Problem:


Score: 400 points

Problem Statement

There is a cave.

The cave has N rooms and M passages. The rooms are numbered 1 to N, and the passages are numbered 1 to M. Passage i connects Room A_i and Room B_i bidirectionally. One can travel between any two rooms by traversing passages. Room 1 is a special room with an entrance from the outside.

It is dark in the cave, so we have decided to place a signpost in each room except Room 1. The signpost in each room will point to one of the rooms directly connected to that room with a passage.

Since it is dangerous in the cave, our objective is to satisfy the condition below for each room except Room 1.

If you start in that room and repeatedly move to the room indicated by the signpost in the room you are in, you will reach Room 1 after traversing the minimum number of passages possible.

Determine whether there is a way to place signposts satisfying our objective, and print one such way if it exists.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 2 \times 10^5

1 \leq A_i, B_i \leq N\ (1 \leq i \leq M)

A_i \neq B_i\ (1 \leq i \leq M)

One can travel between any two rooms by traversing passages.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_M B_M

Output

If there is no way to place signposts satisfying the objective, print No.

Otherwise, print N lines. The first line should contain Yes, and the i-th line (2 \leq i \leq N) should contain the integer representing the room indicated by the signpost in Room i.

Sample Input 1

4 4
1 2
2 3
3 4
4 2

Sample Output 1

Yes
1
2
2

If we place the signposts as described in the sample output, the following happens:

Starting in Room 2, you will reach Room 1 after traversing one passage: (2) \to 1. This is the minimum number of passages possible.

Starting in Room 3, you will reach Room 1 after traversing two passages: (3) \to 2 \to 1. This is the minimum number of passages possible.

Starting in Room 4, you will reach Room 1 after traversing two passages: (4) \to 2 \to 1. This is the minimum number of passages possible.

Thus, the objective is satisfied.

Sample Input 2

6 9
3 4
6 1
2 4
5 3
4 6
1 5
6 2
4 5
5 6

Sample Output 2

Yes
6
5
5
1
1

If there are multiple solutions, any of them will be accepted.



Sample input:
4 4
1 2
2 3
3 4
4 2


Sample output:
Yes
1
2
2

Submission status: Accepted

Solution code:
def main():
    from collections import deque
    N, M = (int(i) for i in input().split())
    G = [[] for _ in range(N)]
    for i in range(M):
        a, b = (int(i) for i in input().split())
        G[a-1].append(b-1)
        G[b-1].append(a-1)

    def bfs(s):
        G_color = ['WHITE' for _ in range(N)]
        G_distance = [float('inf') for _ in range(N)]
        G_parent = ['NIL' for _ in range(N)]
        G_color[s] = 'GRAY'
        G_distance[s] = 0
        Q = deque()
        Q.append(s)
        while Q:
            u = Q.popleft()
            for v in G[u]:
                if G_color[v] == 'WHITE':
                    G_color[v] = 'GRAY'
                    G_distance[v] = G_distance[u] + 1
                    G_parent[v] = u
                    Q.append(v)
            G_color[u] = 'BLACK'
        return G_parent

    par = bfs(0)
    if all(par[i] != 'NIL' for i in range(1, N)):
        print("Yes")
        for i in range(1, N):
            print(par[i]+1)
    else:
        print("No")


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(200000)
from collections import deque


def read():
    N, M = map(int, input().strip().split())
    G = [list() for i in range(N+1)]
    for i in range(M):
        a, b = map(int, input().strip().split())
        G[a].append(b)
        G[b].append(a)
    return N, M, G


def solve(N, M, G, INF = 10**8):
    depth = [-1 for i in range(N+1)]
    landmark = [-1 for i in range(N+1)]
    q = deque()
    q.append(1)
    depth[1] = 0
    while q:
        x = q.popleft()
        d = depth[x]
        for y in G[x]:
            if depth[y] < 0:
                landmark[y] = x
                depth[y] = d + 1
                q.append(y)
    
    if not all([d>=0 for d in depth[1:]]):
        print("No")
    else:
        print("Yes")
        for a in landmark[2:]:
            print(a)


if __name__ == '__main__':
    inputs = read()
    outputs = solve(*inputs)
    if outputs is not None:
        print("%s" % str(outputs))

