O(1) Space solution is based on if dungeon is declared as int ** but not const int **. Since each grid in dungeon is traversed through once, and it can be reused to hold the optimized cost.

```
int calculateMinimumHP(int **dungeon, int m, int n)
{
for ( int i = m - 1; i >= 0; --i )
{
for ( int j = n - 1; j >= 0; --j )
{
if ( i == m - 1 && j == n - 1 )
{
/** heheheheh */
}
else if ( i == m - 1 )
{
/** choose cost as the minimum between current and right */
int right = dungeon[i][ j + 1 ];
if ( right < 0 )
{
dungeon[i][j] += right;
}
}
else if ( j == n - 1 )
{
/** choose cost as the minimum between current and down */
int down = dungeon[ i + 1 ][j];
if ( down < 0 )
{
dungeon[i][j] += down;
}
}
else
{
/** choose the optimized next cost as the maximum between right and down */
int right = dungeon[i][ j + 1 ];
int down = dungeon[ i + 1 ][j];
int next = ( right > down ) ? right : down;
/** choose cost as the minimum between current and next */
if ( next < 0 )
{
dungeon[i][j] += next;
}
}
}
}
int ret = dungeon[0][0];
if ( ret > 0 )
{
return 1;
}
return -ret + 1;
}
```