Issue #3 Subset Sum

dp/is_subset_sum.py

@@ -0,0 +1,65 @@
+"""
+Problem: https://en.wikipedia.org/wiki/Subset_sum_problem
+
+Given a set of integers, is there a non-empty subset whose sum is zero?
+
+>>> isSubsetSum([2, 4, 15, 11, 8], 34)
+True
+>>> isSubsetSum([2, 4, 15, 11, 8], 35)
+False
+>>> isSubsetSumRecursive([2, 4, 15, 11, 8], 34)
+True
+>>> isSubsetSumRecursive([2, 4, 15, 11, 8], 35)
+False
+"""
+
+def isSubsetSum(s, total):
+    """Returns true if there is a subset of s with sum total else false""" 
+    return isSubsetSumHelper(s, len(s), total)
+
+
+def isSubsetSumHelper(s, n, total):
+    """Helper function for dynamic programming implementation""" 
+
+    # The value of subset[i][j] will be true if there is a 
+    # subset of s[0..j-1] with sum equal to i 
+    subset = []
+    # If sum is 0, then answer is true 
+    for i in range(n + 1):
+        subset.append([True])
+
+    # If sum is not 0 and set is empty, then answer is false 
+    for i in range(1, total + 1): 
+      subset[0].append(False) 
+
+    # Fill the subset table in botton up manner 
+    for i in range(1, n + 1): 
+        for j in range(1, total + 1): 
+            if j < s[i-1]: 
+                subset[i].append(subset[i-1][j]) 
+            if j >= s[i-1]: 
+                subset[i].append(subset[i-1][j] or subset[i - 1][j-s[i-1]])
+    return subset[n][total]
+
+
+def isSubsetSumRecursive(s, total):
+    """Returns true if there is a subset of s with sum total else false"""
+    return isSubsetSumRecursiveHelper(s, len(s), total)
+
+
+def isSubsetSumRecursiveHelper(s, n, total): 
+    """Helper function for recursive implentation"""
+    # Base Cases
+    if (total == 0) : 
+        return True
+    if (n == 0 and total != 0) : 
+        return False
+
+    # If last element is greater than total, then ignore it 
+    if (s[n - 1] > total) : 
+        return isSubsetSumRecursiveHelper(s, n - 1, total); 
+
+    # else, check if total can be obtained by any of the following 
+    # (a) including the last element 
+    # (b) excluding the last element    
+    return isSubsetSumRecursiveHelper(s, n-1, total) or isSubsetSumRecursiveHelper(s, n-1, total-s[n-1])

tests/isSubsetSum_test

@@ -0,0 +1,16 @@
+import unittest
+from dp.is_subset_sum import isSubsetSum, isSubsetSumRecursive
+
+
+class test_issubsetsum(unittest.TestCase):
+    def test_isSubsetSum(self):
+        self.assertTrue(isSubsetSum([2, 4, 15, 11, 8], 34))
+        self.assertFalse(isSubsetSum([2, 4, 15, 11, 8], 35))
+
+    def test_isSubsetSumRecursive(self):
+        self.assertTrue(isSubsetSumRecursive([2, 4, 15, 11, 8], 34))
+        self.assertFalse(isSubsetSumRecursive([2, 4, 15, 11, 8], 35))
+
+
+if __name__ == "__main__":
+    unittest.main()