = max(dp[i - 1][w], values[i - 1] + dp[i - 1][w - weights[i - 1]])
+            else:
+                dp[i][w] = dp[i - 1][w]
+
+    return dp[n][W]
+
+# Example usage
+weights = [1, 2, 3]
+values = [10, 20, 30]
+W = 5
+print(f"Maximum value in Knapsack: {knapsack(weights, values, W)}")  # Output: Maximum value in Knapsack: 50

Project-Structure.md

@@ -85,11 +85,15 @@
     * [Test Main](Algorithms_and_Data_Structures/Dijkstra/test_main.py)
   * Dynamic-Programming-Series
     * Basic-Dp-Problems
+      * [Paint House](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Basic-DP-Problems/Paint_House.py)
+      * [Subset Sum](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Basic-DP-Problems/SubSet_Sum.py)
       * Best-Time-To-Buy-And-Sell-Stock
         * [Program](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Basic-DP-Problems/best-time-to-buy-and-sell-stock/program.py)
       * [Climbing-Stairs](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Basic-DP-Problems/climbing-stairs.py)
       * [Fibonacci-Seq](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Basic-DP-Problems/fibonacci-seq.py)
       * [House-Robber](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Basic-DP-Problems/house-robber.py)
+      * [Nth Tribonacci Num](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Basic-DP-Problems/nth_tribonacci_num.py)
+      * [Zero One Knapsack](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Basic-DP-Problems/zero_one_knapsack.py)
     * Hard-Dp-Problems
       * [Cherry-Pick-Algo](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Hard-DP-Problems/cherry-pick-algo.py)
       * [Levenshtein-Distance](Algorithms_and_Data_Structures/Dynamic-Programming-Series/Hard-DP-Problems/levenshtein-distance.py)