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PossibleBipartition.java
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PossibleBipartition.java
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package Leetcode;
import java.util.*;
/**
* @author kalpak
*
* Given a set of N people (numbered 1, 2, ..., N), we would like to split everyone into two groups of any size.
* Each person may dislike some other people, and they should not go into the same group.
*
* Formally, if dislikes[i] = [a, b], it means it is not allowed to put the people numbered a and b into the same group.
* Return true if and only if it is possible to split everyone into two groups in this way.
*
*
* Example 1:
* Input: N = 4, dislikes = [[1,2],[1,3],[2,4]]
* Output: true
* Explanation: group1 [1,4], group2 [2,3]
*
*
* Example 2:
* Input: N = 3, dislikes = [[1,2],[1,3],[2,3]]
* Output: false
*
*
* Example 3:
* Input: N = 5, dislikes = [[1,2],[2,3],[3,4],[4,5],[1,5]]
* Output: false
*
*
* Constraints:
*
* 1 <= N <= 2000
* 0 <= dislikes.length <= 10000
* dislikes[i].length == 2
* 1 <= dislikes[i][j] <= N
* dislikes[i][0] < dislikes[i][1]
* There does not exist i != j for which dislikes[i] == dislikes[j].
*/
public class PossibleBipartition {
public static boolean possibleBipartition(int N, int[][] dislikes) {
int[] vertexColors = new int[N + 1];
Map<Integer, List<Integer>> graph = new HashMap<>();
for (int[] edge : dislikes) {
graph.computeIfAbsent(edge[0], l -> new ArrayList<>()).add(edge[1]);
graph.computeIfAbsent(edge[1], l -> new ArrayList<>()).add(edge[0]);
}
for (int i = 1; i <= N; i++) {
if (vertexColors[i] == 0 && !dfsPossibleBipartition(graph, vertexColors, 1, i)) {
return false;
}
}
return true;
}
private static boolean dfsPossibleBipartition(Map<Integer, List<Integer>> graph, int[] vertexColors, int color, int startNode) {
if (vertexColors[startNode] != 0) {
return vertexColors[startNode] == color;
}
vertexColors[startNode] = color;
for (int next : graph.getOrDefault(startNode, Collections.emptyList())) {
if (!dfsPossibleBipartition(graph, vertexColors, -color, next)) {
return false;
}
}
return true;
}
public static void main(String[] args) {
int[][] dislikes = new int[][]{{1,2},{1,3},{2,4}};
System.out.println(possibleBipartition(4, dislikes));
dislikes = new int[][]{{1,2},{2,3},{3,4},{4,5},{1,5}};
System.out.println(possibleBipartition(5, dislikes));
}
}