11def max_area (height : list [int ]) -> int :
2+ """
3+ Calculate the maximum area of water a container can store, formed by two lines
4+ from the given list of heights and the x-axis.
5+
6+ Parameters:
7+ height (list[int]): A list of integers representing the heights of vertical lines.
8+
9+ Returns:
10+ int: The maximum area of water that can be contained.
11+
12+ """
213 left = 0
314 right = len (height ) - 1
415 max_area = 0
516
617 while left < right :
18+ # Calculate the height and width of the current container
719 curr_height = min (height [left ], height [right ])
820 curr_width = right - left
921 curr_area = curr_height * curr_width
1022
23+ # Update max_area if the current area is larger
1124 max_area = max (curr_area , max_area )
1225
26+ # Move the pointer pointing to the shorter line
1327 if height [left ] < height [right ]:
1428 left += 1
1529 else :
1630 right -= 1
1731
1832 return max_area
19- 33+ 34+ # Approach and Reasoning:
35+ # -----------------------
36+ # - We use the two-pointer technique to solve this problem efficiently.
37+ # - Initialize two pointers, `left` at the start and `right` at the end of the list.
38+ # - The width of the container is the distance between the two pointers.
39+ # - The height of the container is determined by the shorter of the two lines at the pointers.
40+ # - Calculate the area for the current pair of lines and update `max_area` if this area is larger.
41+ # - Move the pointer pointing to the shorter line inward to potentially find a taller line,
42+ # which might result in a larger area.
43+ # - Repeat the process until the two pointers meet.
44+ 45+ # Time Complexity:
46+ # ----------------
47+ # - The time complexity of this approach is O(n), where n is the number of elements in the `height` list.
48+ # - This is because each element is processed at most once as the pointers move towards each other.
49+ 50+ # Space Complexity:
51+ # -----------------
52+ # - The space complexity is O(1) because we are using a constant amount of extra space,
53+ # regardless of the input size.
54+
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