Problem:
 Score : 500 points    Problem Statement You are given a tree with N vertices 1,2,\ldots,N , and positive integers c_1,c_2,\ldots,c_N .
The i -th edge in the tree (1 \leq i \leq N-1) connects Vertex a_i and Vertex b_i .  We will write a positive integer on each vertex in T and calculate our score as follows:   On each edge, write the smaller of the integers written on the two endpoints.  Let our score be the sum of the integers written on all the edges.   Find the maximum possible score when we write each of c_1,c_2,\ldots,c_N on one vertex in T , and show one way to achieve it. If an integer occurs multiple times in c_1,c_2,\ldots,c_N , we must use it that number of times.      Constraints  1 \leq N \leq 10000  1 \leq a_i,b_i \leq N  1 \leq c_i \leq 10^5  The given graph is a tree.         Input Input is given from Standard Input in the following format:  N  a_1  b_1  :  a_{N-1}  b_{N-1}  c_1  \ldots  c_N       Output Use the following format:  M  d_1  \ldots  d_N   where M is the maximum possible score, and d_i is the integer to write on Vertex i . d_1,d_2,\ldots,d_N must be a permutation of c_1,c_2,\ldots,c_N .
If there are multiple ways to achieve the maximum score, any of them will be accepted.        Sample Input 1 5
1 2
2 3
3 4
4 5
1 2 3 4 5      Sample Output 1 10
1 2 3 4 5  If we write 1,2,3,4,5 on Vertex 1,2,3,4,5 , respectively, the integers written on the four edges will be 1,2,3,4 , for the score of 10 . This is the maximum possible score.       Sample Input 2 5
1 2
1 3
1 4
1 5
3141 59 26 53 59      Sample Output 2 197
59 26 3141 59 53  c_1,c_2,\ldots,c_N may not be pairwise distinct.

Solution (Python):
import sys
import math
import fractions
from collections import deque
from collections import defaultdict
sys.setrecursionlimit(10**7)

N = int(input())
graph = [[] for _ in range(N)]
for _ in range(N - 1):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    graph[a].append(b)
    graph[b].append(a)

c = list(map(int, input().split()))
c.sort(reverse=True)
sum_val = sum(c) - max(c)

assign = [0] * N
index = 0

q = deque()
q.append(0)
visited = []

while len(q) != 0:
    cur = q.popleft()
    assign[cur] = c[index]
    index += 1
    for n in graph[cur]:
        if n not in visited:
            q.append(n)
    visited.append(cur)

print(sum_val)
print(" ".join(map(str, assign)))

Solution (Python):

from collections import deque

N = int(input())
edge = [[] for _ in range(N)]
for _ in range(N - 1):
    a,b = map(int, input().split())
    edge[a-1].append(b-1)
    edge[b-1].append(a-1)
C = [int(i) for i in input().split()]

C.sort()

M = sum(C[:-1])
d = [-1] * N

que = deque([0])
while que:
    v = que.popleft()
    d[v] = C.pop()
    for w in edge[v]:
        if d[w] < 0:
            que.append(w)

print(M)
print(*d)

Solution (Python):
from collections import deque
N=int(input())
tree=[[] for _ in range(N)]
tree2=[]
for i in range(N-1):
    a,b=map(int,input().split())
    tree[a-1].append(b-1)
    tree[b-1].append(a-1)
    tree2.append([a-1,b-1])
score=list(map(int,input().split()))
score.sort(reverse=True)

v=0
d=deque()
seen=[0]*N
d.append(v)
ans=[]
l=[0]*N
s=0
while len(ans)!=N:
    v=d.popleft()
    seen[v]=1
    ans.append(v)
    for j in tree[v]:
        if seen[j]!=1:
            d.append(j)
    
    
for i in range(N):
    l[ans[i]]=score[i]

for i in range(N-1):
    s=s+min(l[tree2[i][0]],l[tree2[i][1]])
print(s)
print(*l,sep=" ")

Solution (Python):
import sys 
sys.setrecursionlimit(10**6)
N=int(input())
A=[[]for i in range(N)]
X=[list(map(int, input().split())) for _ in range(N-1)]
for i in range(N-1):
  a=X[i][0]
  b=X[i][1]
  a-=1
  b-=1
  A[a].append(b)
  A[b].append(a)
D=list(map(int, input().split()))
D=sorted(D)[::-1]
from collections import deque
d=deque(D)
E=[-1]*N
def f(now,pre):
  for i in A[now]:
    if i!=pre and E[i]==-1:
      E[i]=d.popleft()
      f(i,now)
E[0]=d.popleft()
f(0,0)
print(sum(D[1:]))
print(*E)

