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: Runtime Error

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())
A = [0] * M
B = [0] * M
G = [[] for _ in range(M)]
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: Runtime Error

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

ans = [-1 for _ in range(n)]
hand = [n+1 for _ in range(n)]
def get(counter, start, ans, hand):
    # counter: 手数
    # start: 出てきた部屋
    for end in maze[start]:
        if counter < hand[end] and end != 0:
            hand[end] = counter+1
            ans[end] = start
            get(counter+1, end, ans, hand)

get(0, 0, ans, hand)
if -1 in ans[1:]:
    print('No')
else:
    print('Yes')
    for i in range(1,n):
        print(ans[i]+1)

Submission status: Runtime Error

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

que = deque([1])
ans = [0 for i in range(M)]
while True:
    cur = que.popleft()
    for item in data[cur-1]:
        if ans[item-1] == 0:
            que.append(item)
            ans[item-1] = cur
    if len(que) == 0: break

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

Submission status: Runtime Error

Solution code:
from collections import deque
import sys
sys.setrecursionlimit(10**7)
N,M=map(int,input().split())
A=[]
B=[]
road=[[] for i in range(M)]
for i in range(M):
  a,b=map(int,input().split())
  road[a-1].append(b-1)
  road[b-1].append(a-1)
visit=[0]*N

q=deque([0])
ans=[0]*N
visit[0]=1
def bfs(q):
  while(q):
    v=q.popleft()
    #print(v)
    for x in road[v]:
      if(visit[x]==0):
        q.append(x)
        #print(q)
        visit[x]=1
        ans[x]=v+1
        #print(x)
bfs(q)
print("Yes")
for i in range(N-1):
  print(ans[i+1])

Submission status: Runtime Error

Solution code:
from collections import deque
N,M=map(int,input().split())
A=[]
B=[]
road=[[] for i in range(M)]
for i in range(M):
  a,b=map(int,input().split())
  road[a-1].append(b-1)
  road[b-1].append(a-1)
visit=[0]*N

q=deque([0])
ans=[0]*N
visit[0]=1
#print(road)
#print(road[1])
def bfs(q):
  while(q):
    v=q.popleft()
    #print(v)
    for x in road[v]:
      if(visit[x]==0):
        q.append(x)
        #print(q)
        visit[x]=1
        ans[x]=v+1
        #print(x)
bfs(q)
print("Yes")
for i in range(N-1):
  print(ans[i+1])

Submission status: Runtime Error

Solution code:
from collections import deque

def bfs(g_list, visited):
    q = deque([1])
    visited[1] = 0
    while q:
        curr_room = q.popleft()
        for next_room in g_list[curr_room]:
            if visited[next_room] >= 0:
                continue
            visited[next_room] = curr_room
            q.append(next_room)


def main():
    n, m = map(int, input().split()) 
    g_list = [ [] for _ in range(m+1)]
    visited = [-1] * (n+1)
    visited[0] = 0
    for i in range(m):
        a, b = map(int, input().split()) 
        g_list[a].append(b)
        g_list[b].append(a)
    bfs(g_list,visited)
    # print(visited)
    ans = visited[2:]
    if -1 in ans:
        print('No')
    else:
        print('Yes')
        for a in ans:
            print(a)

if __name__ == "__main__":
    main()

Submission status: Runtime Error

Solution code:
def resolve():
    from scipy.sparse.csgraph import shortest_path
    from scipy.sparse import csr_matrix
    import numpy as np
    n, m = map(int, input().split())
    edge = np.array([input().split() for _ in range(m)], dtype=np.int64).T
    a = csr_matrix(([1] * m, (edge - 1)), shape=(n, n)).toarray()
    s, p = shortest_path(a, return_predecessors=True,
                         indices=0, directed=False)  # 最短経路p
    if min(s[1:]) < 1:
        print("No")
    else:
        print("Yes")
        for i in p[1:]:
            print(i + 1)


if __name__ == '__main__':
    resolve()

Submission status: Runtime Error

Solution code:
from sys import stdin, setrecursionlimit
from heapq import heappush, heappop

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


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


N, M = map(int, input().split())
A = [0] * M
B = [0] * M
G = [[] for _ in range(M)]
for i in range(M):
    a, b = map(int, input().split())
    G[a-1].append(b-1)
    G[b-1].append(a-1)
    
dist = [INF] * N
prev = [0] * N

pq = [(0, 0)]
while pq:
    d, v = heappop(pq)
    if dist[v] < d:
        continue
    for nv in G[v]:
        if dist[nv] > d + 1:
            dist[nv] = d + 1
            heappush(pq, (dist[nv], nv))
            prev[nv] = v

print('Yes')
for v in prev[1:]:
    print(v+1)

Submission status: Runtime Error

Solution code:
import sys
from collections import deque
def input(): return sys.stdin.readline().rstrip()

