问题
I'm trying to implement a method for adding all possible Hamiltonian cycles to a list using recursion. So far my stopping condition isn't sufficient and I get "OutOfMemoryError: Java heap space" in the line that adds a vertex to a list:
private boolean getHamiltonianCycles(int first, int v, int[] parent,
boolean[] isVisited, List<List<Integer>> cycles) {
isVisited[v] = true;
if (allVisited(isVisited) && neighbors.get(v).contains(new Integer(first))) {
ArrayList<Integer> cycle = new ArrayList<>();
int vertex = v;
while (vertex != -1) {
cycle.add(vertex);
vertex = parent[vertex];
}
cycles.add(cycle);
return true;
} else if (allVisited(isVisited)) {
isVisited[v] = false;
return false;
}
boolean cycleExists = false;
for (int i = 0; i < neighbors.get(v).size(); i++) {
int u = neighbors.get(v).get(i);
parent[u] = v;
if (!isVisited[u]
&& getHamiltonianCycles(first, u, parent, isVisited, cycles)) {
cycleExists = true;
}
}
//if (!cycleExists) {
isVisited[v] = false; // Backtrack
//}
return cycleExists;
}
Can someone please suggest me what I'm doing wrong or is my approach completely incorrect?
EDIT: As suggested in comments, the culprit was the parent array, causing an infinite loop. I wasn't able to correct it and I changed the array to store the child element. Now everything seems to work:
private boolean getHamiltonianCycles(int first, int v, int[] next,
boolean[] isVisited, List<List<Integer>> cycles) {
isVisited[v] = true;
if (allVisited(isVisited) && neighbors.get(v).contains(first)) {
ArrayList<Integer> cycle = new ArrayList<>();
int vertex = first;
while (vertex != -1) {
cycle.add(vertex);
vertex = next[vertex];
}
cycles.add(cycle);
isVisited[v] = false;
return true;
}
boolean cycleExists = false;
for (int u : neighbors.get(v)) {
next[v] = u;
if (!isVisited[u]
&& getHamiltonianCycles(first, u, next, isVisited, cycles)) {
cycleExists = true;
}
}
next[v] = -1;
isVisited[v] = false; // Backtrack
return cycleExists;
}
回答1:
If you is looking for Disjoint Hamiltonian Cycles here have an implementation using Backtracking.
来源:https://stackoverflow.com/questions/16115942/finding-all-hamiltonian-cycles