Cut Tree
Problem Statement :
Given a tree T with n nodes, how many subtrees (T') of T have at most K edges connected to (T - T')? Input Format The first line contains two integers n and K followed by n-1 lines each containing two integers a & b denoting that there's an edge between a & b. Constraints 1 <= K <= n <= 50 Every node is indicated by a distinct number from 1 to n. Output Format A single integer which denotes the number of possible subtrees.
Solution :
Solution in C :
In C++ :
#include<iostream>
#include<string.h>
using namespace std;
#define MAXN 100
int first[MAXN], next1[MAXN], v[MAXN];
int edgeindex;
int n, k;
long long dp[MAXN][MAXN];
bool vis[MAXN];
void addedge(int a, int b)
{
v[edgeindex] = b;
next1[edgeindex] = first[a];
first[a] = edgeindex++;
}
void solve(int cur, int root)
{
if(vis[cur])
return;
for(int i = first[cur]; i != -1; i = next1[i])
{
if(v[i] == root)
continue;
solve(v[i], cur);
for(int j = k; j > 0; --j)
{
int tmp = 0;
for(int x = j; x > 0; x--)
{
dp[cur][j] += dp[cur][j-x] * dp[v[i]][x];
}
dp[cur][j] += dp[cur][j-1];
}
}
return;
}
int main()
{
while(cin>>n>>k)
{
edgeindex = 0;
memset(first, -1, sizeof(first));
memset(dp, 0, sizeof(dp));
memset(vis, false, sizeof(vis));
int a, b;
for(int i = 1; i < n; ++i)
{
cin>>a>>b;
addedge(a, b);
addedge(b, a);
}
for(int i = 1; i <= n; ++i)
{
dp[i][0] = 1;
}
solve(1, -1);
long long ans = 0;
for(int i = 1; i <= n; ++i)
{
for(int j = 0; j < k; ++j)
{
ans += dp[i][j];
}
}
ans += dp[1][k];
cout<<ans+1<<endl;
}
}
In Java :
import java.io.BufferedInputStream;
import java.util.ArrayList;
import java.util.Scanner;
public class Solution {
static long rooted[][] = new long [55][55];
static int size[] = new int[55];
static int outDegree[] = new int[55];
static ArrayList<Integer> tree[] = new ArrayList[55];
static int n;
static int k;
static void dfs(int u, int p) {
size[u] = 1;
for (int v : tree[u]) {
if (v == p) continue;
dfs(v, u);
outDegree[u]++;
size[u] += size[v];
}
//////////////////////////////////////////////////////////////////
long pre[] = rooted[u];
rooted[u][0] = 1;
for (int v : tree[u]) {
if (v == p) continue;
rooted[u] = new long[55];
for (int i=0; i<=k; i++) {
if (i >= 1) rooted[u][i] += pre[i - 1];
for (int j=0; j<=i; j++)
rooted[u][i] += pre[i - j] * rooted[v][j];
}
pre = rooted[u];
}
}
public static void main(String[] args) {
Scanner cin = new Scanner(new BufferedInputStream(System.in));
n = cin.nextInt();
k = cin.nextInt();
for (int i=0; i<n; i++) tree[i] = new ArrayList<Integer>();
for (int i=0; i<n-1; i++) {
int u = cin.nextInt(); u--;
int v = cin.nextInt(); v--;
tree[u].add(v);
tree[v].add(u);
}
dfs(0, -1);
long ans = 0;
for (int i=0; i<n; i++)
if (i == 0)
for (int j=0; j<=k; j++) ans += rooted[i][j];
else
for (int j=1; j<=k; j++) ans += rooted[i][j - 1];
System.out.println(ans + 1);
// for (int i=0; i<n; i++) {
// for (int j=0; j<=k; j++)
// System.out.print(rooted[i][j] + " ");
// System.out.println();
// }
// System.out.println();
}
}
In C :
#include <stdio.h>
#include <stdlib.h>
void dfs(int x,int parent);
int table[50][50]={0},c[50]={0},p[50],q[51]={0},N;
long long dp1[50][51]={0},dp2[50][51]={0},temp[51],ans;
int main(){
int K,x,y,i,j,k;
scanf("%d%d",&N,&K);
for(i=0;i<N-1;i++){
scanf("%d%d",&x,&y);
table[x-1][y-1]=-1;
table[y-1][x-1]=-1;
}
dfs(0,0);
for(i=0;i<N;i++)
if(!c[i])
q[++q[0]]=i;
while(q[0]){
x=q[q[0]--];
dp1[x][0]=dp2[x][0]=1;
for(i=0;i<N;i++)
if(table[x][i]==1){
for(j=1;j<=K;j++)
temp[j]=0;
for(j=1;j<=K;j++){
dp1[x][j]+=dp1[i][j]+dp2[i][j-1];
for(k=0;k<=j;k++)
if(k==1)
temp[j]+=(dp2[i][k]+1)*dp2[x][j-k];
else
temp[j]+=dp2[i][k]*dp2[x][j-k];
}
for(j=1;j<=K;j++)
dp2[x][j]=temp[j];
}
if(x){
c[p[x]]--;
if(!c[p[x]])
q[++q[0]]=p[x];
}
}
for(i=0,ans=0;i<=K;i++)
ans+=dp1[0][i]+dp2[0][i];
printf("%lld",ans);
return 0;
}
void dfs(int x,int parent){
int i;
p[x]=parent;
for(i=0;i<N;i++)
if(table[x][i] && i!=parent){
table[x][i]+=2;
c[x]++;
dfs(i,x);
}
return;
}
In Python3 :
line = input().split()
n = int(line[0])
K = int(line[1])
adjlst = [[1]]
for i in range(n):
adjlst.append([])
adjlst[1].append(0)
for i in range(n - 1):
line = input().split()
x = int(line[0])
y = int(line[1])
adjlst[x].append(y)
adjlst[y].append(x)
def dfs(node, par, adjlst, K):
conlst = [0] * (K + 1)
dislst = [0] * (K + 1)
conlst[0] = 1
for chld in adjlst[node]:
if chld != par:
tcl, tdl = dfs(chld, node, adjlst, K)
# print(str(tcl))
# print(str(tdl))
dislst[0] += tdl[0]
tcl2 = [0] * (K + 1)
for i in range(K):
dislst[i + 1] += tcl[i] + tdl[i + 1]
tcl2[i + 1] += conlst[i]
for i in range(K + 1):
for j in range(K + 1):
if i + j <= K:
tcl2[i + j] += tcl[i] * conlst[j]
conlst = list(tcl2)
return conlst, dislst
conlst, dislst = dfs(1, 0, adjlst, K)
# print(str(conlst))
# print(str(dislst))
ans = sum(conlst) + sum(dislst) + 1
print(str(ans))
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