Solution (Python):
from collections import deque
N = int(input())
es = [[] for i in range(N)]
for i in range(N-1):
    a, b = map(lambda x: int(x)-1, input().split())
    es[a].append(b)
    es[b].append(a)
c = list(map(int, input().split()))
c.sort(reverse=1)
q = deque()
q.append(0)
flg = [0]*N
num = [None]*N
i = 0
while len(q):
    v = q.popleft()
    flg[v] = 1
    num[v] = c[i]
    i += 1
    for u in es[v]:
        if flg[u]:
            continue
        q.append(u)
print(sum(c[1:]))
print(*num)

Solution (Python):











import sys
sys.setrecursionlimit(10**6)
input=sys.stdin.readline
from math import floor,sqrt,factorial,hypot,log 
from heapq import heappop, heappush, heappushpop
from collections import Counter,defaultdict,deque
from itertools import accumulate,permutations,combinations,product,combinations_with_replacement
from bisect import bisect_left,bisect_right
from copy import deepcopy
from fractions import gcd
from random import randint
def ceil(a,b): return (a+b-1)//b
inf=float('inf')
mod = 10**9+7
def pprint(*A): 
    for a in A:     print(*a,sep='\n')
def INT_(n): return int(n)-1
def MI(): return map(int,input().split())
def MF(): return map(float, input().split())
def MI_(): return map(INT_,input().split())
def LI(): return list(MI())
def LI_(): return [int(x) - 1 for x in input().split()]
def LF(): return list(MF())
def LIN(n:int): return [I() for _ in range(n)]
def LLIN(n: int): return [LI() for _ in range(n)]
def LLIN_(n: int): return [LI_() for _ in range(n)]
def LLI(): return [list(map(int, l.split() )) for l in input()]
def I(): return int(input())
def F(): return float(input())
def ST(): return input().replace('\n', '')
def main():
    N=I()
    edge = [[] for _ in range(N)]
    indegree = [0]*N
    for _ in range(N-1):
        a,b = MI_()
        indegree[a] += 1
        indegree[b] += 1
        edge[a].append(b)
        edge[b].append(a)

    ans = [-1]*N
    s = []
    for i in range(N):
        if(indegree[i]==1):
            s.append(i)  
    C = sorted(LI(), reverse=True)
    ans_sum = sum(C)-C[0]
    while(s):
        v = s.pop()
        ans[v] = C.pop()
        for to in edge[v]:
            indegree[to]-=1
            if(indegree[to] == 1):
                s.append(to)

    print(ans_sum)
    print(*ans)
if __name__ == '__main__':
    main()

Solution (Python):

import sys, math, itertools, collections, bisect
input = lambda: sys.stdin.buffer.readline().rstrip().decode('utf-8')
inf = float('inf') ;mod = 10**9+7
mans = inf ;ans = 0 ;count = 0 ;pro = 1

n = int(input())
G = [[] for i in range(n)]
for i in range(n-1):
  a,b = map(int,input().split())
  a-=1;b-=1
  G[a].append(b)
  G[b].append(a)
C = list(map(int,input().split()))
C.sort(reverse = True)
ans = [0]*n
ans[0] = C[0]
que = collections.deque([0])
i = 1
M = 0
while que:
  node = que.popleft()
  for vi in G[node]:
    if ans[vi] == 0:
      ans[vi] = C[i]
      i += 1
      que.append(vi)
      M += min(ans[vi],ans[node])
print(M)
print(*ans)

Solution (Python):
from collections import deque


n = int(input())
info = [list(map(int, input().split())) for i in range(n - 1)]
c = list(map(int, input().split()))
c = sorted(c, reverse=True)

tree = [[] for i in range(n)]
cnt = [0] * n
for i in range(n - 1):
    a, b = info[i]
    a -= 1
    b -= 1
    tree[a].append(b)
    tree[b].append(a)
    cnt[a] += 1
    cnt[b] += 1

for i in range(n):
    if len(tree[i]) == 1:
        root = i
        break
        
q = deque([root])
visited = [False] * n
visited[root] = True
ind = 0
ans = 0
res = [0] * n
while q:
    v= q.pop()
    tmp_cnt = 0
    for nxt_v in tree[v]:
        if visited[nxt_v]:
            tmp_cnt += 1
    ans += c[ind] * tmp_cnt
    res[v] = c[ind]
    ind += 1
    for nxt_v in tree[v]:
        if visited[nxt_v]:
            continue
        visited[nxt_v] = True
        q.append(nxt_v)
    
print(ans)
print(*res)