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-

from collections import defaultdict
from collections import deque

def main():
    n, m = map(int, input().split())
    routes = defaultdict(list)
    for _ in range(m):
        a, b = map(int, input().split())
        routes[a].append(b)
        routes[b].append(a)

    rec = [0] * (n + 1)
    rec[1] = 1
    pos_queue = deque([1])
    while len(pos_queue) > 0:
        p = pos_queue.popleft()
        for next_p in routes[p]:
            if not rec[next_p]:
                rec[next_p] = p
                pos_queue.append(next_p)

    print("Yes")
    print("\n".join(map(str, rec[2:])))


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
def main():
  n,m=map(int,input().split())
  ab=[list(map(int,input().split()))for _ in range(m)]
  g=[[]for _ in range(n)]
  for a,b in ab:
    g[a-1].append(b-1)
    g[b-1].append(a-1)
  from collections import deque
  todo=deque([0])
  seen=[-1]*n
  seen[0]=0
  while todo:
    t=todo.popleft()
    l=g[t]
    for li in l:
      if seen[li]==-1:
        seen[li]=t
        todo.append(li)
  print('Yes')
  for si in seen[1:]:
    print(si+1)
if __name__=='__main__':
  main()

Submission status: Accepted

Solution code:
#D
from collections import deque

N,M = map(int,input().split())
V = [[] for _ in range(N)]

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

visited = [-1]*N
visited[0] = 0
mae = [-1]*N
mae[0] = 0

D = deque()
for v in V[0]:
    visited[v] = 1
    mae[v] = 1
    D.append(v)

while D:
    d = D.popleft()
    Vd = V[d]
    
    for v in Vd:
        if visited[v] == -1:
            visited[v] = visited[d]+1
            mae[v] = d+1
            D.append(v)
        

print("Yes")
for i in range(1,N):
    print(mae[i])

Submission status: Accepted

Solution code:
from collections import deque
N, M  = map(int, input().split())
AB =[[] for i in range(N)]

for i in range(M):
  A, B =map(int, input().split())
  AB[A-1].append(B)
  AB[B-1].append(A)


print("Yes")

D = deque([1])
ans = [0]* N
ans[0] = -1

for i in range(N-1):
  C = D.popleft()
  for j in AB[C-1]:
    if ans[j-1] == 0:
      ans[j-1] = C
      D.append(j)

for i in range(1,N):
  print(ans[i])

Submission status: Accepted

Solution code:
from collections import deque
n,m = map(int,input().split())
ad_ls = [[] for i in range(n+1)]
ls = [0] * (n+1)
done_ls = [0] * (n+1)
for i in range(m):
    a,b = map(int,input().split())
    ad_ls[a].append(b)
    ad_ls[b].append(a)
q = deque()
for node in ad_ls[1]:
    q.append([1,node])
done_ls[1] = 1
while q:
    start, goal = q.popleft()
    if done_ls[goal] != 1:
        ls[goal] = start
        done_ls[goal] = 1
        for node in ad_ls[goal]:
            q.append([goal, node])

res = 1
for node in range(2,n+1):
    if ls[node] == 0:
        res = 0
if res:
    print('Yes')
    for node in range(2,n+1):
        print(ls[node])
else:
    print('No')

Submission status: Accepted

Solution code:
class Dijkstra:
  R = {}
  import heapq
  pop = heapq.heappop
  push = heapq.heappush
  
  def __init__(s, N):
    s.N = N

  def add(s, a, b, x):
    if a not in s.R: s.R[a] = {b: x}
    else: s.R[a][b] = x
    if b not in s.R: s.R[b] = {a: x}
    else: s.R[b][a] = x

  def exe(s, start):
    D = [-1] * s.N 
    q  = []
    s.push(q, [0, start])
    cnt = 0
    while cnt < s.N:
      if len(q) == 0:
        return None
      d, x = s.pop(q)
      if D[x] != -1: continue
      D[x] = d
      cnt += 1
      for i in s.R[x]:
        if D[i] != -1: continue
        j = s.R[x][i]
        s.push(q, [d + j, i])
    return D


