Use hp[i][j] to store the min hp needed at position (i, j), then do the calculation from right-bottom to left-up.

Note: adding dummy row and column would make the code cleaner.

```
class Solution {
public:
int calculateMinimumHP(vector<vector<int> > &dungeon) {
int M = dungeon.size();
int N = dungeon[0].size();
// hp[i][j] represents the min hp needed at position (i, j)
// Add dummy row and column at bottom and right side
vector<vector<int> > hp(M + 1, vector<int>(N + 1, INT_MAX));
hp[M][N - 1] = 1;
hp[M - 1][N] = 1;
for (int i = M - 1; i >= 0; i--) {
for (int j = N - 1; j >= 0; j--) {
int need = min(hp[i + 1][j], hp[i][j + 1]) - dungeon[i][j];
hp[i][j] = need <= 0 ? 1 : need;
}
}
return hp[0][0];
}
};
```