結果

問題 No.3104 Simple Graph Problem
ユーザー tassei903
提出日時 2025-04-11 23:01:43
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 522 ms / 2,000 ms
コード長 4,116 bytes
コンパイル時間 161 ms
コンパイル使用メモリ 82,344 KB
実行使用メモリ 112,280 KB
最終ジャッジ日時 2025-04-11 23:02:12
合計ジャッジ時間 16,909 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 65
権限があれば一括ダウンロードができます

ソースコード

diff # 

import sys
input = lambda :sys.stdin.readline()[:-1]
ni = lambda :int(input())
na = lambda :list(map(int,input().split()))
yes = lambda :print("yes");Yes = lambda :print("Yes");YES = lambda : print("YES")
no = lambda :print("no");No = lambda :print("No");NO = lambda : print("NO")
#######################################################################

from collections import defaultdict
 
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n
 
    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]
 
    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)
 
        if x == y:
            return
 
        if self.parents[x] > self.parents[y]:
            x, y = y, x
 
        self.parents[x] += self.parents[y]
        self.parents[y] = x
 
    def size(self, x):
        return -self.parents[self.find(x)]
 
    def same(self, x, y):
        return self.find(x) == self.find(y)
 
    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]
 
    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]
 
    def group_count(self):
        return len(self.roots())
 
    def all_group_members(self):
        group_members = defaultdict(list)
        for member in range(self.n):
            group_members[self.find(member)].append(member)
        return group_members
 
    def __str__(self):
        return '\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())

# 木のとき葉から一意に操作される
# 偶数長のサイクル
# 奇数長のサイクル がある時必ずできそう

mod = 998244353
n, m = na()
b = na()

uf = UnionFind(n * 2)
g = [[] for i in range(n)]
flag = False
cnt = 0
for i in range(m):
    u, v = na()
    u -= 1
    v -= 1
    if not (uf.same(u, v) or uf.same(u, v + n)):
        uf.union(u, v + n)
        uf.union(u+n, v)
        g[u].append((v, i))
        g[v].append((u, i))
        cnt += 1
    elif uf.same(u, v) and (not flag):
        flag = True
        g[u].append((v, i))
        g[v].append((u, i))
        cnt += 1


if cnt == n - 1:
    dp = [-1] * n
    q = [0]
    seen = [0] * n
    seen[0] = 1
    p = [-1] * n
    pi = [-1] * n
    et = []
    while q:
        x = q.pop()
        et.append(x)
        for y, j in g[x]:
            if not seen[y]:
                p[y] = x
                pi[y] = j
                q.append(y)
                seen[y] = 1
    ans = [0] * m
    for i in et[1:][::-1]:
        ans[pi[i]] = b[i] % mod
        b[p[i]] -= b[i]
        b[p[i]] %= mod
        b[i] = 0
    
    if b[0] == 0:
        print(*ans)
    else:
        print(-1)
else:
    deg = [len(g[i]) for i in range(n)]
    q = [i for i in range(n) if deg[i] == 1]
    ans = [0] * m
    seen = [0] * n
    # print(g)
    while q:
        x = q.pop()
        seen[x] = 1
        for z, j in g[x]:
            if seen[z]:continue
            y = z
            i = j
            break
        ans[i] = b[x]
        b[y] -= b[x]
        b[y] %= mod
        b[x] = 0
        deg[y] -= 1
        if deg[y] == 1:
            q.append(y)
    X = -1
    for i in range(n):
        if deg[i] == 2:
            X = i
            break
    
    P = []
    PI = []
    Y = X
    pre = -1
    T = 0
    while True:
        
        for z, j in g[Y]:
            if z != pre and (not seen[z]):
                P.append(z)
                PI.append(j)
                pre = Y
                Y = z
                break
        else:
            assert False
        T += 1
        # assert T <= n * 2
        if Y == X:
            break
    Z = 0
    for i in P:
        Z += b[i]
    Z = Z * pow(2, mod-2, mod) % mod
    a = [0, 0]
    for i in range(len(P)//2*2):
        a[i % 2] += b[P[i]]

    for i in range(len(P)):
        ans[PI[i]] = (Z - a[i % 2 ^ 1]) % mod
        a[i % 2] -= b[P[i]]
        a[i % 2] += b[P[(i - 1) % len(P)]]
        a[i % 2] %= mod

    print(*ans)
0