Algorithm for finding the minimum number of images needed to erase points in the grid

Question

I saw this programming puzzle on a website and tried to solve it.

PROBLEM

You are given an N x N grid in which there are certain points randomly distributed. You must delete the points using the following valid steps.

• You can either delete all points in the row with one shot.

• Or you can delete all points in a column with one shot.

You should find the minimum number of shots needed to delete all points.

Example

In the next grid, you need three shots: one horizontal and two vertical to remove points.

, , , . , . - , , ?

:

1 <= N <= 1000
0 <= x,y <= 10^9
Time Limit: 2 sec

n - (.. nxn) x, y -

Answer 1

. , , , . , , , (x, y), , row_x column_y. . , , .

O (V * E). .

, pls , , .

Answer 2

. , , .

, N ( , ).

, , + , N. , N = 4, be <= 3, (, ) :

(0,3)
(1,2)
(2,1)
(3,0)

( ), s-, (s choose N). , N - (N/2) choose N, N < 30 .

, , .

Answer 3

, . , , - , .

- . :

• . →

• , . → , .

• , .- > , .

• . → , .

1- :

int minimumNumberOfLines( matrixOfDots ) {
  return min( 1 + minimumNumberOfLines( with row shot ),1 + minimumNumberOfLines( with col shot ), 2 + minimumNumberOfLines( with row and column shot ) ). 
}