N, M = list(map(int, input().split()))
AB = [list(map(int, input().split())) for _ in range(M)]

D = Dijkstra(N)

for a, b in AB:
  D.add(a - 1, b - 1, 1)

L = D.exe(0)

if L == None:
  print("No")
  exit()

R = {}

for i in range(N):
  if L[i] in R:
    R[L[i]].append(i)
  else:
    R[L[i]] = [i]

Ans = [0] * N
for i in R.keys():
  for j in R[i]:
    for k in D.R[j].keys():
      if L[k] == L[j] + 1:
        Ans[k] = j + 1

print("Yes")
for i in range(1, N):
  print(Ans[i])

Submission status: Accepted

Solution code:
from sys import stdin, setrecursionlimit
from collections import deque


def main():
    input = stdin.buffer.readline
    n, m = map(int, input().split())
    g = [[] for _ in range(n)]
    for _ in range(m):
        a, b = map(int, input().split())
        g[a - 1].append(b - 1)
        g[b - 1].append(a - 1)

    result = []

    d = [[10 ** 12, -1] for _ in range(n)]
    d[0] = [0, 0]

    q = deque()
    q.append(0)

    while q:
        now_i = q.popleft()

        for next_i in g[now_i]:
            if d[next_i][0] > d[now_i][0] + 1:
                d[next_i] = [d[now_i][0] + 1, now_i]
                q.append(next_i)

    for di in d:
        if di[0] == 10 ** 12:
            print('No')
            exit()

    print('Yes')
    for di in d[1:]:
        print(di[1] + 1)


if __name__ == "__main__":
    setrecursionlimit(10000)
    main()

Submission status: Accepted

Solution code:
# coding: utf-8
# Your code here!
import sys
readline = sys.stdin.readline
read = sys.stdin.read

n,m,*ab = [int(i) for i in read().split()]

dist = [-1]*n
dist[0] = 0
ans = [-1]*n

g = [[] for _ in range(n)]
M = iter(ab)
for a,b in zip(M,M):
    g[a-1].append(b-1)
    g[b-1].append(a-1)

from collections import deque
q = deque([0])
while q:
    v = q.popleft()
    for c in g[v]:
        if dist[c] == -1:
            dist[c] = dist[v]+1
            ans[c] = v+1
            q.append(c)
    

print("Yes")
print(*ans[1:],sep="\n")

Submission status: Accepted

Solution code:
# coding: utf-8

import sys
import math
import collections
import itertools
import bisect
INF = 10 ** 13
MOD = 10 ** 9 + 7
def input() : return sys.stdin.readline().strip()
def gcd(x, y) : return x if y == 0 else gcd(y, x%y)
def lcm(x, y) : return (x * y) // gcd(x, y)
def I() : return int(input())
def LI() : return [int(x) for x in input().split()]
def RI(N) : return [int(input()) for _ in range(N)]
def LRI(N) : return [[int(x) for x in input().split()] for _ in range(N)]
def LS() : return input().split()
def RS(N) : return [input() for _ in range(N)]
def LRS(N) : return [input().split() for _ in range(N)]
def PL(L) : print(*L, sep="\n")
def YesNo(B) : print("Yes" if B else "No")
def YESNO(B) : print("YES" if B else "NO")

N, M = LI()
AB = LRI(M)

visited = [False] * N

root = [[] for _ in range(N)]
for a, b in AB:
    root[a-1].append(b-1)
    root[b-1].append(a-1)

ret = [-1] * N
Q = collections.deque([[0,0]])
while Q:
    qs = Q.popleft()
    b = qs[0]
    q = qs[1]

    if visited[q]:
        continue
    else:
        visited[q] = True
    
    ret[q] = b

    for r in root[q]:
        Q.append([q, r])

if -1 in ret:
    print("No")
else:
    print("Yes")
    for i, r in enumerate(ret):
        if i == 0:
            continue

        print(r+1)

