Problem
Decide whether people can be assigned to two teams so that each listed pair is on opposite teams. Every person receives exactly one team; either team may be empty. People without a listed pair can go on either team. Check every connected group of constraints.
Implement split_into_two_teams(people, pairs).
Input
people: The number of people, numbered from 1.
pairs: Rows [first_person, second_person] that must be separated.
Output
Return true if any valid assignment exists, otherwise false. Do not return the assignment.
Constraints
1 ≤ people ≤ 100,000. 0…200,000 pairs of distinct person IDs in 1…people. Duplicate pairs are allowed and repeat the same constraint.
Examples
Input:
pairs = [
[1, 2],
[2, 3],
[3, 1]
]
people = 3
Expected output:
expected = FalseInput:
std::vector<std::vector<long long>> pairs = {
{1, 2},
{2, 3},
{3, 1}
};
long long people = 3;
Expected output:
bool expected = false;Input:
long[][] pairs = new long[][] {
new long[] {1, 2},
new long[] {2, 3},
new long[] {3, 1}
};
long people = 3;
Expected output:
bool expected = false;Explanation
If 1 is on team A, 2 must be on B, and 3 must be on A. The last pair then violates the rule.
Input:
pairs = [
[1, 2],
[2, 3]
]
people = 4
Expected output:
expected = TrueInput:
std::vector<std::vector<long long>> pairs = {
{1, 2},
{2, 3}
};
long long people = 4;
Expected output:
bool expected = true;Input:
long[][] pairs = new long[][] {
new long[] {1, 2},
new long[] {2, 3}
};
long people = 4;
Expected output:
bool expected = true;Explanation
Put 1 and 3 on team A and 2 on team B. Person 4 can join either team.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
This is possible exactly when every constraint component can be colored with two different colors.
Hint 2
Traverse each connected component and alternate team assignments across each pair constraint.
Hint 3
If you ever need to give the same person both teams through an odd cycle, the answer becomes false.
Expected complexity
O(people + pairs) time, O(people + pairs) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.