DungeonGame.java

package dynamic_programming;

import java.util.Arrays;

/**
 * Created by gouthamvidyapradhan on 12/07/2017.
 * 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.

 -2 (K)	-3	3
 -5	-10	1
 10	30	-5 (P)

 Notes:

 The knight's health has no upper bound.
 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.

 Solution: O(MxN log Integer.MAX_VALUE)
 Binary search the suitable initial health value in the range (1, Integer.MAX_VALUE) and do a top down DP to check the
 balance health when he reaches princess.
 */
public class DungeonGame {
    private final int[] R = {0, -1};
    private final int[] C = {-1, 0};
    private int DP[][];
    public static void main(String[] args) throws Exception{
        int[][] dungeon = {{200}};
        System.out.println(new DungeonGame().calculateMinimumHP(dungeon));
    }

    public int calculateMinimumHP(int[][] dungeon) {
        DP = new int[dungeon.length][dungeon[0].length];
        int l = 0, h = Integer.MAX_VALUE, ans = 0;
        while(l <= h){
            int m = l + (h - l) / 2;
            for(int i = 0; i < dungeon.length; i ++)
                Arrays.fill(DP[i], Integer.MIN_VALUE);
            DP[0][0] = m + dungeon[0][0];
            if(dp(dungeon, dungeon.length - 1, dungeon[0].length - 1) > 0){
                ans = m;
                h = m - 1;
            }else{
                l = m + 1;
            }
        }
        return ans == 0 ? 1 : ans;
    }

    private int dp(int[][] dungeon, int r, int c){
        if(DP[r][c] != Integer.MIN_VALUE)
            return DP[r][c];
        for(int i = 0; i < 2; i ++){
            int newR = r + R[i];
            int newC = c + C[i];
            if(newR >= 0 && newR < dungeon.length && newC >=0 && newC < dungeon[0].length){
                int life = dp(dungeon, newR, newC);
                if(life <= 0)
                    DP[r][c] = Math.max(DP[r][c], 0);
                else DP[r][c] = Math.max(DP[r][c], dungeon[r][c] + life);
            }

        }
        return DP[r][c];
    }
}