Submission status: Accepted

Solution code:
N,M = map(int,input().split())
A = []
B = []
for m in range(M):
    a,b = map(int,input().split())
    A.append(a)
    B.append(b)
from collections import defaultdict as ddict
route = ddict(list)
for i in range(M):
    route[A[i]].append(B[i])
    route[B[i]].append(A[i])
for i in range(1,N+1):
    if route[i] == []:
        print("No")
        exit()
ans = [0 for i in range(N+1)]
from collections import deque
Q = deque([1])
while Q:
    q = Q.popleft()
    for r in route[q]:
        if ans[r] == 0:
            ans[r] = q
            Q.append(r)
print("Yes")
print(*ans[2:],sep="\n")

Submission status: Accepted

Solution code:
from collections import deque

n, m = map(int, input().split())

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

d = deque()
d.append(0)
ans = [-1] * n
ans[0] = 0
cnt = 0
while d:
    idx = d.popleft()
    for i in route[idx]:
        if ans[i] < 0:
            ans[i] = idx
            d.append(i)
            cnt += 1

if cnt == n - 1:
    print("Yes")
    for i in ans[1:]:
        print(i + 1)
else:
    print("No")

Submission status: Accepted

Solution code:
cin = open(0).read().strip().split('\n')
n,m = map(int, cin[0].split(' '))
ab = [tuple(map(int, a.split(' '))) for a in cin[1:]]

g = [[] for _ in range(n)]
for abi in ab:
    g[abi[0]-1].append(abi[1]-1)
    g[abi[1]-1].append(abi[0]-1)

for ii in range(n):
    g[ii] = sorted(g[ii])

dist = [-1]*n
dist[0] = 0

import queue
q = queue.Queue()
q.put(0)

while not q.empty():
    idx = q.get()
    for i in g[idx]:
        if dist[i] != -1: continue
        q.put(i)
        dist[i] = idx

aa = min(dist)
if aa == -1:
    print('No')
else:
    print('Yes')
    for a in dist[1:]:
        print(a+1)

Submission status: Accepted

Solution code:
from sys import stdin, setrecursionlimit
from collections import deque

setrecursionlimit(10 ** 9)
INF = 1 << 60


def input():
    return stdin.readline().strip()


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

dist = [-1] * N
dist[0] = 0
prev = [0] * N
q = deque([0])
while q:
    v = q.popleft()
    for nv in G[v]:
        if dist[nv] == -1:
            q.append(nv)
            dist[nv] = dist[v] + 1
            prev[nv] = v
    
print('Yes')
for v in prev[1:]:
    print(v+1)

Submission status: Accepted

Solution code:
from collections import deque

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

mark=[-1]*n
mark[0]=0
check=[0]*n
check[0]=1

que=deque()
que.append(0)

while que:
    p=que.popleft()
    for i in g[p]:
        if check[i]:
            continue
        check[i]=1
        mark[i]=p+1
        que.append(i)

if -1 in mark:
    print("No")
else:
    print("Yes")
    print(*mark[1:],sep="\n")

Submission status: Accepted

Solution code:


import sys
from collections import defaultdict, deque

sys.setrecursionlimit(10 ** 7)
# ----------

INF = float("inf")
MOD = 10 ** 9 + 7
# ----------

N, M = map(int, input().split())
G = defaultdict(list)
for i in range(M):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    G[a].append(b)
    G[b].append(a)


q = deque()

# 0 を頂点とする
ans = [-1 for _ in range(N)]
ans[0] = 0
q.append(0)

while q:
    v = q.popleft()
    for u in G[v]:
        if ans[u] != -1:
            continue
        ans[u] = v + 1
        q.append(u)

print('Yes')
for i in range(1,N):
    print(ans[i])

Submission status: Accepted

Solution code:
N, M = map(int, input().split())
root = [[] for _ in range(N)]
for _ in range(M):
    A, B = map(int, input().split())
    root[A-1].append(B-1)
    root[B-1].append(A-1)
ans = [[-1, -1] for _ in range(N)]

