Mock CCC '22 Contest 1 J1 - Square Root Decomposition - Olympiads Online Judge

Mock CCC '22 Contest 1 J1 - Square Root Decomposition

Points: 3

Time limit: 0.25s

Memory limit: 256M

Author:

Problem type

Bob is practicing square root decomposition!

The problem Bob is doing involves breaking a number $N$ ~N~ into $B$ ~B~ groups. It is said to be optimal if $B$ ~B~ is closest to $\sqrt{N}$ ~\sqrt{N}~.

He currently has $2$ ~2~ candidates for $B$ ~B~: integers $i$ ~i~ and $j$ ~j~. If $i$ ~i~ and $j$ ~j~ are squared, which one is closer to $N$ ~N~?

The data guarantee that one candidate will be closer than the other.

Constraints

$1 \le N, i, j \le 10^4$ ~1 \le N, i, j \le 10^4~

$i \ne j$ ~i \ne j~

Input Specification

The first line will contain $N$ ~N~.

The second line will contain $i$ ~i~.

The third and final line will contain $j$ ~j~.

Output Specification

On one line, output 1 if $i^2$ ~i^2~ is closer to $N$ ~N~ or 2 if $j^2$ ~j^2~ is.

Sample Input 1

9
3
4

Sample Output 1

Sample Input 2

16
5
3

Sample Output 2

Comments

-1

Raynfall commented on Feb. 18, 2025, 12:22 a.m. ← edited →

Possible spoiler, but I had tried to square the distances between N and i/j squared to find the positive distance, but that caused a WA .Since the distances are being compared and their actual value doesn't matter, why wouldn't this work?

0

stephengzy___PYTHON commented on Jan. 1, 2026, 8:33 p.m.

Take i = 3, N = 4, j = 5

Your solution would find a difference of 1 each, so it would assume that the two are the same distance apart.

But 16-9 = 7 and 25-16 = 9, so your solution is incorrect.