Hungarian Algorithm

Took me forever to figure out how to even write this code...still no idea how it REALLY works

/**
 * Hungarian Algorithm for calculating the maximum weight matching of a bipartite graph
 * @param cost - cost of matching person i to task j
 * @return [i]= the j matched with i
 */
public int[] maxBipartiteMatching(int[][] cost){
	int n=cost.length;
	int x = -1,y=-1;
	int[][] match=new int[2][n],label=new int[2][n],prev=new int[2][n], slack=new int[2][n];
	for(int i=0;i<n;i++)for(int j=0;j<n;j++)label[0][i]=Math.max(label[0][i], cost[i][j]);
	for(int[] i:match)Arrays.fill(i, -1);
	for(int rnd=0;rnd<n;rnd++){
		HashSet<Integer> s=new HashSet<Integer>(),t=new HashSet<Integer>();
		Queue<Integer> q=new LinkedList<Integer>();
		for(int[] i:prev)Arrays.fill(i, -1);
		for(int i=0;i<n;i++)if(match[0][i]==-1){//find an unmatched x
			q.offer(i);
			x=i;
			s.add(i);
			prev[0][x]=-2;
			break;
		}
		for(int i=0;i<n;i++){
			slack[0][i]=label[0][x]+label[1][i]-cost[x][i];
			slack[1][i]=x;
		}
		OUT:
		while(true){
			while(!q.isEmpty()){
				int cur=q.poll();
				for(int i=0;i<n;i++)if(!t.contains(i)&&cost[cur][i]==label[0][cur]+label[1][i]){
					int m=match[1][i];
					prev[1][i]=cur;
					if(m==-1){
						y=i;
						break OUT;
					}
					t.add(i);
					q.offer(m);
					s.add(m);
					prev[0][m]=i;
					for(int j=0;j<n;j++)if(slack[0][j]> label[0][m]+label[1][j]-cost[m][j]){
						slack[0][j]=label[0][m]+label[1][j]-cost[m][j];
						slack[1][j]=m;
					}
				}
			}
			int min=Integer.MAX_VALUE;
			int mini = 0;
			for(int i=0;i<n;i++)if(!t.contains(i)&&slack[0][i]<min){
				min=slack[0][i];
				mini=i;
			}
			for(int i=0;i<n;i++){
				if(s.contains(i))label[0][i]-=min;
				if(t.contains(i))label[1][i]+=min;
				else slack[0][i]-=min;
			}
			t.remove(mini);
			q.offer(slack[1][mini]);
		}
		while(y!=-2){
			match[1][y]=prev[1][y];
			match[0][match[1][y]]=y;
			y=prev[0][match[1][y]];
		}
	}
	return match[0];
}