subset_sum_all_approaches.py

knapsack/subset_sum_all_approaches.py

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+"""
+Given a set of integers and a target sum, determine if there exists a subset whose sum equals the target.
+Return True if such a subset exists, otherwise return False.
+"""
+------------------------------------------------------Recursion-Approach-------------------------------------------------------------------------
+
+def is_subset_sum_recursive(arr, n, target):
+ # Base cases
+ if target == 0:
+ return True
+ if n == 0:
+ return False
+
+ # If last element is greater than target, ignore it
+ if arr[n-1] > target:
+ return is_subset_sum_recursive(arr, n-1, target)
+
+ # Check if including or excluding the current item achieves the target
+ return is_subset_sum_recursive(arr, n-1, target) or is_subset_sum_recursive(arr, n-1, target - arr[n-1])
+
+arr = [3, 34, 4, 12, 5, 2]
+target = 9
+n = len(arr)
+print(is_subset_sum_recursive(arr, n, target)) # Output: True
+
+arr = [3, 34, 4, 12, 5, 2]
+target = 30
+n = len(arr)
+print(is_subset_sum_recursive(arr, n, target)) # Output: False
+
+-------------------------------------------------------Memoization-Approach-------------------------------------------------------------------------
+
+def is_subset_sum_memo(arr, n, target, memo):
+ # Base cases
+ if target == 0:
+ return True
+ if n == 0:
+ return False
+
+ # If this subproblem has already been solved
+ if memo[n][target] is not None:
+ return memo[n][target]
+
+ # If last element is greater than target, ignore it
+ if arr[n-1] > target:
+ memo[n][target] = subset_sum_memo(arr, n-1, target, memo)
+ else:
+ # Check if including or excluding the current item achieves the target
+ memo[n][target] = subset_sum_memo(arr, n-1, target, memo) or subset_sum_memo(arr, n-1, target - arr[n-1], memo)
+
+ return memo[n][target]
+
+# Helper function
+def subset_sum_memo_helper(arr, target):
+ n = len(arr)
+ memo = [[None] * (target + 1) for _ in range(n + 1)]
+ return is_subset_sum_memo(arr, n, target, memo)
+
+arr = [3, 34, 4, 12, 5, 2]
+target = 9
+print(subset_sum_memo_helper(arr, target)) # Output: True
+
+arr = [3, 34, 4, 12, 5, 2]
+target = 30
+print(subset_sum_memo_helper(arr, target)) # Output: False
+
+-------------------------------------------------------Top-Down-Approach--------------------------------------------------------------------
+
+def is_subset_sum_dp(arr, target):
+ n = len(arr)
+ # Create a (n+1) x (target+1) DP table
+ dp = [[False] * (target + 1) for _ in range(n + 1)]
+
+ # Initialize the table: If target is 0, answer is True
+ for i in range(n + 1):
+ dp[i][0] = True
+
+ # Fill the DP table
+ for i in range(1, n + 1):
+ for j in range(1, target + 1):
+ if arr[i-1] > j:
+ dp[i][j] = dp[i-1][j]
+ else:
+ dp[i][j] = dp[i-1][j] or dp[i-1][j - arr[i-1]]
+
+ return dp[n][target]
+
+arr = [3, 34, 4, 12, 5, 2]
+target = 9
+print(is_subset_sum_dp(arr, target)) # Output: True
+
+arr = [3, 34, 4, 12, 5, 2]
+target = 30
+print(is_subset_sum_dp(arr, target)) # Output: False