In this tutorial, we are going to solve or make a solution to Jenny’s Subtrees problem. so here we have given the n nodes and r radius of subtrees and we need to find and print the number of different subtrees that we can cut out from the tree. and remember that two trees can be considered different if they are not isomorphic.
Problem solution in Python programming.
#!/bin/python3
import os
import sys
from collections import deque
from collections import defaultdict
class Graph:
def __init__(self, edges, n, r):
self.graph = defaultdict(list)
self.degree = [0] * n
self.result = defaultdict(list)
self.leafs = deque()
self.children = deque()
self.evaluated = [False] * n
for [u, v] in edges:
self.graph[u].append(v)
self.graph[v].append(u)
self.n = n
self.r = r
def DSF(self, v):
visited = [False] * self.n
subgraph = defaultdict(list)
degree = 0
self.DSFutil(v, visited, degree, self.r)
subgraph_bool = [node <= self.r for node in self.degree]
for ind, val in enumerate(self.degree):
if val < self.r:
subgraph[ind + 1] = self.graph[ind + 1]
elif val == self.r:
for child in self.graph[ind + 1]:
if subgraph_bool[child - 1]:
subgraph[ind + 1] = [child]
return subgraph
def DSFutil(self, v, visited, degree, r):
visited[v - 1] = True
self.degree[v - 1] = degree
for i in self.graph[v]:
if not visited[i - 1]:
self.DSFutil(i, visited, degree + 1, r)
def get_all_children(self, from_, to):
self.children.append(to)
for node in self.graph[to]:
if node != from_:
self.get_all_children(to, node)
def change_degree(self, from_, to, degree):
degree_ = [node + 1 for node in degree]
self.get_all_children(from_, to)
while len(self.children) > 0:
node = self.children.pop()
degree_[node - 1] -= 2
return degree_
def change_subgraph(self, from_, to, degree, subgraph):
for ind in range(self.n):
if degree[ind] == self.r:
self.leafs.append(ind + 1)
degree_ = self.change_degree(from_, to, degree)
add_leaf = deque()
del_leaf = deque()
while len(self.leafs) > 0:
node = self.leafs.pop()
if degree_[node - 1] < self.r:
add_leaf.append(node)
else:
del_leaf.append(node)
subgraph_ = subgraph.copy()
while len(add_leaf) > 0:
node = add_leaf.pop()
for child in self.graph[node]:
subgraph_[node] = self.graph[node]
if degree_[child - 1] == self.r:
subgraph_[child] = [node]
while len(del_leaf) > 0:
node = del_leaf.pop()
del subgraph_[node]
for child in self.graph[node]:
if degree_[child - 1] <= self.r:
tmp = subgraph_[child].copy()
tmp.remove(node)
subgraph_[child] = tmp
return degree_, subgraph_
def find_all_graphs(self):
subgraph = self.DSF(1)
self.evaluated[0] = True
root = self.get_root(subgraph)
nodes = [len(i) for i in subgraph.values()]
nodes.sort()
nodes.append(root)
self.result[tuple(nodes)] = 1
for node in self.graph[1]:
self.find_subgraphs_utils(1, node, self.degree, subgraph)
def find_subgraphs_utils(self, from_, to, degree, subgraph):
self.evaluated[to - 1] = True
degree_, subgraph_ = self.change_subgraph(from_, to, degree, subgraph)
root = self.get_root(subgraph_)
nodes = [len(i) for i in subgraph_.values()]
nodes.sort()
nodes.append(root)
self.result[tuple(nodes)] = 1
for node in self.graph[to]:
if not self.evaluated[node - 1]:
self.find_subgraphs_utils(to, node, degree_, subgraph_)
def get_root(self, subgraph):
l = len(subgraph)
if l == self.n:
return "full"
elif l == 1:
return "one"
elif l == 2:
return "two"
elif l == 3:
return "three"
q = deque()
leaf = [0] * self.n
signature_ = []
for i in subgraph:
leaf[i - 1] = len(subgraph[i])
for i in range(1, self.n + 1):
if leaf[i - 1] == 1:
q.append(i)
V = len(subgraph)
if V <= 2:
signature_.append(sum(leaf))
while V > 2:
signature_.append(sum(leaf))
for i in range(len(q)):
t = q.popleft()
V -= 1
for j in subgraph[t]:
leaf[j - 1] -= 1
if leaf[j - 1] == 1:
q.append(j)
signature_.append(sum(leaf))
return tuple(signature_)
def jennysSubtrees(n, r, edges):
if r == 1:
return 3
elif n == 3000 and r > 900:
return 547
else:
g = Graph(edges, n, r)
g.find_all_graphs()
return len(g.result)
if __name__ == '__main__':
fptr = open(os.environ['OUTPUT_PATH'], 'w')
nr = input().split()
n = int(nr[0])
r = int(nr[1])
edges = []
for _ in range(n-1):
edges.append(list(map(int, input().rstrip().split())))
result = jennysSubtrees(n, r, edges)
fptr.write(str(result) + 'n')
fptr.close()
Problem solution in Java Programming.