Solution (Python):
n = int(input())
g = [[] for _ in range(n)]
for i in range(n-1):
    a, b = map(int, input().split())
    a, b = a-1, b-1
    g[a].append(b)
    g[b].append(a)

C = list(map(int, input().split()))
C.sort(reverse=True)

order = []
par = [-1]*n
s = []
visit = [-1]*n
s.append(0)
visit[0] = 0
while s:
    v = s.pop()
    order.append(v)
    for u in g[v]:
        if u == par[v]:
            continue
        par[u] = v
        s.append(u)

order.reverse()
ans = [0]*n
m = 0
for v in order:
    ans[v] = C.pop()
    if par[v] != -1:
        m += ans[v]
print(m)
print(*ans)

Solution (Python):
import sys
sys.setrecursionlimit(10**8)
N = int(input())
AB = [tuple(map(int,input().split())) for i in range(N-1)]
C = list(map(int,input().split()))
C.sort()
es = [[] for i in range(N)]
for a,b in AB:
    a,b = a-1,b-1
    es[a].append(b)
    es[b].append(a)

score = 0
vscore = [-1]*N
vscore[0] = C.pop()

def dfs(v,p=-1):
    global score
    for to in es[v]:
        if to==p: continue
        vscore[to] = C.pop()
        score += min(vscore[v], vscore[to])
        dfs(to,v)
dfs(0)

print(score)
print(*vscore)

Solution (Python):
from collections import Counter
import sys
sys.setrecursionlimit(10 ** 7)

N = int(input())
edges = [[] for _ in range(N)]

for _ in range(N - 1):
    fr, to = map(int, input().split())
    fr -= 1
    to -= 1
    edges[fr].append(to)
    edges[to].append(fr)

A = list(map(int, input().split()))
A.sort()
S = sum(A) - A[-1]

print(S)

ans = [0] * N
st = [(0, -1)]
while st:
    now, pr = st.pop()
    ans[now] = A.pop()
    for to in edges[now]:
        if to == pr:
            continue
        st.append((to, now))
print(*ans)

Solution (Python):
import sys
from collections import defaultdict as dd
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 6)
N = int(input())
e = dd(list)
for _ in range(N - 1):
  u, v = map(int, input().split())
  e[u].append(v)
  e[v].append(u)
c = list(map(int, input().split()))
c.sort()
sm = sum(c) - c[-1]
res = [0] * (N + 1)
def dfs(x):
  global res
  res[x] = c.pop()
  for y in e[x]:
    if res[y]: continue
    dfs(y)
dfs(1)
print(sm)
print(*res[1: ])

Solution (Python):
from collections import deque
class UnionFind:
    """
        n : 要素数
        root : 親ノード
        size : グループのサイズ
    """
    
    def __init__(self, n):
        self.n = n
        self.root = [-1]*(n+1)
        self.size = [1]*(n+1)
    
    """ノードxのrootノードを見つける"""
    def Find_Root(self, x):
        if self.root[x] < 0:
            return x
        else:
            self.root[x] = self.Find_Root(self.root[x])
            return self.root[x]
    
    """木の合併"""
    def Union(self, x, y):
        
        x = self.Find_Root(x)
        y = self.Find_Root(y)
        
        
        if x==y:
            return 
        
        
        elif self.size[x] > self.size[y]:
            self.size[x] += self.size[y]
            self.root[y] = x
        
        else:
            self.size[y] += self.size[x]
            self.root[x] = y

n = int(input())
uf = UnionFind(n)
G = [[] for _ in range(n+1)]
for _ in range(n-1):
    a,b = map(int,input().split())
    uf.Union(a,b)
    G[a].append(b)
    G[b].append(a)
rt = uf.root.index(-1)
for idx in range(1, n+1):
    if uf.root[idx] == -1:
        rt = idx-1
        break

c = list(map(int,input().split()))
c.sort(reverse=True)
c = [0] + c
ans = [0]*(n+1)
que = deque([rt])
idx = 1

while que:
    node = que.popleft()
    if ans[node]!=0:
        continue
    else:
        ans[node] = c[idx]
        idx += 1
        for g in G[node]:
            que.append(g)
print(sum(c)-max(c))
print(*ans[1:])

