Hanging line method
- use
To solve the biggest sub-matrix-matrix satisfies a condition
- practice
With a line (vertical line are seemingly) does not satisfy the left or right until it reaches the boundary constraint or
- definition
\ (left [i] [J] \) : Representative from \ ((i, j) \ ) can reach the leftmost position
\ (right [I] [J] \) : Representative from \ ((i, j) \ ) can reach the rightmost position
\ (up [I] [J] \) : Representative from \ ((i, j) \ ) extend upwardly longest length .
- State transition
\[left[i][j]=max(left[i][j],left[i-1][j])\]
\[right[i][j]=min(right[i][j],right[i-1][j])\]
- As for why recurrence formula in the case of one of the considerations?
Because \ (up \) to define arrays, \ (up \) array represents the maximum length of the scale-up, it is necessary to consider the case where the upper hierarchy.
Reference Hirofumi: Https://Rpdreamer.Blog.Luogu.Org/p1169