174. Dungeon Game

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.

//TODO: add the table

The trick here is to go from dungeon place holds princess, and at each point, the knight's minimum hp should be either 1 or more(if the dungeon cell contains demons). depends on later need, this why you have to go from bottom right to top-left.

public class Solution {
    public int calculateMinimumHP(int[][] dungeon) {
        int m = dungeon.length;
        int n = dungeon[0].length;
        int[][] hp = new int[m][n];

        hp[m-1][n-1] = Math.max(1, 1 - dungeon[m-1][n-1]);
        for(int k=n-2; k>=0; k--){
            hp[m-1][k] = Math.max(1, hp[m-1][k+1] - dungeon[m-1][k]);
        }
        for(int k = m-2; k>=0; k--){
            hp[k][n-1] = Math.max(1, hp[k+1][n-1] - dungeon[k][n-1]);
        }
        for(int i= m-2; i>=0; i--){
            for(int j = n-2; j>=0; j--){
                hp[i][j] = Math.max(1, Math.min(hp[i+1][j], hp[i][j+1]) - dungeon[i][j]);
            }
        }

        return hp[0][0];
    }
}