Beautiful Towers II — LeetCode 2866 Python Solution

MediumStackArrayMonotonic Stack
Problem
#2866
Pattern
Stack
Reading time
6 min

The problem

You are given a 0-indexed array maxHeights of n integers. You are tasked with building n towers in the coordinate line.

Example

Input
maxHeights = [5,3,4,1,1]
Output
13
Explanation
One beautiful configuration with a maximum sum is heights = [5,3,3,1,1]. This configuration is beautiful since:

Python solution

Python
class Solution:
    def maximumSumOfHeights(self, maxHeights: List[int]) -> int:
        n = len(maxHeights)
        stk = []
        left = [-1] * n
        for i, x in enumerate(maxHeights):
            while stk and maxHeights[stk[-1]] > x:
                stk.pop()
            if stk:
                left[i] = stk[-1]
            stk.append(i)
        stk = []
        right = [n] * n
        for i in range(n - 1, -1, -1):
            x = maxHeights[i]
            while stk and maxHeights[stk[-1]] >= x:
                stk.pop()
            if stk:
                right[i] = stk[-1]
            stk.append(i)
        f = [0] * n
        for i, x in enumerate(maxHeights):
            if i and x >= maxHeights[i - 1]:
                f[i] = f[i - 1] + x
            else:
                j = left[i]
                f[i] = x * (i - j) + (f[j] if j != -1 else 0)
        g = [0] * n
        for i in range(n - 1, -1, -1):
            if i < n - 1 and maxHeights[i] >= maxHeights[i + 1]:
                g[i] = g[i + 1] + maxHeights[i]
            else:
                j = right[i]
                g[i] = maxHeights[i] * (j - i) + (g[j] if j != n else 0)
        return max(a + b - c for a, b, c in zip(f, g, maxHeights))

Complexity

MeasureComplexity
TimeO(n)
SpaceO(n) auxiliary

Pattern: Stack

When the most recent unresolved thing is the one that matters, use a stack. LeetCode 2866. Beautiful Towers II is filed here because LeetCode tags it Stack, which is the vocabulary this hub collects.

The stack guide has the Python template for the pattern and the 194 LeetCode problems that use it.

Related problems

Frequently asked questions

How hard is LeetCode 2866. Beautiful Towers II?
LeetCode 2866. Beautiful Towers II is rated Medium on LeetCode.
What is the time complexity of LeetCode 2866. Beautiful Towers II?
The Python solution on this page runs in O(n).
What is the space complexity of LeetCode 2866. Beautiful Towers II?
The Python solution on this page uses O(n) auxiliary space.
What topics does LeetCode 2866. Beautiful Towers II cover?
LeetCode 2866. Beautiful Towers II is tagged Stack, Array and Monotonic Stack on LeetCode.

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