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 o