main.cpp

// Source: https://leetcode.com/problems/is-graph-bipartite
// Title: Is Graph Bipartite?
// Difficulty: Medium
// Author: Mu Yang <http://muyang.pro>

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// There is an **undirected** graph with `n` nodes, where each node is numbered between `0` and `n - 1`. You are given a 2D array `graph`, where `graph[u]` is an array of nodes that node `u` is adjacent to. More formally, for each `v` in `graph[u]`, there is an undirected edge between node `u` and node `v`. The graph has the following properties:
//
// - There are no self-edges (`graph[u]` does not contain `u`).
// - There are no parallel edges (`graph[u]` does not contain duplicate values).
// - If `v` is in `graph[u]`, then `u` is in `graph[v]` (the graph is undirected).
// - The graph may not be connected, meaning there may be two nodes `u` and `v` such that there is no path between them.
//
// A graph is **bipartite** if the nodes can be partitioned into two independent sets `A` and `B` such that **every** edge in the graph connects a node in set `A` and a node in set `B`.
//
// Return `true` if and only if it is **bipartite**.
//
// **Example 1:**
// https://assets.leetcode.com/uploads/2020/10/21/bi2.jpg
//
// ```
// Input: graph = [[1,2,3],[0,2],[0,1,3],[0,2]]
// Output: false
// Explanation: There is no way to partition the nodes into two independent sets such that every edge connects a node in one and a node in the other.```
//
// **Example 2:**
// https://assets.leetcode.com/uploads/2020/10/21/bi1.jpg
//
// ```
// Input: graph = [[1,3],[0,2],[1,3],[0,2]]
// Output: true
// Explanation: We can partition the nodes into two sets: {0, 2} and {1, 3}.```
//
// **Constraints:**
//
// - `graph.length == n`
// - `1 <= n <= 100`
// - `0 <= graph[u].length < n`
// - `0 <= graph[u][i] <= n - 1`
// - `graph[u]`does not contain`u`.
// - All the values of `graph[u]` are **unique**.
// - If `graph[u]` contains `v`, then `graph[v]` contains `u`.
//
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

#include <queue>
#include <vector>

using namespace std;

// BFS
class Solution {
 public:
  bool isBipartite(vector<vector<int>>& graph) {
    int n = graph.size();

    // Prepare
    auto que = queue<int>();
    auto colors = vector<int>(n, 0);  // 0: unknown, +-1: color

    // Loop
    for (auto start = 0; start < n; ++start) {
      if (colors[start] != 0) continue;  // visited
      que.push(start);
      colors[start] = 1;

      while (!que.empty()) {
        auto node = que.front();
        auto color = colors[node];
        que.pop();

        for (auto next : graph[node]) {
          if (colors[next] != 0) {  // visited
            if (colors[next] == color) return false;
          } else {  // not visited
            colors[next] = -color;
            que.push(next);
          }
        }
      }
    }

    return true;
  }
};