S = [[0, 0, 0]]

while len(S) > 0:
    S_ = []
    for s in S:
        if ans[s[0]][0] == -1 or s[2] < ans[s[0]][0]:
            ans[s[0]][0] = s[2]
            ans[s[0]][1] = s[1]
            for next in root[s[0]]:
                S_.append([next, s[0], s[2]+1])
    S = S_

print("Yes")
for a in ans[1:]:
    print(a[1]+1)

Submission status: Accepted

Solution code:
N,M=map(int,input().split())
P=[[] for i in range(N+1)]
for i in range(M):
  a,b=map(int,input().split())
  P[a].append(b)
  P[b].append(a)
#AB=[list(map(int,input().split())) for i in range(M)]
ans=[0]*N
con=set()
now=[1]
while now!=[]:
  _now=[]
  for n in now:
    for p in P[n]:
      if p in con:
        continue
      ans[p-1]=n
      _now.append(p)
      con.add(p)
    #con.add(n)
  now=_now
print('Yes')
for a in ans[1:]:
  print(a)

Submission status: Accepted

Solution code:
N, M = map(int, input().split())
from collections import defaultdict
d = defaultdict(list)

for _ in range(M):
  A, B = map(int, input().split())
  d[A].append(B)
  d[B].append(A)

# print(d)

ans = [0] * (N+1)
visited = {1}

current = [1]
for _ in range(N):
  # print(current)
  nxt = []
  for e in current:
    for e2 in d[e]:
      if not e2 in visited:
        ans[e2] = e
        visited.add(e2)
        nxt.append(e2)
  if nxt:
    current = nxt
  else:
    break

if len(visited) == N:
  print('Yes')
  for i in range(2, 1+N):
    print(ans[i])
else:
  print('No')

Submission status: Accepted

Solution code:
from collections import deque, defaultdict

def bfs(i, V, E):
    S = deque()
    S.append(i)
    V[i] = 1
    while(len(S) > 0):
        vi = S.popleft()
        for j in E[vi]:
            if V[j] == 0:
                V[j] = vi
                S.append(j)
    return V

n, m = map(int, input().split())
V = [0 for _ in range(n + 1)]
E = [[] for _ in range(n + 1)]
for i in range(m):
    a, b = map(int, input().split())
    E[a].append(b)
    E[b].append(a)
V = bfs(1, V, E)
print('Yes')
print(*V[2:], sep='\n')

Submission status: Accepted

Solution code:
from collections import deque
N,M=map(int,input().split())
tr=[[] for _ in range(N)]
for _ in range(M):
    a,b=map(int,input().split())
    tr[a-1].append(b-1)
    tr[b-1].append(a-1)
ans=[-1]*N
q=deque([0])
v=[True]*N
x=[True]*N
while q:
    t=q.popleft()
    if v[t]:
        v[t]=False
        for j in tr[t]:
            if x[j]:
                x[j]=False
                ans[j]=t
                q.append(j)
print('Yes')
for i in range(1,N):
    print(ans[i]+1)

Submission status: Accepted

Solution code:
n,m=map(int,input().split())
path=[[] for i in range(n+1)]
anser=[0 for i in range(n+1)]
for i in range(m):
  a,b=map(int,input().split())
  path[a].append(b)
  path[b].append(a)
nowlis=[1]
nowdone=1
anser[1]=1
while nowdone<n:
  now=nowlis.pop(0)
  done=path[now]
  for i in done:
    if anser[i]==0:
      anser[i]=now
      nowlis.append(i)
      nowdone+=1
  #print("anser",anser)
nuki=anser.pop(0)
nuku=anser.pop(0)
print("Yes")
for i in anser:
  print(i)

Submission status: Accepted

Solution code:
def d_double_dots():
    from collections import deque
    N, M = [int(i) for i in input().split()]
    Edges = [[int(i) - 1 for i in input().split()] for j in range(M)]  # 0-indexed

    graph = [[] for _ in range(N)]
    for a, b in Edges:
        graph[a].append(b)
        graph[b].append(a)

    ans = [-1] * N
    is_visit = [False] * N
    queue = deque([0])
    while queue:
        v = queue.pop()
        for u in graph[v]:
            if not is_visit[u]:
                is_visit[u] = True
                ans[u] = v
                queue.appendleft(u)
    ans = ['Yes'] + list(map(lambda x: x + 1, ans[1:]))
    return '\n'.join(map(str, ans))

print(d_double_dots())

