#977954 (PyPy3) No.2764 Warp Drive Spacecraft

• 問題: No.2764 Warp Drive Spacecraft
• ユーザー: magurofly
• 提出日時: 2024-04-29 11:36:41
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 1,667 ms / 3,000 ms
• コード長: 2,408 bytes
• コンパイル時間: 201 ms
• コンパイル使用メモリ: 82,816 KB
• 実行使用メモリ: 216,136 KB
• 最終ジャッジ日時: 2024-07-17 20:23:08
• 合計ジャッジ時間: 28,361 ms
• ジャッジサーバーID （参考情報）: judge2 / judge4

ファイルパターン	結果
sample	AC * 4
other	AC * 35

ソースコード

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import heapq
INF = 2 * 10**18
class StaticCHT:
    # funcs: 一次関数 f(x)=ax+b: (a, b) のリスト
    def __init__(self, funcs):
        by_a = {}
        for a, b in funcs:
            if a in by_a:
                by_a[a] = min(by_a[a], b)
            else:
                by_a[a] = b
        funcs = sorted(by_a.items(), key = lambda f: -f[0])
        # 交点を求める
        self.points = []
        self.funcs = [funcs[0]]
        for i in range(len(funcs) - 1):
            a1, b1 = funcs[i]
            a2, b2 = funcs[i + 1]
            self.points.append((b1 - b2, a2 - a1))
            self.funcs.append((a2, b2))
            while len(self.points) >= 2:
                p1, q1 = self.points[-2]
                p2, q2 = self.points[-1]
                if p1 * q2 <= p2 * q1:
                    break
                self.funcs.pop(-2)
                self.points.pop()
                self.points.pop()
                a1, b1 = self.funcs[-2]
                a2, b2 = self.funcs[-1]
                self.points.append((b1 - b2, a2 - a1))
    
    # 点 x における最小値を求める
    def min(self, x):
        l, r = 0, len(self.points)
        while l < r:
            mid = (l + r) // 2
            p, q = self.points[mid]
            if x * q <= p:
                l = mid + 1
            else:
                r = mid
        a, b = self.funcs[l]
        return a * x + b
def dijkstra(graph, start, inf = 10**18):
    dist = [inf] * len(graph)
    dist[start] = 0
    pq = []
    heapq.heappush(pq, (0, start))
    while pq:
        d, u = heapq.heappop(pq)
        if d > dist[u]:
            continue
        for v, w in graph[u]:
            if dist[v] > d + w:
                dist[v] = d + w
                heapq.heappush(pq, (d + w, v))
    return dist
N, M = map(int, input().split())
W = list(map(int, input().split()))
edges = [list(map(int, input().split())) for _ in range(M)]
graph = [[] for _ in range(N)]
for u, v, t in edges:
    graph[u - 1].append((v - 1, t))
    graph[v - 1].append((u - 1, t))
dist_s = dijkstra(graph, 0, INF)
dist_t = dijkstra(graph, N - 1, INF)
ans = dist_s[N - 1]
# dist_s[i] + dist_t[j] + W[i] * W[j]
funcs = []
for j in range(N):
    if dist_t[j] < INF:
        funcs.append((W[j], dist_t[j]))
cht = StaticCHT(funcs)
for i in range(N):
    if dist_s[i] < INF:
        ans = min(ans, dist_s[i] + cht.min(W[i]))
print(ans)
 
 
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