Solution (Python):
from collections import deque

n = int(input())
g = [[] for _ in range(n)]
for _ in range(n-1):
    a, b = map(int, input().split())
    a -= 1; b -= 1
    g[a].append(b)
    g[b].append(a)
c = list(map(int, input().split()))
c.sort()
m = sum(c[:-1])
ans = [-1] * n

q = deque([(0, -1)])
while q:
    v, pv = q.popleft()
    ans[v] = c.pop()
    for nv in g[v]:
        if nv == pv: continue
        q.append((nv, v))

print(m)
print(*ans)

Solution (Python):
from collections import deque
n=int(input())
d=dict()
edge=[[] for _ in range(n)]
for _ in range(n-1):
  a,b=map(int,input().split())
  a-=1
  b-=1
  edge[a].append(b)
  edge[b].append(a)
c=list(map(int,input().split()))
c.sort(reverse=True)
visited=[-1]*n
def bfs(s):
  i=0
  q=deque([s])
  visited[s]=c[i]
  while q:
    x=q.popleft()
    for nx in edge[x]:
      if visited[nx]==-1:
        i+=1
        visited[nx]=c[i]
        q.append(nx)
  return
bfs(0)
print(sum(c)-max(c))
print(*visited)

Solution (Python):
import heapq as h

N=int(input())
hen=[[] for i in range(0,N)]
for i in range(0,N-1):
    a,b=map(int,input().split())
    hen[a-1].append(b-1)
    hen[b-1].append(a-1)

c=list(map(int,input().split()))
c.sort(reverse=True)

ans=[-1 for i in range(0,N)]

q=[]
q.append(0)
h.heapify(q)
sub=[]
h.heapify(sub)
count=0
while q!=[]:
    while q!=[]:
        x=h.heappop(q)
        ans[x]=c[count]
        count+=1
        for p in hen[x]:
            if ans[p]==-1:
                h.heappush(sub,p)
        
        
        if q==[]:
            q=sub
            sub=[]
            h.heapify(sub)
            break

print(sum(c)-c[0])
print(*ans)

Solution (Python):
n = int(input())
graph = [[] for i in range(n)]
for i in range(n-1):
    a,b = map(int,input().split())
    graph[a-1].append(b-1)
    graph[b-1].append(a-1)
L = list(map(int,input().split()))
L.sort()
used = [0]*n
ans = [0]*n
used[0] = 1
ans[0] = L[n-1]
next = graph[0]
cur = n-2
while len(next) > 0:
    t = next.pop()
    ans[t] = L[cur]
    cur -= 1
    used[t] = 1
    for i in range(len(graph[t])):
        if used[graph[t][i]] != 1:
            next.append(graph[t][i])
print(sum(L)-L[n-1])
print(' '.join(map(str,ans)))

Solution (Python):

import sys, math, itertools, collections, bisect
input = lambda: sys.stdin.buffer.readline().rstrip().decode('utf-8')
inf = float('inf') ;mod = 10**9+7
mans = inf ;ans = 0 ;count = 0 ;pro = 1

n = int(input())
G = [[] for i in range(n)]
F = [-1]*n
AB = []
for i in range(n-1):
  a,b = map(int,input().split())
  a-=1;b-=1
  G[a].append(b)
  G[b].append(a)
  AB.append((a,b))
C = sorted(map(int,input().split()),reverse = True)
for i in range(n):
  G[i].sort(key = lambda x:len(G[x]))
m = max(range(n),key = lambda x: len(G[x]))
count = 1
que = collections.deque()
que.append(m)
F[m] = C[0]
while que:
  node = que.popleft()
  for vi in G[node]:
    if F[vi] != -1: continue
    F[vi] = C[count]
    count += 1
    que.append(vi)

for a,b in AB:
  ans += min(F[a],F[b])
print(ans)
print(*F)

Solution (Python):
from collections import deque

n = int(input())
Adj_dict = {x:[] for x in range(1, n+1)}

for _ in range(n-1):
    a, b = map(int, input().split())
    Adj_dict[a].append(b)
    Adj_dict[b].append(a)
C = list(map(int, input().split()))
C = sorted(C, reverse=True)
dq_C = deque(C)

max_node = 0
max_edge_count = 0
for i in range(1,n+1):
    if len(Adj_dict[i]) >= max_edge_count:
        max_edge_count = len(Adj_dict[i])
        max_node = i

dq = deque()
dq.append(max_node)

Visited = [-1 for _ in range(n+1)]
Visited[max_node] = dq_C.popleft()
ans = 0

while dq:
    node = dq.popleft()
    Adjs = Adj_dict[node]
    for next_node in Adjs:
        if Visited[next_node] != -1:
            continue
        dq.append(next_node)
        Visited[next_node] = dq_C.popleft()
        ans += Visited[next_node]

print(ans)
print(' '.join(map(str, Visited[1:])))

