// Source : https://oj.leetcode.com/problems/dungeon-game/
// Author : Hao Chen
// Date   : 2015-01-16

/********************************************************************************** 
 * 
 * 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.  
 * 
 * Credits:Special thanks to @stellari for adding this problem and creating all test cases.
 *               
 **********************************************************************************/

class Solution {
    public:
        int calculateMinimumHP(vector<vector<int> > &dungeon) {
            int row = dungeon.size();
            int col = row>0 ? dungeon[0].size() : 0;
            if (row<=0 || col <=0) return 0;

            //dp[r][c] = min( max( dp[r+1][c] - dungeon[r][c], 1), max( dp[r][c+1] - dungeon[r][c], 1) );
            int dp[row][col];
            memset(dp, 0, sizeof(dp));

            for(int r=row-1; r>=0; r--){
                for (int c=col-1; c>=0; c--){

                    /*if (r == row - 1 && c == col - 1 ){
                      dp[r][c] = max(1 - dungeon[r][c], 1);
                      }else if ( r == row - 1 ) {
                      dp[r][c] = max(dp[r][c+1] - dungeon[r][c], 1);
                      }else if ( c == col - 1 ) {
                      dp[r][c] = max(dp[r+1][c] - dungeon[r][c], 1);
                      }else{
                      dp[r][c] = min( max( dp[r+1][c] - dungeon[r][c], 1), max( dp[r][c+1] - dungeon[r][c], 1) );
                      }*/

                    if (r == row - 1 && c == col - 1 ){
                        dp[r][c] = max(1 - dungeon[r][c], 1);
                    }else{ 
                        int h1 = ( c == col-1  ) ? INT_MAX : max(dp[r][c+1] - dungeon[r][c], 1);
                        int h2 =  ( r == row-1 ) ? INT_MAX : max(dp[r+1][c] - dungeon[r][c], 1);

                        dp[r][c] = min( h1, h2 );
                    }

                }
            }

            return dp[0][0];


        }
};