Create DungeonGame.java

The DungeonGame class implements a solution to the Dungeon Game problem using dynamic programming. The goal is to determine the minimum initial health points needed for a knight to survive a dungeon represented by a 2D grid, where each cell contains a health value that can be positive or negative. The knight moves from the top-left corner to the bottom-right corner, and the solution calculates the minimum health required to ensure the knight's health never drops to zero or below at any point.

Author: Tsurya06

src/main/java/com/thealgorithms/dynamicprogramming/DungeonGame.java

@@ -0,0 +1,38 @@
+package com.thealgorithms.dynamicprogramming;
+
+public class DungeonGame {
+
+    public static int calculateMinimumHP(int[][] dungeon) {
+        int m = dungeon.length;
+        int n = dungeon[0].length;
+        int[][] dp = new int[m][n];
+
+        dp[m - 1][n - 1] = Math.max(1, 1 - dungeon[m - 1][n - 1]);
+
+        for (int i = m - 2; i >= 0; i--) {
+            dp[i][n - 1] = Math.max(1, dp[i + 1][n - 1] - dungeon[i][n - 1]);
+        }
+
+        for (int j = n - 2; j >= 0; j--) {
+            dp[m - 1][j] = Math.max(1, dp[m - 1][j + 1] - dungeon[m - 1][j]);
+        }
+
+        for (int i = m - 2; i >= 0; i--) {
+            for (int j = n - 2; j >= 0; j--) {
+                int minHealthOnExit = Math.min(dp[i + 1][j], dp[i][j + 1]);
+                dp[i][j] = Math.max(1, minHealthOnExit - dungeon[i][j]);
+            }
+        }
+
+        return dp[0][0];
+    }
+
+    public static void main(String[] args) {
+        int[][] dungeon = {
+            { -2, -3, 3 },
+            { -5, -10, 1 },
+            { 10, 30, -5 }
+        };
+        System.out.println(calculateMinimumHP(dungeon)); // Output: 7
+    }
+}