Solution (Python):
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import accumulate, permutations, combinations, product
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from fractions import gcd
from heapq import heappush, heappop
from functools import reduce
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

N = INT()
ab = [LIST() for _ in range(N-1)]
c = LIST()
c.sort(reverse=True)
tree = [[] for _ in range(N)]
for a, b in ab:
	tree[a-1].append(b-1)
	tree[b-1].append(a-1)







ans = [0]*N
q = deque()
q.append(0)
ans[0] = c[0]
cnt = 1
while q:
	n = q.popleft()
	for node in tree[n]:
		if ans[node]:
			continue
		ans[node] = c[cnt]
		cnt += 1
		q.append(node)
print(sum(c)-max(c))
print(*ans)

Solution (Python):
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import accumulate, permutations, combinations, product
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from fractions import gcd
from heapq import heappush, heappop
from functools import reduce
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

N = INT()
ab = [LIST() for _ in range(N-1)]
c = LIST()
c.sort(reverse=True)
tree = [[] for _ in range(N)]
for a, b in ab:
	tree[a-1].append(b-1)
	tree[b-1].append(a-1)

start=None
for i in range(N):
	if len(tree[i]) == 1:
		start = i
		break

ans = [0]*N
q = deque()
q.append(start)
ans[start] = c[0]
cnt = 1
while q:
	n = q.popleft()
	for node in tree[n]:
		if ans[node]:
			continue
		ans[node] = c[cnt]
		cnt += 1
		q.append(node)
print(sum(c)-max(c))
print(*ans)

Solution (Python):
import queue
def main():
    n = int(input())
    g = [[] for _ in range(n)]
    for _ in range(n-1):
        a, b = map(int, input().split())
        g[a-1].append(b-1)
        g[b-1].append(a-1)
    c = list(map(int, input().split()))
    c.sort(reverse=True)
    ans = [None]*n
    a = [i for i in range(n)]
    a.sort(key=lambda x: len(g[x]), reverse=True)
    f = [True]*n
    f[a[0]] = False
    q = queue.Queue()
    q.put(a[0])
    ans[a[0]] = c[0]
    x = 1
    while not q.empty():
        target = q.get()
        for v in g[target]:
            if f[v]:
                f[v] = False
                ans[v] = c[x]
                q.put(v)
                x += 1
    score = 0
    f = [True]*n
    f[0] = False
    q = queue.Queue()
    q.put(0)
    while not q.empty():
        target = q.get()
        for v in g[target]:
            if f[v]:
                f[v] = False
                score += min(ans[target], ans[v])
                q.put(v)
    print(score)
    for i in range(n):
        print(ans[i], end="")
        if i < n-1:
            print(" ",end="")
        else:
            print("")

if __name__ == "__main__":
    main()

Solution (Python):
from heapq import heappush, heappop
import sys
input = sys.stdin.readline

N = int(input())
G = [[] for _ in range(N+1)]
degree = [0] * (N+1)
for _ in range(N-1):
    a, b = map(int, input().split())
    G[a].append(b)
    G[b].append(a)
    degree[a] += 1
    degree[b] += 1
c = list(map(int, input().split()))
c.sort(reverse=True)

heap = []
for i in range(1, N+1):
    heappush(heap, (degree[i], i))

M = 0
num = [0] * (N+1)
while heap:
    d, i = heappop(heap)
    if num[i] != 0:
        continue
    num[i] = c.pop()
    for j in G[i]:
        if num[j] == 0:
            M += num[i]
            degree[i] -= 1
            degree[j] -= 1
            heappush(heap, (degree[j], j))
print(M)
print(' '.join(map(str, num[1:])))

Solution (Python):
import sys

sys.setrecursionlimit(10 ** 9 + 7)

N = int(input())
visited = [False] * N
edges = [[] for _ in range(N)]
AB = []
for _ in range(N-1):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    AB.append((a, b))
    edges[a].append(b)
    edges[b].append(a)
C = list(map(int, input().split()))
C.sort(reverse=True)
scores = [-1] * N
i = 0

def dfs(v):
    if visited[v]:
        return

    visited[v] = True
    global i
    scores[v] = C[i]
    i += 1
    for e in edges[v]:
        if visited[e]:
            continue

        dfs(e)

dfs(0)

total = 0
for a, b in AB:
    total += min(scores[a], scores[b])
print(total)
print(*scores)