Submission status: Accepted

Solution code:
import threading, queue
N, M = map(int, input().split())

ans = [-1 for i in range(N+1)]
E = [ [] for i in range(N+1)]

for i in range(M):
  a, b = map(int, input().split())
  E[a].append(b)
  E[b].append(a)

q = queue.Queue(N)
q.put(1)
ans[1] = 0
while q.empty() == False:
  t = q.get()
  for j in E[t]:
    if ans[j] == -1:
      ans[j] = t
      q.put(j)
  

#Output

print('Yes')
for i in range(2,N+1):
  print(ans[i])

Submission status: Accepted

Solution code:
from collections import defaultdict
from collections import deque
N,M=list(map(int,input().split()))
root = defaultdict(list)

for _ in range(M):
    A,B=list(map(int,input().split()))    
    root[A].append(B)
    root[B].append(A)

visited = [-1]*(N+1)
queue = deque([1])
visited[1] = 0
while queue:
    x = queue.popleft()
    for nex in root[x]:
        if visited[nex] == -1:
            visited[nex] = x
            queue.append(nex)

for i in range(2,N+1):
    if visited[i]==-1:
        print('No')
        exit()
print('Yes')
for i in range(2,N+1):
    print(visited[i])

Submission status: Accepted

Solution code:
from collections import deque
n, m = map(int, input().split())
G = [[] for _ in range(n)]
q = deque([])
d = [float("inf")]*n
p = [0]*n
for _ in range(m):
    u, v = map(int, input().split())
    G[u-1].append(v-1)
    G[v-1].append(u-1)
d[0] = 0
q.append(0)
while q:
    v = q.popleft()
    for u in G[v]:
        if d[v] + 1 < d[u]:
            d[u] = d[v] + 1
            p[u] = v + 1
            q.append(u)
print("Yes")
for i in range(1, n):
    print(p[i])

Submission status: Accepted

Solution code:
from collections import defaultdict, deque

N, M = map(int, input().split())
edges = defaultdict(list)

for _ in range(M):
    u, v = map(int, input().split())
    edges[u - 1].append((v - 1, 1))
    edges[v - 1].append((u - 1, 1))

checked = [None] * N
checked[0] = 0

que = deque([0])

while que:
    u = que.popleft()
    for v, w in edges[u]:
        if checked[v] is not None:
            continue
        if edges[v] != []:
            que.append(v)
        checked[v] = u

print('Yes')
for i in range(N - 1):
    print(checked[i + 1] + 1)

Submission status: Accepted

Solution code:
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 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

def dijkstra(E, start):
    N_d = len(E)
    dist = [INF] * N_d
    dist[start] = 0
    q = [(0, start)]
    while q:
        dist_v, v = heappop(q)
        if dist[v] != dist_v:
            continue
        for u, dist_vu in E[v]:
            dist_u = dist_v + dist_vu
            if dist_u < dist[u]:
                dist[u] = dist_u
                heappush(q, (dist_u, u))
    return dist

N, M = MAP()
L = [LIST() for i in range(M)]
graph = defaultdict(list)

q = deque([0])
for a, b in L:
    graph[a-1].append(b-1)
    graph[b-1].append(a-1)


# put = [0] * N
visited = [False] * N
goto = [INF] * N
dist = [INF] * N

dist[0] = 0
while q:
    a = q.popleft()
    visited[a] = True
    for node in graph[a]:
        if dist[node] > dist[a] + 1:
            dist[node] = dist[a] + 1
            # print("node, a", node, a, dist[node], dist[a])
            goto[node] = a
            q.append(node)

if False in visited:
    print("No")
else:
    print("Yes")
    for g in goto[1:]:
        print(g+1)

