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leetcode/algorithms/cpp/dungeonGame/dungeonGame.cpp at master · fallleaves/leetcode · GitHub
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dungeonGame.cpp
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//
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
];
}
};
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