[sounmind] WEEK 6 SOLUTIONS

container-with-most-water/sounmind.py

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+from typing import List
+
+
+class Solution:
+    def maxArea(self, heights: List[int]) -> int:
+        """
+        Find the maximum area that can form a container with the most water.
+
+        Problem: Given n non-negative integers representing heights of vertical lines,
+        find two lines that together with the x-axis forms a container that holds the most water.
+
+        Approach:
+        - Use two pointers technique starting from both ends of the array
+        - Calculate area at each step and keep track of maximum
+        - Move the pointer with smaller height inward (since it limits the container height)
+
+        Proof of correctness:
+        - Every time we move a pointer, the width decreases by 1.
+        - Why we move the pointer with smaller height:
+          1) If we keep the smaller height and move the taller pointer instead,
+             the width decreases but the height remains limited by the smaller value,
+             so the area will always decrease.
+          2) However, if we move the pointer with smaller height, we might find a taller line.
+             In this case, even though width decreases, height might increase enough
+             to create a larger area.
+        - This way, we examine all possible combinations that could give us the maximum area.
+        - We only explore combinations that have the potential to create an area larger
+          than the maximum we've found so far.
+
+        Time Complexity: O(n) where n is the length of heights array
+        Space Complexity: O(1) using constant extra space
+
+        Args:
+            heights: List of heights of the vertical lines
+
+        Returns:
+            Maximum water area that can be contained
+        """
+        max_area = 0  # Initialize the maximum area to 0
+        left, right = 0, len(heights) - 1  # Start with leftmost and rightmost positions
+
+        # Continue until the pointers meet
+        while left < right:
+            # Calculate width between current lines (difference in positions)
+            width = right - left
+
+            # Height is limited by the shorter line
+            current_height = min(heights[left], heights[right])
+
+            # Calculate current area and update max_area if larger
+            current_area = width * current_height
+            max_area = max(max_area, current_area)
+
+            # Move the pointer with smaller height inward
+            # (Moving the smaller one gives potential for larger area since
+            # width will decrease but height might increase)
+            if heights[left] < heights[right]:
+                left += 1
+            else:
+                right -= 1
+
+        return max_area