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0678-valid-parenthesis-string/0678-valid-parenthesis-string.py

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+class Solution:
+    def checkValidString(self, s: str) -> bool:
+        """
+        Complexities:
+        Time:  O(n)
+        Space: O(n)
+
+        where n = len(s)
+        """
+
+        bracketCount = 0
+        starCount = 0
+        starIndecies = []
+        usedStars = 0
+
+        # Forward pass - allocate as many *s to be (
+        # - when allocating a star, always use the star that appears first
+        for i, l in enumerate(s):
+            if l == '(':
+                bracketCount += 1
+            elif l == '*':
+                starCount += 1
+                starIndecies.append(i)
+            elif bracketCount > 0:
+                bracketCount -= 1
+            elif starCount > 0:
+                starCount -= 1
+                usedStars += 1
+            else:
+                return False
+
+        # There are already matching opening/closing brackets
+        # - all stars are assigned empty string
+        if bracketCount == 0:
+            return True
+
+        # There are more closed brackets needed than the amount of remaining stars
+        if bracketCount > 0 and bracketCount > starCount:
+            return False
+
+        # Backward pass - allocate as many *s to be )
+        # - the first `usedStars` stars are considered used from the forward pass
+        firstViableStar = starIndecies[usedStars]
+        bracketCount = 0
+        starCount = 0
+        for i in range(len(s) - 1, 0, -1):
+            l = s[i]
+
+            if l == ')':
+                bracketCount += 1
+            elif l == '*':
+                starCount += 1 if i >= firstViableStar else 0
+            elif bracketCount > 0:
+                bracketCount -= 1
+            elif starCount > 0:
+                starIndecies.pop(0)
+                starCount -= 1
+            else:
+                return False
+
+        return True