Maximum Number of Books You Can Take — LeetCode 2355 Python Solution

The problem

You are given a 0-indexed integer array books of length n where books[i] denotes the number of books on the ith shelf of a bookshelf. You are going to take books from a contiguous section of the bookshelf spanning from l to r where 0 <= l <= r < n.

Example

Input

books = [8,5,2,7,9]

Output

19

Explanation

- Take 1 book from shelf 1.

Python solution

class Solution:
    def maximumBooks(self, books: List[int]) -> int:
        nums = [v - i for i, v in enumerate(books)]
        n = len(nums)
        left = [-1] * n
        stk = []
        for i, v in enumerate(nums):
            while stk and nums[stk[-1]] >= v:
                stk.pop()
            if stk:
                left[i] = stk[-1]
            stk.append(i)
        ans = 0
        dp = [0] * n
        dp[0] = books[0]
        for i, v in enumerate(books):
            j = left[i]
            cnt = min(v, i - j)
            u = v - cnt + 1
            s = (u + v) * cnt // 2
            dp[i] = s + (0 if j == -1 else dp[j])
            ans = max(ans, dp[i])
        return ans

Complexity

Pattern: Stack

When the most recent unresolved thing is the one that matters, use a stack. LeetCode 2355. Maximum Number of Books You Can Take 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