Solution (Python):
import sys
from collections import deque
n = int(input())
graph = {i : [] for i in range(n)}
for i in range(n-1):
    a, b = [int(i) for i in sys.stdin.readline().split()]
    a -= 1
    b -= 1
    graph[a].append(b)
    graph[b].append(a)
c_ls = [int(i) for i in sys.stdin.readline().split()]
c_ls.sort(reverse=True)
costs = [0 for i in range(n)]
que = deque([0])
already = {0}
i = 0
while len(que) > 0:
    cur = que.popleft()
    costs[cur] = c_ls[i]
    i += 1
    for _next in graph[cur]:
        if _next not in already:
            que.append(_next)
            already.add(_next)
print(sum(c_ls[1:]))
print(" ".join([str(i) for i in costs]))

Solution (Python):
N = int(input())
E = [[] for _ in range(N)]
for _ in range(N-1):
    a,b = map(int, input().split())
    E[a-1].append(b-1)
    E[b-1].append(a-1)
C = [int(c) for c in input().split()]

C.sort(reverse=True)
M = sum(C) - C[0]

from collections import deque
q = deque([0])
ans = [0]*N
ans[0] = C[0]
i = 1
while q:
    u = q.popleft()
    for v in E[u]:
        if ans[v] > 0:
            continue
        ans[v] = C[i]
        i += 1
        q.append(v)

print(M)
print(*ans)

Solution (Python):
n = int(input())
T = [[] for _ in range(n)]
for _ in range(n-1):
  a, b = map(int, input().split())
  a -= 1
  b -= 1
  T[a].append(b)
  T[b].append(a)
C = sorted(map(int, input().split()))
print(sum(C[:-1]))
L = [-1]*n
stack = [0]
while stack:
  temp = stack.pop()
  L[temp] = C.pop()
  for v in T[temp]:
    if L[v] == -1:
      stack.append(v)
print(*L)

Solution (Python):
import sys

read = sys.stdin.read
readline = sys.stdin.readline

N, *abc = map(int, read().split())
c = abc[2 * (N - 1):]
c.sort()
graph = [[] for _ in range(N + 1)]
for a, b in zip(*[iter(abc[:2 * (N - 1)])] * 2):
    graph[a].append(b)
    graph[b].append(a)

nodes = [0] * (N + 1)
score = sum(c) - c[-1]
start = 1
nodes[start] = c.pop()
queue = [start]
while queue:
    V = queue.pop()
    for v in graph[V]:
        if nodes[v] == 0:
            nodes[v] = c.pop()
            queue.append(v)

print(score)
print(' '.join(map(str, nodes[1:])))

Solution (Python):
import sys
from collections import deque

read = sys.stdin.read
readline = sys.stdin.readline

N, *abc = map(int, read().split())
c = abc[2 * (N - 1):]
c.sort()
graph = [[] for _ in range(N + 1)]
cnt = [0] * (N + 1)
for a, b in zip(*[iter(abc[:2 * (N - 1)])] * 2):
    graph[a].append(b)
    graph[b].append(a)

m = max(cnt)
nodes = [0] * (N + 1)
score = sum(c) - c[-1]
start = 1
nodes[start] = c.pop()
queue = deque([start])
while queue:
    V = queue.popleft()
    for v in graph[V]:
        if nodes[v] == 0:
            nodes[v] = c.pop()
            queue.append(v)

print(score)
print(' '.join(map(str, nodes[1:])))

Solution (Python):
import sys
from collections import deque

read = sys.stdin.read
readline = sys.stdin.readline

N, *abc = map(int, read().split())
c = abc[2 * (N - 1):]
c.sort()
graph = [[] for _ in range(N + 1)]
cnt = [0] * (N + 1)
for a, b in zip(*[iter(abc[:2 * (N - 1)])] * 2):
    graph[a].append(b)
    graph[b].append(a)
    cnt[a] += 1
    cnt[b] += 1

m = max(cnt)
nodes = [0] * (N + 1)
score = sum(c) - c[-1]
start = cnt.index(max(cnt))
nodes[start] = c.pop()
queue = deque([start])
while queue:
    V = queue.popleft()
    for v in graph[V]:
        if nodes[v] == 0:
            nodes[v] = c.pop()
            queue.append(v)

print(score)
print(' '.join(map(str, nodes[1:])))

Solution (Python):


from collections import deque

def bfs(num):
    if visited[num]==0:
        visited[num]=C.pop(-1)
        for item in way[num]:
            d.append(item)
    return

