resolve #174

Author: aylei

Diff for: src/lib.rs

@@ -160,3 +160,4 @@ mod n0169_majority_element;
 mod n0171_excel_sheet_column_number;
 mod n0172_factorial_trailing_zeroes;
 mod n0173_binary_search_tree_iterator;
+mod n0174_dungeon_game;

Diff for: src/n0174_dungeon_game.rs

@@ -0,0 +1,112 @@
+/**
+ * [174] Dungeon Game
+ *
+ * <style type="text/css">table.dungeon, .dungeon th, .dungeon td {
+ *   border:3px solid black;
+ * }
+ * 
+ *  .dungeon th, .dungeon td {
+ *     text-align: center;
+ *     height: 70px;
+ *     width: 70px;
+ * }
+ * </style>
+ * 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.
+ * 
+ * <table class="dungeon">
+ * 	<tbody>
+ * 		<tr>
+ * 			<td>-2 (K)</td>
+ * 			<td>-3</td>
+ * 			<td>3</td>
+ * 		</tr>
+ * 		<tr>
+ * 			<td>-5</td>
+ * 			<td>-10</td>
+ * 			<td>1</td>
+ * 		</tr>
+ * 		<tr>
+ * 			<td>10</td>
+ * 			<td>30</td>
+ * 			<td>-5 (P)</td>
+ * 		</tr>
+ * 	</tbody>
+ * </table>
+ * 
+ *  
+ * 
+ * Note:
+ * 
+ * 
+ * 	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.
+ * 
+ * 
+ */
+pub struct Solution {}
+
+// submission codes start here
+
+/*
+ DP, 即从每个格子出发到达终点所需的最小生命值为 hp[i][j]
+
+ 则显然, hp[M-1][N-1] = min(dungeon[M-1][N-1], 0) + 1;
+
+ hp[i][j] = min(min(hp[i+1][j], hp[i][j+1]) - dungeon[i][j], 1);
+
+ 倒推到 hp[0][0] 即可
+
+ 其实可以优化成 O(M+N) 空间复杂度, 从斜对角线往后推就只需要保存一个小数组, 但是下面这样更简明
+ */
+impl Solution {
+    pub fn calculate_minimum_hp(dungeon: Vec<Vec<i32>>) -> i32 {
+        let (height, width) = (dungeon.len(), dungeon[0].len());
+        // Using dummy row to simplify logic
+        let mut hp = vec![vec![i32::max_value(); width+1]; height+1];
+        hp[height][width-1] = 1;
+        hp[height-1][width] = 1;
+        for i in (0..height).rev() {
+            for j in (0..width).rev() {
+                hp[i][j] = i32::max(i32::min(hp[i+1][j], hp[i][j+1]) - dungeon[i][j], 1);
+            }
+        }
+        hp[0][0]
+    }
+}
+
+// submission codes end
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_174() {
+        assert_eq!(
+            Solution::calculate_minimum_hp(
+                vec![
+                    vec![-2,-3,3],
+                    vec![-5,-10,1],
+                    vec![10,30,-5],
+                ]),
+            7);
+        assert_eq!(
+            Solution::calculate_minimum_hp(
+                vec![
+                    vec![1,-4,5,-99],
+                    vec![2,-2,-2,-1]]),
+            3);
+    }
+}