Add solutions for Combination Sum and Expression Add Operators

CombinationSum.py

@@ -0,0 +1,59 @@
+# Time Complexity : O(2^(m+n)) where m is the length of candidates and n is the target
+# Space Complexity : O(n)
+# Did this code successfully run on Leetcode : Yes
+# Any problem you faced while coding this : No
+
+# The approach is to do exhaustive solution to find all the path that match the target. Once we find the target
+# then add it to the result.
+
+class Solution:
+    def combinationSum01Recursion(self, candidates: List[int], target: int) -> List[List[int]]:
+        self.result = []
+        self.helper(candidates, 0, [], target)
+        return self.result
+
+    def helper(self, candidates, idx, path, target):
+        # Base case
+        if idx == len(candidates) or target < 0:
+            return
+        if target == 0:
+            self.result.append(list(path))
+            return
+        # Logic
+        # 0
+        self.helper(candidates, idx + 1, path, target)
+        # 1
+        path.append(candidates[idx])
+        self.helper(candidates, idx, path, target - candidates[idx])
+        # backtracking
+        path.pop()
+
+# Time Complexity : O(2^(m+n)) where m is the length of candidates and n is the target
+# Space Complexity : O(n)
+# Did this code successfully run on Leetcode : Yes
+# Any problem you faced while coding this : No
+
+#Almost similar approach as 01 with backtracking. Here we run a loop with a pivot and then chose the candidates and add to the path
+# and then subtract from the target for the next recursion step.
+
+class Solution:
+    def combinationSumIterativeRecursion(self, candidates: List[int], target: int) -> List[List[int]]:
+        self.result = []
+        self.helper(candidates, 0, [], target)
+        return self.result
+
+    def helper(self, candidates, pivot, path, target):
+
+        if target < 0:
+            return
+
+        if target == 0:
+            self.result.append(path.copy())
+
+        for i in range(pivot, len(candidates)):
+            # action
+            path.append(candidates[i])
+            # recurse
+            self.helper(candidates, i, path, target - candidates[i])
+            # backtrack
+            path.pop()

ExpressionAddOperators.py

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+# Time Complexity : O(4^n) nested recursion
+# Space Complexity : O(n^2)
+# Did this code successfully run on Leetcode : Yes
+# Any problem you faced while coding this : No
+
+# The approach is to split the numbers first and then for each number we have 3 options(+,- and *).
+# To do the calculation as runtime, we can use calc and tail which is the previous change to have the consideration of multiplication
+# as we have to give precedence to * before + and -
+
+
+class Solution:
+    def addOperatorsRecursion(self, num: str, target: int) -> List[str]:
+        result = []
+
+        def helper(pivot, calc, tail, path):
+
+            if pivot == len(num):
+                if target == calc:
+                    result.append(path)
+                return
+            # logic
+            for i in range(pivot, len(num)):
+                # Preceding 0
+                if (i != pivot and num[pivot] == '0'): continue
+                curr = int(num[pivot:i + 1])
+                if (pivot == 0):
+                    helper(i + 1, curr, curr, path + str(curr))
+                else:
+                    # three options
+                    # +
+                    helper(i + 1, calc + curr, +curr, path + "+" + str(curr))
+                    # -
+                    helper(i + 1, calc - curr, -curr, path + "-" + str(curr))
+                    # *
+                    helper(i + 1, calc - tail + tail * curr, tail * curr, path + "*" + str(curr))
+
+        helper(0, 0, 0, "")
+
+        return result
+
+# The time and space complexity is same. Just a bit of optimization using the path as list and later join before adding it to the result
+# Also because of that we have to do backtracking.
+class Solution:
+    def addOperators(self, num: str, target: int) -> List[str]:
+        result = []
+
+        def helper(pivot, calc, tail, path):
+            # Base case
+            if pivot == len(num):
+                if target == calc:
+                    result.append("".join(path))
+                return
+            # logic
+            for i in range(pivot, len(num)):
+                # Preceding 0
+                if (i != pivot and num[pivot] == '0'): continue
+                curr = int(num[pivot:i + 1])
+                if (pivot == 0):
+                    path.append(str(curr))
+                    helper(i + 1, curr, curr, path)
+                    path.pop()
+                else:
+                    # three options
+                    # +
+                    path.append("+")
+                    path.append(str(curr))
+                    helper(i + 1, calc + curr, +curr, path)
+                    path.pop()
+                    path.pop()
+                    # -
+                    path.append("-")
+                    path.append(str(curr))
+                    helper(i + 1, calc - curr, -curr, path)
+                    path.pop()
+                    path.pop()
+                    # *
+                    #action
+                    path.append("*")
+                    path.append(str(curr))
+                    #recurse
+                    helper(i + 1, calc - tail + tail * curr, tail * curr, path)
+                    #backtrack
+                    path.pop()
+                    path.pop()
+
+        helper(0, 0, 0, [])
+
+        return result