We have a sequence of books
: the i
-th book has thickness books[i][0]
and
height books[i][1]
.
We want to place these books in order onto bookcase shelves that have
total width shelf_width
.
We choose some of the books to place on this shelf (such that the sum of their
thickness is <= shelf_width
), then build another level of shelf of the
bookcase so that the total height of the bookcase has increased by the maximum
height of the books we just put down. We repeat this process until there are
no more books to place.
Note again that at each step of the above process, the order of the books we place is the same order as the given sequence of books. For example, if we have an ordered list of 5 books, we might place the first and second book onto the first shelf, the third book on the second shelf, and the fourth and fifth book on the last shelf.
Return the minimum possible height that the total bookshelf can be after placing shelves in this manner.
Example 1:
Input: books = [[1,1],[2,3],[2,3],[1,1],[1,1],[1,1],[1,2]], shelf_width = 4
Output: 6
Explanation:
The sum of the heights of the 3 shelves are 1 + 3 + 2 = 6.
Notice that book number 2 does not have to be on the first shelf.
Constraints:
1 <= books.length <= 1000
1 <= books[i][0] <= shelf_width <= 1000
1 <= books[i][1] <= 1000
# @lc code=start
using LeetCode
function min_height_shelves(books::Vector{Vector{Int}}, shelf_width::Int)
n = length(books)
dp = OffsetArray(fill(typemax(Int) >> 1, n + 1), -1)
dp[0] = 0
for i in 1:n
idx, width, height = i - 1, books[i][1], books[i][2]
while width <= shelf_width
dp[i] = min(dp[i], dp[idx] + height)
idx == 0 && break
height = max(height, books[idx][2])
width += books[idx][1]
idx -= 1
end
end
dp[end]
end
# @lc code=end
min_height_shelves (generic function with 1 method)
This notebook was generated using Literate.jl.