LeetCode - Is Graph Bipartite?
Given an undirected graph, return true if and only if it is bipartite. Recall that a graph is bipartite if we can split it's set of nodes into two independent subsets A and B such that every edge in the graph has one node in A and another node in B. The graph is given in the following form: graph[i] is a list of indexes j for which the edge between nodes i and j exists. Each node is an integer between 0 and graph.length - 1. There are no self edges or parallel edges: graph[i] does not contain i, and it doesn't contain any element twice. Example 1: Input: [[1,3], [0,2], [1,3], [0,2]] Output: true Explanation: The graph looks like this: 0----1 | | | | 3----2 We can divide the vertices into two groups: {0, 2} and {1, 3}. Example 2: Input: [[1,2,3], [0,2], [0,1,3], [0,2]] Output: false Explanation: The graph looks like this: 0----1 | \ | | \ | 3----2 We cannot find a way to divide the set of nodes into two independent subsets.
原来输入数组中的graph[i],表示顶点i所有相邻的顶点,比如对于例子1来说,顶点0和顶点1,3相连,顶点1和顶点0,2相连,顶点2和结点1,3相连,顶点3和顶点0,2相连。这道题让我们验证给定的图是否是二分图,所谓二分图,就是可以将图中的所有顶点分成两个不相交的集合,使得同一个集合的顶点不相连。为了验证是否有这样的两个不相交的集合存在,我们采用一种很机智的染色法,大体上的思路是要将相连的两个顶点染成不同的颜色,一旦在染的过程中发现有两连的两个顶点已经被染成相同的颜色,说明不是二分图。这里我们使用两种颜色,分别用1和-1来表示,初始时每个顶点用0表示未染色,然后遍历每一个顶点,如果该顶点未被访问过,则调用递归函数,如果返回false,那么说明不是二分图,则直接返回false。如果循环退出后没有返回false,则返回true。在递归函数中,如果当前顶点已经染色,如果该顶点的颜色和将要染的颜色相同,则返回true,否则返回false。如果没被染色,则将当前顶点染色,然后再遍历与该顶点相连的所有的顶点,调用递归函数,如果返回false了,则当前递归函数的返回false,循环结束返回true,参见代码如下:
class Solution { public boolean isBipartite(int[][] graph) { if(graph == null){ return false; } int v = graph.length; //if we only have 2 vertices, then it's a Bipartite if(v <= 2){ return true; } int[] colors = new int[v]; for(int i = 0; i < v; i++){ if(colors[i] == 0 && !valid(graph, i, 1, colors)){ return false; } } return true; } private boolean valid (int[][] graph, int cur, int color, int[] colors){ if(colors[cur] != 0){ return colors[cur] == color; } colors[cur] = color; for(int i : graph[cur]){ if(!valid(graph, i, color * -1, colors)){ return false; } } return true; } }
posted on 2018-09-21 11:35 IncredibleThings 阅读(127) 评论(0) 编辑 收藏 举报