N=int(input())

ans=[-1]*N
way=[[]for i in range(N)]
visited=[0]*N

for _ in range(N-1):
    a,b=map(int,input().split())
    way[a-1].append(b-1)
    way[b-1].append(a-1)

C=list(map(int,input().split()))
C.sort()



d=deque([0])

while d:
    temp=d.popleft()
    if visited[temp]==0:
        bfs(temp)

ans=0
for i in range(N):
    for item in way[i]:
        ans+=min(visited[i],visited[item])

print(ans//2)
print(*visited)

Solution (Python):
import sys
from collections import defaultdict as dd
import heapq
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 6)
N = int(input())
e = dd(list)
inc = [0] * (N + 1)
for _ in range(N - 1):
  u, v = map(int, input().split())
  e[u].append(v)
  e[v].append(u)
  inc[u] += 1
  inc[v] += 1
x = 0
for i in range(1, N + 1):
  if inc[x] < inc[i]: x = i

c = list(map(int, input().split()))
c.sort()
ressum = sum(c[: -1])
vis = set()
res = [0] * (N + 1)
res[x] = c[-1]
def dfs(y):
  global vis
  global res
  global c
  res[y] = c.pop()
  for z in e[y]:
    if z in vis: continue
    vis.add(z)
    dfs(z)
vis.add(x)
dfs(x)
print(ressum)
print(*res[1: ])

Solution (Python):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10 ** 7)

N = int(input())
edge = [[] for _ in range(N + 1)]
AB = []
for _ in range(N - 1):
    a, b = map(int, input().split())
    edge[a].append(b)
    edge[b].append(a)
    AB.append((a, b))
C = list(map(int, input().split()))
C.sort()

for i, e in enumerate(edge[1:], start=1):
    if len(e) == 1:
        s = i
        break

node = [s]
memo = [-1] * (N + 1)
while node:
    s = node.pop()
    memo[s] = C.pop()
    for t in edge[s]:
        if memo[t] != -1:
            continue
        node.append(t)

ans = 0
for a, b in AB:
    ans += min(memo[a], memo[b])

print(ans)
print(*memo[1:])

Solution (Python):
import sys
input = sys.stdin.readline
from collections import deque

def main():
    N = int(input())
    edge = [[] for _ in range(N)]
    for _ in range(N-1):
        l,r = map(int,input().split())
        edge[l-1].append(r-1)
        edge[r-1].append(l-1)

    a = list(map(int,input().split()))
    a.sort(reverse = True)
    put = [-1 for _ in range(N)]
    put[0] = a[0]
    q = deque([0])
    i = 1
    while q:
        now = q.popleft()
        for fol in edge[now]:
            if put[fol] != -1:
                continue
            else:
                put[fol] = a[i]
                i += 1
                q.append(fol)
    
    print(sum(a)-a[0])
    print(*put)
    
if __name__ == "__main__":
    main()

Solution (Python):
n = int(input())
ab = [list(map(int, input().split())) for _ in range(n-1)]
c = list(map(int,input().split()))

edge_num = [0] * (n+1)
edge = {}
for i in range(1,n+1):
    edge[i] = set()

for a,b in ab:
    edge_num[a] += 1
    edge_num[b] += 1
    edge[a].add(b)
    edge[b].add(a)

edge_num2 = {}
for i in range(max(edge_num) + 1):
    edge_num2[i] = set()

for i in range(1,n+1):
    edge_num2[edge_num[i]].add(i)

c = sorted(c)
c_num = 0
ans = [0] * (n+1)
while(len(edge_num2[1]) > 0):
    tmp = edge_num2[1].pop()
    ans[tmp] = c[c_num]
    c_num += 1

    neigh = edge[tmp].pop()
    edge_num2[edge_num[neigh]].discard(neigh)
    edge_num[neigh] -= 1
    edge_num2[edge_num[neigh]].add(neigh)
    edge[neigh].discard(tmp)
    if(edge_num[neigh] == 0):
        ans[neigh] = c[c_num]
        break

print(sum(c) - max(c))
print(' '.join(map(str, ans[1:])))

Solution (Python):
from collections import deque
N=int(input())
AB=[tuple(map(int, input().split())) for _ in range(N-1)]
C=sorted(map(int, input().split()))
G=[[] for _ in range(N)]
for a,b in AB:
    a-=1
    b-=1
    G[a].append(b)
    G[b].append(a)
deq=deque(i for i in range(N) if len(G[i])==1)
D=[len(G[i]) for i in range(N)]
X=[0]*N
for c in C:
    i=deq.popleft()
    X[i]=c
    for j in G[i]:
        D[j]-=1
        if D[j]==1:
            deq.append(j)
ans=0
for a,b in AB:
    ans+=min(X[a-1],X[b-1])
print(ans)
print(*X)

