結果

問題 No.2786 RMQ on Grid Path
ユーザー lam6er
提出日時 2025-03-31 17:28:06
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 3,874 ms / 6,000 ms
コード長 3,549 bytes
コンパイル時間 460 ms
コンパイル使用メモリ 82,644 KB
実行使用メモリ 318,360 KB
最終ジャッジ日時 2025-03-31 17:29:49
合計ジャッジ時間 74,562 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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 * 2
other AC * 35
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
from sys import stdin
from collections import deque

def main():
    H, W = map(int, stdin.readline().split())
    grid = []
    for _ in range(H):
        row = list(map(int, stdin.readline().split()))
        grid.append(row)
    
    edges = []
    for i in range(H):
        for j in range(W):
            current = i * W + j
            current_val = grid[i][j]
            if i < H - 1:
                ni, nj = i + 1, j
                neighbor = ni * W + nj
                weight = max(current_val, grid[ni][nj])
                edges.append((weight, current, neighbor))
            if j < W - 1:
                ni, nj = i, j + 1
                neighbor = ni * W + nj
                weight = max(current_val, grid[ni][nj])
                edges.append((weight, current, neighbor))
    
    edges.sort()
    
    parent = list(range(H * W))
    def find(u):
        while parent[u] != u:
            parent[u] = parent[parent[u]]
            u = parent[u]
        return u
    
    mst_edges = []
    for weight, u, v in edges:
        u_root = find(u)
        v_root = find(v)
        if u_root != v_root:
            parent[v_root] = u_root
            mst_edges.append((u, v, weight))
            mst_edges.append((v, u, weight))
    
    adj = [[] for _ in range(H * W)]
    for u, v, w in mst_edges:
        adj[u].append((v, w))
    
    root = 0
    parent_list = [-1] * (H * W)
    edge_weight = [0] * (H * W)
    depth = [0] * (H * W)
    
    queue = deque([root])
    parent_list[root] = -1
    depth[root] = 0
    
    while queue:
        u = queue.popleft()
        for v, w in adj[u]:
            if parent_list[v] == -1 and v != parent_list[u]:
                parent_list[v] = u
                edge_weight[v] = w
                depth[v] = depth[u] + 1
                queue.append(v)
    
    MAX_LOG = 20
    jump = [[-1] * (H * W) for _ in range(MAX_LOG)]
    max_edge = [[0] * (H * W) for _ in range(MAX_LOG)]
    
    for u in range(H * W):
        jump[0][u] = parent_list[u]
        max_edge[0][u] = edge_weight[u]
    
    for k in range(1, MAX_LOG):
        for u in range(H * W):
            if jump[k-1][u] != -1:
                jump[k][u] = jump[k-1][jump[k-1][u]]
                max_edge[k][u] = max(max_edge[k-1][u], max_edge[k-1][jump[k-1][u]])
            else:
                jump[k][u] = -1
                max_edge[k][u] = 0
    
    def get_lca(u, v):
        if depth[u] < depth[v]:
            u, v = v, u
        for k in reversed(range(MAX_LOG)):
            if depth[u] - (1 << k) >= depth[v]:
                u = jump[k][u]
        if u == v:
            return u
        for k in reversed(range(MAX_LOG)):
            if jump[k][u] != -1 and jump[k][u] != jump[k][v]:
                u = jump[k][u]
                v = jump[k][v]
        return jump[0][u]
    
    def get_max(u, anc):
        if u == anc:
            return 0
        max_e = 0
        current = u
        for k in reversed(range(MAX_LOG)):
            if depth[current] - (1 << k) >= depth[anc]:
                max_e = max(max_e, max_edge[k][current])
                current = jump[k][current]
        return max_e
    
    Q = int(stdin.readline())
    for _ in range(Q):
        rs, cs, rt, ct = map(int, stdin.readline().split())
        rs -= 1
        cs -= 1
        rt -= 1
        ct -= 1
        u = rs * W + cs
        v = rt * W + ct
        lca = get_lca(u, v)
        max_u = get_max(u, lca)
        max_v = get_max(v, lca)
        print(max(max_u, max_v))

if __name__ == "__main__":
    main()
0