Create DungeonGame.cpp

Use hp[i][j] to store the min hp needed at position (i, j), then do the calculation from right-bottom to left-up.

Note: adding dummy row and column would make the code cleaner.

DungeonGame.cpp

@@ -0,0 +1,29 @@
+/*
+The demons had captured the princess 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 was initially positioned in the top-left room and must fight his way through 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 
+(represented by negative integers), so the knight loses health upon entering these rooms; other rooms are either empty (represented as 0) or contain magic orbs 
+that increase the knight's health (represented by positive integers). To reach the princess as quickly as possible, the knight decides to move only rightward or
+downward in each step.Return the knight's minimum initial health so that he can rescue the princess. Note that 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.
+*/
+
+class Solution {
+public:
+    int calculateMinimumHP(vector<vector<int> > &dungeon) {
+        int M = dungeon.size();
+        int N = dungeon[0].size();
+        // hp[i][j] represents the min hp needed at position (i, j)
+        // Add dummy row and column at bottom and right side
+        vector<vector<int> > hp(M + 1, vector<int>(N + 1, INT_MAX));
+        hp[M][N - 1] = 1;
+        hp[M - 1][N] = 1;
+        for (int i = M - 1; i >= 0; i--) {
+            for (int j = N - 1; j >= 0; j--) {
+                int need = min(hp[i + 1][j], hp[i][j + 1]) - dungeon[i][j];
+                hp[i][j] = need <= 0 ? 1 : need;
+            }
+        }
+        return hp[0][0];
+    }
+};