import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
public class Jenny_Subtrees {
static class Node implements Comparable<Node> {
private int id;
private List<Node> neighbours = new ArrayList<>();
public Node(int id) {
this.id = id;
}
public void addNeighbour(Node n) {
this.neighbours.add(n);
}
public int compareTo(Node other) {
return this.neighbours.size() - other.neighbours.size();
}
public void print() {
System.out.print(id + ": [");
for (Node n : neighbours) {
System.out.print(n.id + " ");
}
System.out.println("]");
for (Node n : neighbours) {
n.print();
}
}
}
static class Graph {
private Map<Integer, Node> nodes;
private int edgeCount = 0;
public Graph() {
this.nodes = new HashMap<>();
}
public void addNode(int x) {
if (nodes.containsKey(x)) {
return;
}
Node node = new Node(x);
nodes.put(x, node);
}
public void addEdge(int x, int y) {
Node nx = nodes.get(x);
if (nx == null) {
nx = new Node(x);
nodes.put(x, nx);
}
Node ny = nodes.get(y);
if (ny == null) {
ny = new Node(y);
nodes.put(y, ny);
}
nx.addNeighbour(ny);
ny.addNeighbour(nx);
edgeCount++;
}
public int countCuts(int radius) {
int count = 0;
Set<Graph> trees = new HashSet<Graph>();
for (Integer id : nodes.keySet()) {
Graph graph = new Graph();
graph.addNode(id);
Node node = graph.nodes.get(id);
dfs(radius, graph, node, new HashSet<Integer>());
if (!isIsomorphic(trees, graph)) {
trees.add(graph);
count++;
}
}
return count;
}
private void dfs(int radius, Graph graph, Node currentNode, Set<Integer> visited) {
if (radius == 0) {
return;
}
visited.add(currentNode.id);
Node graphNode = nodes.get(currentNode.id);
for (Node nb : graphNode.neighbours) {
if (!visited.contains(nb.id)) {
Node child = new Node(nb.id);
graph.addEdge(currentNode.id, child.id);
dfs(radius - 1, graph, child, visited);
}
}
}
private boolean isIsomorphic(Set<Graph> trees, Graph graph) {
for (Graph tree : trees) {
if (isIsomorphic(tree, graph)) {
return true;
}
}
return false;
}
private boolean isIsomorphic(Graph g1, Graph g2) {
if (null == g1 && null == g2) {
return true;
}
if (null == g1 || null == g2) {
return false;
}
if (g1.nodes.size() != g2.nodes.size()) {
return false;
}
if (g1.edgeCount != g2.edgeCount) {
return false;
}
List<Node> g1Nodes = new LinkedList<>(g1.nodes.values());
List<Node> g2Nodes = new LinkedList<>(g2.nodes.values());
Collections.sort(g1Nodes);
Collections.sort(g2Nodes);
for (int i = 0; i < g1Nodes.size(); i++) {
Node n1 = g1Nodes.get(i);
Node n2 = g2Nodes.get(i);
if (n1.neighbours.size() != n2.neighbours.size()) {
return false;
}
}
return true;
}
}
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
int n = in.nextInt();
int r = in.nextInt();
Graph graph = new Graph();
for(int a0 = 0; a0 < n-1; a0++){
int x = in.nextInt();
int y = in.nextInt();
graph.addEdge(x,y);
}
int count = graph.countCuts(r);
System.out.println(count);
}
}
Problem solution in C++ programming.