# print(dist)
# print(goto)
# print(visited)

Submission status: Accepted

Solution code:
from heapq import heappush, heappop
import sys
input = sys.stdin.buffer.readline

n, m = map(int, input().split())

neighbor = [[] for _ in range(n+1)]

for i in range(m):
    A, B = map(int, input().split())
    neighbor[A].append(B)
    neighbor[B].append(A)

h = []

heappush(h, (0, 1, 0))

ans = [0] * (n+1)
while h:
    step, cur, prev = heappop(h)

    for i in neighbor[cur]:
        if ans[i] == 0:
            ans[i] = cur
            heappush(h, (step+1, i, cur))

print('Yes')
for i in range(2, n+1):
    print(ans[i])

Submission status: Accepted

Solution code:
n, m = map(int, input().split())
ab = [[] for i in range(n)]
for i in range(m):
    a, b = map(int, input().split())
    ab[a - 1].append(b)
    ab[b - 1].append(a)
flag = [False for i in range(n)]
prev = [float("inf") for i in range(n)]

num = [i for i in ab[0]]
for i in num:
    prev[i - 1] = 1
    flag[i - 1] = True
flag[0] = True
while num:
    test = num.pop(0)
    for i in ab[test - 1]:
        if flag[i - 1] == False:
            prev[i - 1] = test
            flag[i - 1] = True
            num.append(i)
print("Yes")
for i in range(n - 1):
    print(prev[i + 1])

Submission status: Accepted

Solution code:
n,m = [int(x) for x in input().split()]
g = [[] for x in range(n)]
for i in range(m):
    a,b = [int(x)-1 for x in input().split()]
    g[a].append(b)
    g[b].append(a)

d = [-1]*n
d[0] = 0
from collections import deque
q = deque()
q.append(0)
ans = [0]*n
while q:
    p = q.popleft()
    for i in g[p]:
        if d[i]==-1:
            q.append(i)
            d[i] = d[p]+1
            ans[i] = p+1
if min(ans)>=0:
    print("Yes")
    for i in ans[1:]:
        print(i)
else:
    print("No")

Submission status: Accepted

Solution code:
from collections import deque


def main():
    N, M = map(int, input().split())
    G = [set() for _ in range(N)]
    for i in range(M):
        A, B = map(lambda x: int(x) - 1, input().split())
        G[A].add(B)
        G[B].add(A)

    vis = [-1] * N
    vis[0] = 0
    q = deque([0])

    while q:
        v = q.popleft()
        for n in G[v]:
            if vis[n] != -1:
                continue
            vis[n] = v
            q.append(n)

    print('Yes')
    print("\n".join(map(lambda x: str(x + 1), vis[1:])))


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
n,m = map(int,input().split())
t = []
l = [0]*(n+1)
for i in range(n+1):
    t.append([])
for i in range(m):
    a,b = map(int,input().split())
    t[a].append(b)
    t[b].append(a)
x = [1]
p = 0
while(p < n):
    for i in range(len(t[x[p]])):
        c = t[x[p]][i]
        if(l[c] == 0):
            x.append(c)
            l[c] = x[p]
    p += 1
print("Yes")
for i in range(2,n+1):
    print(l[i])

Submission status: Accepted

Solution code:
# # -*- coding: utf-8 -*-

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

#
import collections
buf = collections.deque()
parents = [-1 for _ in range(N)]

parents[0] = 0
buf.append(0)

while buf:
    src = buf.popleft()
    for dst in graph[src]:
        if parents[dst] == -1:
            parents[dst] = src
            buf.append(dst)

if all([p != -1 for p in parents]):
    print('Yes')
    for p in parents[1:]:
        print(p+1)
else:
    print('No')

Submission status: Accepted

Solution code:
n, m = map(int, input().split())
l = [[] for _ in range(n)]

ans = [None] * (n)
queue = [0]

ans[0] = 0

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

def bfs(r):
    for i in l[r]:
        if (ans[i] == None):
            queue.append(i)
            ans[i] = r + 1  #index との整合性
    queue.pop(0)

while (len(queue) > 0):
    bfs(queue[0])

if(None not in ans):
    print("Yes")
    for i in ans[1:]:
        print(i)
else:
    print("No")
#print(ans)

