結果

問題 No.1207 グラフX
ユーザー lam6er
提出日時 2025-03-20 18:48:02
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 786 ms / 2,000 ms
コード長 2,671 bytes
コンパイル時間 209 ms
コンパイル使用メモリ 82,296 KB
実行使用メモリ 228,984 KB
最終ジャッジ日時 2025-03-20 18:49:41
合計ジャッジ時間 31,074 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
sample AC * 3
other AC * 46
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 # 

MOD = 10**9 + 7

def main():
    import sys
    input = sys.stdin.read
    data = input().split()
    idx = 0
    N = int(data[idx]); idx +=1
    M = int(data[idx]); idx +=1
    X = int(data[idx]); idx +=1
    
    edges = []
    for _ in range(M):
        x = int(data[idx])-1; idx +=1
        y = int(data[idx])-1; idx +=1
        z = int(data[idx]); idx +=1
        edges.append((x, y, z))
    
    # Kruskal's algorithm to build MST
    parent = list(range(N))
    def find(u):
        while parent[u] != u:
            parent[u] = parent[parent[u]]
            u = parent[u]
        return u
    
    def union(u, v):
        u_root = find(u)
        v_root = find(v)
        if u_root == v_root:
            return False
        parent[v_root] = u_root
        return True
    
    mst_edges = []
    for x, y, z in edges:
        if union(x, y):
            mst_edges.append((x, y, z))
    
    # Build adjacency list for MST
    adj = [[] for _ in range(N)]
    for x, y, z in mst_edges:
        adj[x].append((y, z))
        adj[y].append((x, z))
    
    # Iterative DFS to compute subtree sizes and collect parent-child edges
    from collections import deque
    root = 0
    visited = [False] * N
    stack = [(root, -1)]  # (node, parent)
    subtree_size = [1] * N
    parent_child_z = []  # (child, parent, z)
    
    # Iterative DFS
    stack = []
    stack.append((root, -1))
    while stack:
        node, parent_node = stack.pop()
        if node < 0:
            # Post-processing, after children are processed
            node = ~node
            for neighbor, z in adj[node]:
                if neighbor == parent_node:
                    continue
                subtree_size[node] += subtree_size[neighbor]
            continue
        if visited[node]:
            continue
        visited[node] = True
        # Push the node back with a marker to indicate post-processing
        stack.append((~node, parent_node))
        # Push children in reverse order to process them in order
        # Iterate through all neighbors, but process only children
        for neighbor, z in reversed(adj[node]):
            if neighbor == parent_node:
                continue
            stack.append((neighbor, node))
            # Record the parent-child edge and its z
            parent_child_z.append((neighbor, node, z))
    
    total = 0
    for child, parent_node, z in parent_child_z:
        s = subtree_size[child]
        term = s * (N - s)
        # Compute X^z mod MOD
        pow_x_z = pow(X, z, MOD)
        term = term * pow_x_z % MOD
        total = (total + term) % MOD
    
    print(total % MOD)

if __name__ == "__main__":
    main()
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