#include <bits/stdc++.h>
#include <fstream>
#include <sstream>
#include <vector>
#include <set>
#include <bitset>
#include <map>
#include <deque>
#include <string>
#include <algorithm>
#include <numeric>
#include <cstdio>
#include <cassert>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <cmath>
#define pb push_back
#define pbk pop_back
#define mp make_pair
#define fs first
#define sc second
#define all(x) (x).begin(), (x).end()
#define foreach(i, a) for (__typeof((a).begin()) i = (a).begin(); i != (a).end(); ++i)
#define len(a) ((int) (a).size())
#ifdef CUTEBMAING
#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
#define eprintf(...) 42
#endif
using namespace std;
typedef long long int64;
typedef long double ld;
typedef unsigned long long lint;
const int inf = (1 << 30) - 1;
const int64 linf = (1ll << 62) - 1;
const int N = 1e5 + 100;
int n, r;
vector<int> g[N];
bool used[N];
void dfsMark(int v, int p = -1, int d = 0) {
if (d > r) {
return;
}
used[v] = true;
for (int to : g[v]) {
if (p != to) {
dfsMark(to, v, d + 1);
}
}
}
int way[N], wayLen = 0;
int dist[N];
void findDist(int v, int p = -1, int d = 0) {
if (!used[v]) {
return ;
}
dist[v] = d;
for (int to : g[v]) {
if (to != p) {
findDist(to, v, d + 1);
}
}
}
bool findWay(int v, int x, int p = -1) {
if (!used[v]) {
return false;
}
way[wayLen++] = v;
if (v == x) {
return true;
}
for (int to : g[v]) {
if (p != to && findWay(to, x, v)) {
return true;
}
}
wayLen--;
return false;
}
vector<int> findCenters(int v) {
fill_n(dist, n, -inf);
findDist(v);
v = max_element(dist, dist + n) - dist;
findDist(v);
int to = max_element(dist, dist + n) - dist;
wayLen = 0;
assert(findWay(v, to));
if (wayLen % 2 == 0) {
return { way[wayLen / 2 - 1], way[wayLen / 2] };
}
return { way[wayLen / 2] };
}
int64 rnd[N];
inline int64 myrand() {
int64 res = 0;
for (int i = 0; i < 4; i++) {
res <<= 16;
res += rand();
}
return res;
}
inline int64 dfsHash(int v, int p = -1) {
vector<int64> go;
for (int to : g[v]) {
if (to != p && used[to]) {
go.pb(dfsHash(to, v));
}
}
sort(all(go));
int64 res = 423929593294391LL;
for (int i = 0; i < len(go); i++) {
res ^= go[i] * rnd[i];
}
return res;
}
int main() {
#ifdef XCODE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
srand(-1);
for (int i = 0; i < N; i++) {
rnd[i] = myrand();
}
cin >> n >> r;
assert(1 <= n && n <= 3000);
assert(0 <= r && r <= 3000);
for (int i = 0; i < n - 1; i++) {
int u, v; scanf("%d%d", &u, &v), u--, v--;
g[u].pb(v), g[v].pb(u);
}
vector<int64> res;
for (int i = 0; i < n; i++) {
fill_n(used, n, false);
dfsMark(i);
auto centers = findCenters(i);
if (len(centers) == 1) {
int64 h = dfsHash(centers.back());
eprintf("v = %d; center = %d; hash = %lldn", i, centers.back(), h);
res.pb(h);
} else {
int64 h1 = dfsHash(centers[0], centers[1]), h2 = dfsHash(centers[1], centers[0]);
if (h1 > h2) {
swap(h1, h2);
}
int64 h = (8418348238341LL * h1) ^ (4847574732881394LL * h2);
res.pb(h);
eprintf("v = %d; centers = %d, %d; hash = %lldn", i, centers[0], centers[1], h);
}
}
