1105

1101-1200/1105_filling_bookcase_shelves.rb

@@ -0,0 +1,28 @@
+# @param {Integer[][]} books
+# @param {Integer} shelf_width
+# @return {Integer}
+def min_height_shelves(books, shelf_width)
+ # defining dp[i] as the min height for placing i books (IN ORDER)
+ dp = Array.new(books.size + 1, Float::INFINITY)
+ dp[0] = 0
+ (0...books.size).each { |i|
+ # for the next i-th book
+ w, h = books[i]
+ # we can:
+ # place it on another level
+ dp[i+1] = dp[i] + h
+ # collect books [j..i-1] and place them at the same level, 0 <= j < i
+ (i-1).downto(0) { |j|
+ w += books[j][0]
+ # Note that we need to place books IN ORDER
+ # so we cannot place the i-th book at the same level of books [j..i-2] which above the (i-1)th book
+ # therefor, if the width of books [j..i] is out of the shelf width, we stop
+ break if w > shelf_width
+
+ h = [h, books[j][1]].max
+ dp[i+1] = [dp[i+1], dp[j] + h].min
+ }
+ }
+
+ dp[books.size]
+end