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| 1 | +// Source : https://leetcode.com/problems/dungeon-game/ |
| 2 | +// Author : henrytien |
| 3 | +// Date : 2022年02月03日 |
| 4 | + |
| 5 | +/***************************************************************************************************** |
| 6 | + * |
| 7 | + * The demons had captured the princess and imprisoned her in the bottom-right corner of a dungeon. |
| 8 | + * The dungeon consists of m x n rooms laid out in a 2D grid. Our valiant knight was initially |
| 9 | + * positioned in the top-left room and must fight his way through dungeon to rescue the princess. |
| 10 | + * |
| 11 | + * The knight has an initial health point represented by a positive integer. If at any point his |
| 12 | + * health point drops to 0 or below, he dies immediately. |
| 13 | + * |
| 14 | + * Some of the rooms are guarded by demons (represented by negative integers), so the knight loses |
| 15 | + * health upon entering these rooms; other rooms are either empty (represented as 0) or contain magic |
| 16 | + * orbs that increase the knight's health (represented by positive integers). |
| 17 | + * |
| 18 | + * To reach the princess as quickly as possible, the knight decides to move only rightward or downward |
| 19 | + * in each step. |
| 20 | + * |
| 21 | + * Return the knight's minimum initial health so that he can rescue the princess. |
| 22 | + * |
| 23 | + * Note that any room can contain threats or power-ups, even the first room the knight enters and the |
| 24 | + * bottom-right room where the princess is imprisoned. |
| 25 | + * |
| 26 | + * Example 1: |
| 27 | + * |
| 28 | + * Input: dungeon = [[-2,-3,3],[-5,-10,1],[10,30,-5]] |
| 29 | + * Output: 7 |
| 30 | + * Explanation: The initial health of the knight must be at least 7 if he follows the optimal path: |
| 31 | + * RIGHT-> RIGHT -> DOWN -> DOWN. |
| 32 | + * |
| 33 | + * Example 2: |
| 34 | + * |
| 35 | + * Input: dungeon = [[0]] |
| 36 | + * Output: 1 |
| 37 | + * |
| 38 | + * Constraints: |
| 39 | + * |
| 40 | + * m == dungeon.length |
| 41 | + * n == dungeon[i].length |
| 42 | + * 1 <= m, n <= 200 |
| 43 | + * -1000 <= dungeon[i][j] <= 1000 |
| 44 | + ******************************************************************************************************/ |
| 45 | + |
| 46 | +#include "../inc/ac.h" |
| 47 | +class Solution |
| 48 | +{ |
| 49 | +public: |
| 50 | + int calculateMinimumHP(vector<vector<int>> &dungeon) |
| 51 | + { |
| 52 | + int m = dungeon.size(); |
| 53 | + int n = dungeon[0].size(); |
| 54 | + |
| 55 | + vector<int> dp(n + 1, INT_MAX); |
| 56 | + dp[n - 1] = 1; |
| 57 | + |
| 58 | + for (int i = m - 1; i >= 0; i--) |
| 59 | + { |
| 60 | + for (int j = n - 1; j >= 0; j--) |
| 61 | + { |
| 62 | + int need = min(dp[j], dp[j + 1]) - dungeon[i][j]; |
| 63 | + dp[j] = need <= 0 ? 1 : need; |
| 64 | + } |
| 65 | + } |
| 66 | + return dp[0]; |
| 67 | + } |
| 68 | +}; |
| 69 | + |
| 70 | +int main() |
| 71 | +{ |
| 72 | + // https://leetcode.com/problems/dungeon-game/discuss/52774/C%2B%2B-DP-solution |
| 73 | + vector<vector<int>> dungeon{{0, -3}}; |
| 74 | + cout << Solution().calculateMinimumHP(dungeon) << "\n"; |
| 75 | + return 0; |
| 76 | +} |
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