solve: Dungeon Game

Author: 0x01f7

README.md

@@ -108,7 +108,7 @@
 | 187 | [Repeated DNA Sequences][p187]                                      | [Ruby][s187]  | Medium      |
 | 186 | [Reverse Words in a String II][p186]                                |    :lock:     | Medium      |
 | 179 | [Largest Number][p179]                                              | [Ruby][s179]  | Medium      |
-| 174 | [Dungeon Game][p174]                                                |               | Hard        |
+| 174 | [Dungeon Game][p174]                                                | [Ruby][s174]  | Hard        |
 | 173 | [Binary Search Tree Iterator][p173]                                 | [Ruby][s173]  | Medium      |
 | 172 | [Factorial Trailing Zeroes][p172]                                   | [Ruby][s172]  | Easy        |
 | 171 | [Excel Sheet Column Number][p171]                                   | [Ruby][s171]  | Easy        |
@@ -633,6 +633,7 @@
 [s188]:./algorithms/best_time_to_buy_and_sell_stock_iv.rb
 [s187]:./algorithms/repeated_dna_sequences.rb
 [s179]:./algorithms/largest_number.rb
+[s174]:./algorithms/dungeon_game.rb
 [s173]:./algorithms/binary_search_tree_iterator.rb
 [s172]:./algorithms/factorial_trailing_zeroes.rb
 [s171]:./algorithms/excel_sheet_column_number.rb

algorithms/dungeon_game.rb

@@ -0,0 +1,70 @@
+# https://leetcode.com/problems/dungeon-game/
+#
+# The demons had captured the princess (P) and imprisoned her in the
+# bottom-right corner of a dungeon. The dungeon consists of M x N
+# rooms laid out in a 2D grid. Our valiant knight (K) was initially
+# positioned in the top-left room and must fight his way through the
+# dungeon to rescue the princess.
+#
+# The knight has an initial health point represented by a positive
+# integer. If at any point his health point drops to 0 or below,
+# he dies immediately.
+#
+# Some of the rooms are guarded by demons, so the knight loses health
+# (negative integers) upon entering these rooms; other rooms are
+# either empty (0's) or contain magic orbs that increase the knight's
+# health (positive integers).
+#
+# In order to reach the princess as quickly as possible, the knight
+# decides to move only rightward or downward in each step.
+#
+# Write a function to determine the knight's minimum initial health
+# so that he is able to rescue the princess.
+#
+# For example, given the dungeon below, the initial health of the
+# knight must be at least 7 if he follows the optimal path
+# RIGHT -> RIGHT -> DOWN -> DOWN.
+#
+#     +-------+-------+-------+
+#     |       |       |       |
+#     | -2(K) |   -3  |   3   |
+#     |       |       |       |
+#     +-------+-------+-------+
+#     |       |       |       |
+#     |  -5   |  -10  |   1   |
+#     |       |       |       |
+#     +-------+-------+-------+
+#     |       |       |       |
+#     |  10   |   30  | -5(P) |
+#     |       |       |       |
+#     +-------+-------+-------+
+#
+# Notes:
+#
+#     + The knight's health has no upper bound.
+#     + Any room can contain threats or power-ups, even the first room
+#       the knight enters and the bottom-right room where the princess
+#       is imprisoned.
+
+
+# @param {Integer[][]} dungeon
+# @return {Integer}
+def calculate_minimum_hp(dungeon)
+  m, n = dungeon.size, dungeon[0].size
+    dp = Array.new(m) { Array.new(n, 0) }
+
+  dp[-1][-1] = [1 - dungeon[-1][-1], 1].max
+  (m - 2).downto(0) { |i| dp[i][-1] = [dp[i + 1][-1] - dungeon[i][-1], 1].max }
+  (n - 2).downto(0) { |j| dp[-1][j] = [dp[-1][j + 1] - dungeon[-1][j], 1].max }
+
+  (m - 2).downto(0) do |i|
+    (n - 2).downto(0) do |j|
+      dp[i][j] = [
+        [dp[i + 1][j] - dungeon[i][j], 1].max,
+        [dp[i][j + 1] - dungeon[i][j], 1].max
+      ].min
+    end
+  end
+
+  dp[0][0]
+end