**Dungeon Game** **LeetCode Solution | LeetCode Problems For Beginners | LeetCode Problems & Solutions | Improve Problem Solving Skills | LeetCode Problems Java | LeetCode Solutions in C++**

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In this post, you will find the solution for the **Dungeon Game** **in C++, Java & Python-LeetCode problem**. We are providing the **correct and tested solutions** to coding problems present on **LeetCode**. If you are not able to solve any problem, then you can take help from our Blog/website.

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** Link for the Problem** – Dungeon Game– LeetCode Problem

Dungeon Game– LeetCode Problem

**Problem:**

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.

**Example 1:**

Input:dungeon = [[-2,-3,3],[-5,-10,1],[10,30,-5]]Output:7Explanation:The initial health of the knight must be at least 7 if he follows the optimal path: RIGHT-> RIGHT -> DOWN -> DOWN.

**Example 2:**

Input:dungeon = [[0]]Output:1

**Constraints:**

`m == dungeon.length`

`n == dungeon[i].length`

`1 <= m, n <= 200`

`-1000 <= dungeon[i][j] <= 1000`

Dungeon Game– LeetCode Solutions

Dungeon GameSolution in C++:

class Solution { public: int calculateMinimumHP(vector<vector<int>>& dungeon) { const int m = dungeon.size(); const int n = dungeon[0].size(); vector<vector<int>> dp(m + 1, vector<int>(n + 1, INT_MAX)); dp[m][n - 1] = 1; dp[m - 1][n] = 1; for (int i = m - 1; i >= 0; --i) for (int j = n - 1; j >= 0; --j) { dp[i][j] = min(dp[i + 1][j], dp[i][j + 1]) - dungeon[i][j]; dp[i][j] = max(dp[i][j], 1); } return dp[0][0]; } };

Dungeon GameSolution in Java:

class Solution { public int calculateMinimumHP(int[][] dungeon) { final int m = dungeon.length; final int n = dungeon[0].length; int[][] dp = new int[m + 1][n + 1]; Arrays.stream(dp).forEach(A -> Arrays.fill(A, Integer.MAX_VALUE)); dp[m][n - 1] = 1; dp[m - 1][n] = 1; for (int i = m - 1; i >= 0; --i) for (int j = n - 1; j >= 0; --j) { dp[i][j] = Math.min(dp[i + 1][j], dp[i][j + 1]) - dungeon[i][j]; dp[i][j] = Math.max(dp[i][j], 1); } return dp[0][0]; } }

Dungeon GameSolution in Python:

class Solution: def calculateMinimumHP(self, dungeon: List[List[int]]) -> int: m = len(dungeon) n = len(dungeon[0]) dp = [math.inf] * (n + 1) dp[n - 1] = 1 for i in reversed(range(m)): for j in reversed(range(n)): dp[j] = min(dp[j], dp[j + 1]) - dungeon[i][j] dp[j] = max(dp[j], 1) return dp[0]

**Time:**O(mn)*O*(*mn*)**Space:**O(mn) \to O(n)*O*(*mn*)→*O*(*n*)