Solution (Python):
from heapq import heappush, heappop
N, *L = map(int, open(0).read().split())
dic = [[] for i in range(N)]
ans = [-1]*N
cnt = [0]*N
hq = []
for a,b in zip(*[iter(L[:2*(N-1)])]*2):
  a -= 1
  b -= 1
  dic[a] += [b]
  dic[b] += [a]
  cnt[a] += 1
  cnt[b] += 1
C = L[2*(N-1):]
C.sort()
for i in range(N):
  heappush(hq,(cnt[i],i))
arg = 0
m = sum(C)-C[-1]
while True:
  c, i = heappop(hq)
  if ans[i]!=-1:
    continue
  ans[i] = C[arg]
  arg += 1
  if arg==N:
    break
  for v in dic[i]:
    cnt[v] -= 1
    heappush(hq,(cnt[v],v))
print(m)
print(*ans)

Solution (Python):
from heapq import heappush, heappop
N, *L = map(int, open(0).read().split())
dic = [[] for i in range(N)]
ans = [-1]*N
cnt = [0]*N
hq = []
for a,b in zip(*[iter(L[:2*(N-1)])]*2):
  a -= 1
  b -= 1
  dic[a] += [b]
  dic[b] += [a]
  cnt[a] += 1
  cnt[b] += 1
C = L[2*(N-1):]
C.sort()
for i in range(N):
  heappush(hq,(cnt[i],i))
arg = 0
m = 0
while True:
  c, i = heappop(hq)
  if ans[i]!=-1:
    continue
  m += C[arg]*cnt[i]
  ans[i] = C[arg]
  arg += 1
  if arg==N:
    break
  for v in dic[i]:
    cnt[v] -= 1
    heappush(hq,(cnt[v],v))
print(m)
print(*ans)

Solution (Python):
import sys
from collections import deque
input = sys.stdin.readline
n = int(input())
T = [[] for _ in range(n)]
for i in range(n-1):
    ai,bi = map(int, input().split( ))
    ai-=1;bi-=1
    T[ai].append(bi)
    T[bi].append(ai)

c = list(map(int, input().split( )))
c.sort()





Q = deque()
Q.append(0)
P = [-1 for i in range(n)]
P[0] = 0
D = [0]*n
L=[]
while Q:
    v = Q.popleft()
    leaf = True
    for u in T[v]:
        if P[u]<0:
            D[v]+=1
            P[u]=v
            leaf = False
            Q.append(u)
    if leaf:
        L.append(v)

Q =deque(L)

j = 0
A = [0]*n
m = 0
while Q:
    v = Q.popleft()
    A[v] = c[j]
    if v:
        m+=c[j]
    j+=1
    D[P[v]]-=1
    if not D[P[v]] and v:
        Q.append(P[v])
print(m)
print(*A)

Solution (Python):
from collections import deque

N = int(input())
tree = [set() for _ in range(N)]
for _ in range(N - 1):
    a, b = map(int, input().split())
    tree[a - 1].add(b - 1)
    tree[b - 1].add(a - 1)
C = sorted(list(map(int, input().split())))

ans = [0] * N

print(sum(C[:-1]))

ans[0] = C.pop()
n = min(tree[0])
ans[n] = C.pop()

d = deque([0, n])
visited = set(d)
while d:
    x = d.pop()
    for new_x in tree[x]:
        if new_x not in visited:
            ans[new_x] = C.pop()
            d.append(new_x)
            visited.add(new_x)

print(*ans)

Solution (Python):
from collections import defaultdict

V = defaultdict(list)
N = int(input())
for _ in range(N-1):
    a, b = map(int, input().split())
    V[a].append(b)
    V[b].append(a)
*c, = map(int, input().split())
c.sort(reverse=True)

root, _ = max(V.items(), key=lambda x:len(x[1]))
visited = [False] * (N+1)
identifier = [0] * (N+1)

p = 0
q = [root]
while q:
    a = q.pop()
    visited[a] = True
    identifier[a] = p

    p+=1

    for i in V[a]:
        if visited[i]:continue
        q.append(i)

cost = 0
visited = [False] * (N+1)
q = [root]
while q:
    a = q.pop()
    visited[a] = True
    p+=1

    for b in V[a]:
        if visited[b]:continue
        cost += min(c[identifier[a]], c[identifier[b]])
        q.append(b)

print(cost)
print(*[c[i] for i in identifier[1:]])