Submission status: Accepted

Solution code:
def main():
    import sys
    from collections import deque
    sys.setrecursionlimit(10**6)
    input = sys.stdin.readline
    N, M = [int(x) for x in input().strip().split()]
    G = [deque([]) for _ in range(N)]
    for m in range(M):
        a, b = [int(x) for x in input().strip().split()]
        G[a-1].append(b)
        G[b-1].append(a)
    
    vec = [-1] * N
    q = deque([(0, 1)])
    while q:
        cur, np = q.popleft()
        if vec[np-1] == -1:
            vec[np-1] = cur
            for g in G[np-1]:
                q.append((np, g))
    
    if -1 in vec:
        print('No')
    else:
        print('Yes')
        for v in vec[1:]:
            print(v)

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
n, m = map(int, input().split())
g = [[] for _ in range(n)]

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

dist = [-1]*n
dist[0] = 0
prev = [-1]*n

que = [0]
pos = 0
while pos < len(que) :
	v = que[pos]; pos += 1;
	for w in g[v]:
		if dist[w] == -1 :
			dist[w] = dist[v] + 1
			prev[w] = v;
			que.append(w)

if -1 in dist :
	print("No");
else :
	print("Yes");
	for i in range(1,n):
		print(prev[i]+1);

Submission status: Accepted

Solution code:
import sys
from functools import lru_cache
from collections import deque
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 9)

def main():
    n, m = map(int, input().split())
    rooms = [set() for _ in range(n)] 
    for _ in range(m):
        a, b = map(int, input().split())
        a -= 1
        b -= 1
        rooms[a].add(b)
        rooms[b].add(a)
    checked = set({0})
    # min_path = 0
    # print(rooms)
    queue = deque([])
    queue.append((0, 0, 0)) # room number, min path
    ans = [(-1, 10 ** 7)] * n
    while len(queue) > 0:
        # checked.add(current_room)
        current, path, parent = queue.popleft()
        # print(current)
        # print(current, path)
        if ans[current][0] == -1 or path <= ans[current][1]:
            ans[current] = (parent, path)
        # print(rooms[current])
        for i in rooms[current]:
            if i not in checked:
                queue.append((i, path + 1, current))
                checked.add(i)
    print('Yes')
    for i in range(1, n):
        print(ans[i][0] + 1)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
n,m=map(int, input().split())
es=[[] for i in range(n)]

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

from heapq import heappush, heappop

def dijkstra(edges, size, source):
    # edge=探索するグラフ
    # size=グラフの点の数
    # source=スタート点
    distance = [float('inf')] * size
    muki=[size]*size
    distance[source] = 0
    visited = [False] * size
    pq = []
    heappush(pq, (0, source))
    while pq:
        dist_v, v = heappop(pq)
        visited[v] = True
        for u, weight in edges[v]:
            if not visited[u]:
                new_dist = dist_v + weight
                if distance[u] > new_dist:
                    muki[u]=v
                    distance[u] = new_dist
                    heappush(pq, (new_dist, u))
    return distance, muki

dis, muki=dijkstra(es,n,0)

if n not in muki[1:]:
    print('Yes')
    for i in range(1,n):
        print(muki[i]+1)
else:
    print('No')

Submission status: Accepted

Solution code:
from collections import defaultdict, deque


def main():
    N, M = map(int, input().split())
    AB = [list(map(int, input().split())) for _ in range(M)]

    route = defaultdict(list)
    for ab in AB:
        route[ab[0]].append(ab[1])
        route[ab[1]].append(ab[0])

    ans = [-1] * N
    ans[0] = 0
    que = deque([1])

    while(len(que) != 0):
        v = que.popleft()

        for nv in route[v]:
            if ans[nv-1] != -1:
                continue

            ans[nv-1] = v
            que.append(nv)

    if -1 in ans:
        print('No')
        exit()

    print('Yes')
    for i in range(1, N):
        print(ans[i])


if __name__ == "__main__":
    main()