CCC '22 J5 - Square Pool - Olympiads Online Judge

CCC '22 J5 - Square Pool

Points: 10 (partial)

Time limit: 1.0s

Memory limit: 1G

Problem types

Canadian Computing Competition: 2022 Stage 1, Junior #5

Ron wants to build a square pool in his square $N$ ~N~-by- $N$ ~N~ yard, but his yard contains $T$ ~T~ trees. Your job is to determine the side length of the largest square pool he can build.

Input Specification

The first line of input will be an integer $N$ ~N~ with $N \ge 2$ ~N \ge 2~. The second line will be the positive integer $T$ ~T~ where $T < N^2$ ~T < N^2~. The remaining input will be $T$ ~T~ lines, each representing the location of a single tree. The location is given by two positive integers, $R$ ~R~ and then $C$ ~C~, separated by a single space. Each tree is located at row $R$ ~R~ and column $C$ ~C~ where rows are numbered from top to bottom from $1$ ~1~ to $N$ ~N~ and columns are numbered from left to right from $1$ ~1~ to $N$ ~N~. No two trees are at the same location.

The following table shows how the available 15 marks are distributed.

Marks Awarded	Length/Width of Yard	Number of Trees
$3$ ~3~ marks	$N \le 50$ ~N \le 50~	$T = 1$ ~T = 1~
$5$ ~5~ marks	$N \le 50$ ~N \le 50~	$T \le 10$ ~T \le 10~
$4$ ~4~ marks	$N \le 500\,000$ ~N \le 500\,000~	$T \le 10$ ~T \le 10~
$3$ ~3~ marks	$N \le 500\,000$ ~N \le 500\,000~	$T \le 100$ ~T \le 100~

Output Specification

Output one line containing $M$ ~M~ which is the largest positive integer such that some $M$ ~M~-by- $M$ ~M~ square contained entirely in Ron's yard does not contain any of the $T$ ~T~ trees.

Sample Input 1

5
1
2 4

Output for Sample Input 1

Explanation of Output for Sample Input 1

A picture of the yard is below. The location of the tree is marked by and one of several $3$ ~3~-by- $3$ ~3~ squares that do not contain the tree is highlighted. All larger squares contain a tree.

Sample Input 2

Output for Sample Input 2

Explanation of Output for Sample Input 2

A picture of the yard is below. The location of each tree is marked by and one of several $7$ ~7~-by- $7$ ~7~ squares that do not contain a tree is highlighted. All larger squares contain a tree.

Comments

1

epicgamergirl999 commented on Feb. 21, 2024, 5:24 p.m.

J5, 10 points....

0

Alex_Tsvik commented on Feb. 13, 2024, 4:28 p.m.

Omg, $500\,000^2$ ~500\,000^2~ cells in grid of Ron's yard. This is what brute force really is.

0

noahzho commented on Feb. 15, 2024, 12:49 a.m.

ignore comment i'm not thinking straight today

6

Archeiid commented on Feb. 15, 2023, 11:38 a.m. ← edited →

I've been writting a functional method to find the maximum space available,for the whole afternoon.Yet nothing came out.This is a hard one...

3

Ethereal_Liu1029 commented on Oct. 22, 2022, 6:27 p.m.

I have no idea why it always tell me index error