結果

問題 No.2764 Warp Drive Spacecraft
ユーザー LyricalMaestro
提出日時 2025-01-03 02:26:00
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,051 ms / 3,000 ms
コード長 2,894 bytes
コンパイル時間 335 ms
コンパイル使用メモリ 82,560 KB
実行使用メモリ 186,152 KB
最終ジャッジ日時 2025-01-03 02:26:38
合計ジャッジ時間 35,944 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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ファイルパターン 結果
sample AC * 4
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 # 

## https://yukicoder.me/problems/no/2764

import heapq
from collections import deque

MAX_INT = 10 ** 18

def dijkstra(N, next_nodes, src):
    fix = [MAX_INT] * N
    seen = [MAX_INT] * N
    seen[src] = 0
    queue = []
    heapq.heappush(queue, (0, src))
    while len(queue) > 0:
        cost, v = heapq.heappop(queue)
        if fix[v] < MAX_INT:
            continue

        fix[v] = cost
        for w, t in next_nodes[v]:
            if fix[w] < MAX_INT:
                continue

            new_cost = t + cost
            if seen[w] > new_cost:
                seen[w] = new_cost
                heapq.heappush(queue, (new_cost, w))
    return fix

def main():
    N, M = map(int, input().split())
    W = list(map(int, input().split()))

    next_nodes = [[] for _ in range(N)]
    for _ in range(M):
        u, v, t = map(int, input().split())
        next_nodes[u - 1].append((v - 1, t))
        next_nodes[v - 1].append((u - 1, t))
    
    dists_from_s = dijkstra(N, next_nodes, 0)
    dists_from_t = dijkstra(N, next_nodes, N - 1)

    lines_w = {}
    for i in range(N):
        if dists_from_s[i] < MAX_INT:
            if W[i] not in lines_w:
                lines_w[W[i]] = dists_from_s[i]
            else:
                lines_w[W[i]] = min(lines_w[W[i]], dists_from_s[i])
    lines = [(w, d) for w, d in lines_w.items()]
    lines.sort(key=lambda x : x[0], reverse=True)

    def compare(p1, p0):
        if p1[0] * p0[1] > p1[1] * p0[0]:
            return 1
        elif p1[0] * p0[1] < p1[1] * p0[0]:
            return -1
        else:
            return 0

    # convex hull trick
    stack = deque()
    for w, d in lines:
        while len(stack) > 0:
            w0, d0, p0 = stack[-1]
            p1 = (d - d0, w0 - w)
            # p1 > p0
            if compare(p1, p0) == 0:
                stack.pop()
                break
            elif compare(p1, p0) < 0:
                stack.pop()
            else:
                break

        if len(stack) == 0:
            stack.append((w, d, (0, 1)))
        else:
            stack.append((w, d, p1))

    intervals = []
    while len(stack) > 0:
        intervals.append(stack.popleft())

    answer = dists_from_s[N - 1]
    for i in range(N):
        if dists_from_t[i] < MAX_INT:
            w = W[i]

            low = 0
            high = len(intervals) - 1
            while high - low > 1:
                mid = (high + low) // 2
                if compare((w, 1), intervals[mid][2]) >= 0:
                    low = mid
                else:
                    high = mid
            if compare((w, 1), intervals[high][2]) >= 0:
                v = high
            else:
                v = low
            
            w0, d0, _ = intervals[v]
            ans = w * w0 + d0 + dists_from_t[i]
            answer = min(answer, ans)
    print(answer)









if __name__ == "__main__":
    main()
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