785.Is Graph Bipartite?
===

###### tags: `Medium`,`Graph`,`DFS`,`BFS`

[785. Is Graph Bipartite?](https://leetcode.com/problems/is-graph-bipartite/)

### 題目描述

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***.

### 範例

**Example 1:**


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:**


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`.

### 解答
#### Python

class Solution:
    def isBipartite(self, graph: List[List[int]]) -> bool:
        n = len(graph)
        colors = [0] * n
        
        def dfs(node, color = 1):
            if colors[node] != 0:
                return colors[node] == color
            colors[node] = color
            for nei in graph[node]:
                if not dfs(nei, -color):
                    return False
            return True
        
        for i in range(n):
            if colors[i] == 0:
                if not dfs(i):
                    return False
        return True

> [name=Yen-Chi Chen][time=Sat, May 20, 2023]

### Reference
[Bipartite Graph](https://web.ntnu.edu.tw/~algo/BipartiteGraph.html)

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