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

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

    que = deque()
    que.append(1)
    front = [-1] * (N + 1)
    front[1] = 1
    while que:
        point = que.popleft()
        for i in root[point]:
            if front[i] > 0:
                continue
            front[i] = point
            que.append(i)

    if min(front[2:]) < 0:
        print('No')
    else:
        print('Yes')
        for i in range(2, N + 1):
            print(front[i])

if __name__ == '__main__':
    main()

Submission status: Runtime Error

Solution code:
from collections import deque

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

visited = [False for _ in range(n)]

visited[0] = True
ans = [-1 for _ in range(n)]
d = deque()
d.append(0)
while len(d) > 0:
    now = d.popleft()
    for v in to[now]:
        if ans[v] > -1:
            continue
        ans[v] = now
        d.append(v)

print("Yes")
for i in range(1, len(ans)):
    print(ans[i]+1)

Submission status: Runtime Error

Solution code:
def main():

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

    import numpy as np
    import scipy.sparse as sp
    ab = [list(map(int, input().split())) for _ in [0]*m]
    g = [[] for _ in [0]*n]
    [g[a-1].append(b-1) for a, b in ab]
    [g[b-1].append(a-1) for a, b in ab]

    data = [1 for a, b in ab]
    row = [a-1 for a, b in ab]
    col = [b-1 for a, b in ab]
    matrix = sp.csr_matrix((data, (row, col)), shape=(n, n), dtype=np.int32)
    d = sp.csgraph.dijkstra(matrix, indices=0)

    print("Yes")
    for i in range(1, n):
        minimum = 10**9
        dire = None
        for j in g[i]:
            if d[j] < minimum:
                minimum = d[j]
                dire = j
        print(dire+1)


main()

Submission status: Runtime Error

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

ans = [-1]*N
T = [0]
while len(T)>0:
  P = T
  T = []
  for x in P:
    for e in E[x]:
      if ans[e]==-1:
        T += [e]
        ans[e] = x

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

Submission status: Runtime Error

Solution code:
def main():
    n, m = map(int, input().split())
    ab = [list(map(int, input().split())) for _ in [0]*m]
    g = [[] for _ in [0]*n]
    [g[a-1].append(b-1) for a, b in ab]
    [g[b-1].append(a-1) for a, b in ab]

    import numpy as np
    import scipy.sparse.csgraph as sp
    inf = float('inf')
    d = np.full((n, n), inf)
    for i in range(n):
        d[i][i] = 0
    for a, b in ab:
        d[a-1][b-1] = 1
        d[b-1][a-1] = 1
    # indices=xでxからの単一始点に,return_predecessors=Trueで経路が出る
    s = sp.shortest_path(d, indices=0)
    print("Yes")
    for i in range(1, n):
        minimum = 10**9
        dire = None
        for j in g[i]:
            if s[j] < minimum:
                minimum = s[j]
                dire = j
        print(dire+1)


main()

Submission status: Runtime Error

Solution code:
from sys import stdin, setrecursionlimit
input = stdin.buffer.readline
setrecursionlimit(10 ** 7)

from heapq import heappush, heappop
from bisect import bisect_left, bisect_right
from collections import deque, defaultdict
from itertools import combinations, permutations, combinations_with_replacement
from itertools import accumulate
from math import ceil, sqrt, pi

MOD = 10 ** 9 + 7
INF = 10 ** 18

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

graph = [[] for _ in range(N + 1)]
arrow = [0] * (N + 1)

for a, b in AB:
    graph[a].append(b)
    graph[b].append(a)
    
def bfs(st, graph):
    INF = 10 ** 18
    dist = [0] * len(graph)
    dist[st] = 1
    queue = deque([st])
    while queue:
        q = queue.popleft()
        for r in graph[q]:
            if dist[r] == 0:
                dist[r] = q
                queue.append(r)
    return dist

answer = bfs(1, graph)[2:]
print("Yes")
for a in answer:
    print(a)

Submission status: Runtime Error

Solution code:
I cant solve the problem.

Submission status: Runtime Error

Solution code:
from collections import deque
def bfs(graph, N, start):
    visited = [0] * N
    visited[start] = 1
    que = deque([start])
    while que:
        node = que.popleft()
        for n in graph[node]:
            if not visited[n]:
                visited[n] = node + 1
                que.append(n)
    return visited

N, M = map(int, input().split())
graph = [[] for _ in range(M)]
for _ in range(M):
    a, b = map(lambda n: int(n) - 1, input().split())
    graph[a].append(b)
    graph[b].append(a)
visited = bfs(graph, N, 0)[1:]
if all(visited):
    print("Yes")
    print(*visited, sep="\n")
else:
    print("No")

Submission status: Runtime Error

Solution code:

def inpl():
    return list(map(int, input().split()))


N, M = inpl()

lines = [[] for _ in range(N)]
for _ in range(M):
    a, b = inpl()
    a -= 1
    b -= 1
    lines[a].append(b)
    lines[b].append(a)


ans = [-1] * N


def dfs(s, b):
    global ans

    if ans[s] != -1:
        return
    else:
        ans[s] = b
        for t in lines[s]:
            dfs(t, s)


dfs(0, 0)


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