Time Limit Exceeded error

[loves]

I am going to solve leetcode problem.

It passed some test cases but failed one case. It said Time Limit Exceeded

class Solution:
    from typing import List
    def maxArea(self, height: List[int]) -> int:
       
        result = 0
        
        for i in range(len(height)):
            for j in range(len(height)):
                if i > j:
                    continue
                if i != j:
                    result = max(result, min(height[i], height[j]) * abs(j - i))
        return result            

s = Solution()
height = 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print(s.maxArea(height))

[deanhystad]

Your solution is slow because the algorithm is inefficient. You are computing every possible volume (area) and picking the max. With 5000 heights this is 4999 * 4999 / 2 volumes to calculate and compare. When I run your solution it took 19 seconds.

Take some time and think about the problem instead of the code. There is a way to solve this problem with less than 5000 calculations and comparisons.

I'll give you three hints.
1. Solving for height[0], height[4999] is a good first guess because width is important.
2. The shorter "wall" limits the volume.
3. Draw a bar chart on paper with different sized walls when thinking about the problem.

I have a solution that runs in 0.0193 seconds and it isn't using any fancy Python to speed things up. Just an efficient algorithm.

[deanhystad]

One other thing. This is not important for this challenge because your solution will not have loops inside loops, but there is a better way to do the looping you were doing in your OP.

class Solution:
    def maxArea(self, height):
        result = 0
        for i in range(len(height)-1):
            for j in range(i+1, len(height)):
                result = max(result, min(height[i], height[j]) * (j - i))
        return result            

This shaves about 10 seconds off your code. This makes sense because the iterations are cut in half.

[loves]

One other thing. This is not important for this challenge because your solution will not have loops inside loops, but there is a better way to do the looping you were doing in your OP.

class Solution:
    def maxArea(self, height):
        result = 0
        for i in range(len(height)-1):
            for j in range(i+1, len(height)):
                result = max(result, min(height[i], height[j]) * (j - i))
        return result            

This shaves about 10 seconds off your code. This makes sense because the iterations are cut in half.

It's better but still time out.

[deanhystad]

As I said, you need a different algorithm. Doing something 2500 times less often can really save a lot of time.

Even though there are 5000 numbers and around 12.5 million different volumes, the max volume only changed 8 times after my initial guess.

Output:
Left Right Max Area
   1  4999 18446310 <- First guess
   2  4999 38399634
   2  4998 39681177
   2  4995 42214282
   3  4995 45715908
   7  4995 47420445
  72  4994 48146940
  73  4983 48392994
  84  4982 48431514 <- Max area

[Sofia_Grace]

Hi
PM Sent. Please check.

Thanks
Sofia