समस्या
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.
सीमाएँ
1 ≤ people ≤ 100,000. 0…200,000 pairs of distinct person IDs in 1…people. Duplicate pairs are allowed and repeat the same constraint.
उदाहरण
इनपुट:
pairs = [
[1, 2],
[2, 3],
[3, 1]
]
people = 3
अपेक्षित आउटपुट:
expected = Falseइनपुट:
std::vector<std::vector<long long>> pairs = {
{1, 2},
{2, 3},
{3, 1}
};
long long people = 3;
अपेक्षित आउटपुट:
bool expected = false;इनपुट:
long[][] pairs = new long[][] {
new long[] {1, 2},
new long[] {2, 3},
new long[] {3, 1}
};
long people = 3;
अपेक्षित आउटपुट:
bool expected = false;व्याख्या
If 1 is on team A, 2 must be on B, and 3 must be on A. The last pair then violates the rule.
इनपुट:
pairs = [
[1, 2],
[2, 3]
]
people = 4
अपेक्षित आउटपुट:
expected = Trueइनपुट:
std::vector<std::vector<long long>> pairs = {
{1, 2},
{2, 3}
};
long long people = 4;
अपेक्षित आउटपुट:
bool expected = true;इनपुट:
long[][] pairs = new long[][] {
new long[] {1, 2},
new long[] {2, 3}
};
long people = 4;
अपेक्षित आउटपुट:
bool expected = true;व्याख्या
Put 1 and 3 on team A and 2 on team B. Person 4 can join either team.
कैसे हल करें
पहले खुद कोशिश करें, फिर एक-एक करके संकेत खोलें।
संकेत 1
यह तभी possible है जब हर constraint component को दो अलग colors में color किया जा सके।
संकेत 2
हर connected component को traverse करो और हर pair constraint पर team assignments alternate करो।
संकेत 3
अगर odd cycle की वजह से किसी person को दोनों teams में देना पड़े, तो answer false हो जाता है।
अपेक्षित जटिलता
समय O(people + pairs), अतिरिक्त स्थान O(people + pairs)
संदर्भ
यह चुनौती CodeUtility के लिए अनुकूलित की गई है। ऊपर दिए गए स्टेटमेंट और सीमाओं का पालन करें।