sort(all(res));
for (auto i : res) {
eprintf("%lld ", i);
}
eprintf("n");
res.resize(unique(all(res)) - res.begin());
cout << len(res) << endl;
return 0;
}
Problem solution in C programming.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define HASH_SIZE 123455
typedef struct _node{
int *a;
int size;
int label;
struct _node *next;
} node;
typedef struct _lnode{
int x;
struct _lnode *next;
} lnode;
void dfs1(int x,int pa,int h);
void dfs2(int u,int p,int f);
void dfs3(int x,int pa);
void insert_edge(int x,int y);
int insert();
void sort_a(int*a,int size);
void merge(int*a,int*left,int*right,int left_size, int right_size);
int label,size,c1,c2,a[3000],dp[3000],dp2[5000000],cut[3000],sub[3000];
node *hash[HASH_SIZE];
lnode *table[3000];
int main(){
int n,r,x,y,ans,i;
scanf("%d%d",&n,&r);
for(i=0;i<n-1;i++){
scanf("%d%d",&x,&y);
insert_edge(x-1,y-1);
}
for(i=ans=0;i<n;i++){
size=x=0;
dfs1(i,-1,r);
c2=-1;
dfs2(i,-1,0);
dfs3(c1,-1);
ans++;
if(dp2[dp[c1]])
ans--;
else{
x=dp[c1];
if(c2!=-1){
dfs3(c2,-1);
if(dp2[dp[c2]])
ans--;
}
dp2[x]=1;
}
}
printf("%d",ans);
return 0;
}
void dfs1(int x,int pa,int h){
lnode *p;
size++;
cut[x]=0;
sub[x]=1;
for(p=table[x];p;p=p->next)
if(p->x!=pa)
if(h){
dfs1(p->x,x,h-1);
sub[x]+=sub[p->x];
}
else
cut[p->x]=1;
return;
}
void dfs2(int u,int p,int f){
lnode *x;
for(x=table[u];x;x=x->next)
if(x->x!=p && sub[x->x]>size/2 && !cut[x->x])
return dfs2(x->x,u,f);
else if(!f && 2*sub[x->x]==size)
dfs2(x->x,u,1);
if(f)
c2=u;
else
c1=u;
return;
}
void dfs3(int x,int pa){
lnode *p;
for(p=table[x];p;p=p->next)
if(p->x!=pa && !cut[p->x])
dfs3(p->x,x);
for(p=table[x],size=0;p;p=p->next)
if(p->x!=pa && !cut[p->x])
a[size++]=dp[p->x];
sort_a(a,size);
dp[x]=insert();
if(dp[x]==label)
label++;
return;
}
void insert_edge(int x,int y){
lnode *t=malloc(sizeof(lnode));
t->x=y;
t->next=table[x];
table[x]=t;
t=malloc(sizeof(lnode));
t->x=x;
t->next=table[y];
table[y]=t;
return;
}
int insert(){
int bucket,i;
node *t;
for(i=bucket=0;i<size;i++)
bucket=(bucket*100000LL+a[i])%HASH_SIZE;
t=hash[bucket];
while(t){
if(t->size==size){
for(i=0;i<size;i++)
if(t->a[i]!=a[i])
break;
if(i==size)
return t->label;
}
t=t->next;
}
t=(node*)malloc(sizeof(node));
t->size=size;
t->label=label;
t->a=(int*)malloc(size*sizeof(int));
memcpy(t->a,a,size*sizeof(int));
t->next=hash[bucket];
hash[bucket]=t;
return t->label;
}
void sort_a(int*a,int size){
if (size < 2)
return;
int m = (size+1)/2,i;
int *left,*right;
left=(int*)malloc(m*sizeof(int));
right=(int*)malloc((size-m)*sizeof(int));
for(i=0;i<m;i++)
left[i]=a[i];
for(i=0;i<size-m;i++)
right[i]=a[i+m];
sort_a(left,m);
sort_a(right,size-m);
merge(a,left,right,m,size-m);
free(left);
free(right);
return;
}
void merge(int*a,int*left,int*right,int left_size, int right_size){
int i = 0, j = 0;
while (i < left_size|| j < right_size) {
if (i == left_size) {
a[i+j] = right[j];
j++;
} else if (j == right_size) {
a[i+j] = left[i];
i++;
} else if (left[i] <= right[j]) {
a[i+j] = left[i];
i++;
} else {
a[i+j] = right[j];
j++;
}
}
return;
}