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.

public int calculateMinimumHP(int[][] dungeon) { if (dungeon == null || dungeon.length == 0 || dungeon[0].length == 0) { return 0; } int row = dungeon.length; int col = dungeon[0].length; //dp[i][j]: the minimum hp knight need to have at dungeon[i][j] int[][] dp = new int[row][col]; //init bottom-right cell dp[row - 1][col - 1] = Math.max(1 - dungeon[row - 1][col - 1], 1); //init rightmost rooms for (int i = row - 2; i >= 0; i--) { dp[i][col - 1] = Math.max(dp[i + 1][col - 1] - dungeon[i][col - 1], 1); } //init bottom rooms for (int j = col - 2; j >= 0; j--) { dp[row - 1][j] = Math.max(dp[row - 1][j + 1] - dungeon[row - 1][j], 1); } //dp for (int i = row - 2; i >= 0; i--) { for (int j = col - 2; j >= 0; j--) { dp[i][j] = Math.max(Math.min(dp[i][j + 1] - dungeon[i][j], dp[i + 1][j] - dungeon[i][j]), 1); } } return dp[0][0]; }