PROBLEM LINK:
Contest Division 1
Contest Division 2
Contest Division 3
Contest Division 4
Setter: Tejas Pandey
Tester: Nishank Suresh, Utkarsh Gupta
Editorialist: Pratiyush Mishra
DIFFICULTY:
1713
PREREQUISITES:
None
PROBLEM:
A segment is a range of non-negative integers L, L + 1, L + 2, \ldots, R, denoted [L, R] where L \leq R.
Chef has a set S consisting of all segments [L, R] such that either L + R = X or L\cdot R = Y.
For example, if X = 5 and Y = 6, then Chef’s set is S = \{[0, 5], [1, 4], [1, 6], [2, 3]\}.
Given the integers X and Y, can you help Chef find two non-intersecting segments from his set S? If it is not possible to find two such non-intersecting segments, print -1. If there are multiple possible answers, you may output any of them.
Note: Two segments are said to be non-intersecting if they have no number in common. For example, [1, 4] and [10, 42] are non-intersecting, while [1, 4] and [4, 6] are not since they have 4 in common.
EXPLANATION:
Observation 1: The smallest interval [L,R] such that L+R = X would be:
Any other interval would overlap the above one.
So we can choose one of the intervals as above and then loop through all possible intervals such that L \times R = Y and for each interval we check if the two intersect each other or not.
TIME COMPLEXITY:
O(\sqrt{N}), for each test case.
SOLUTION:
Editorialist’s Solution
Setter’s Solution
Tester1’s Solution
Tester2’s Solution