Sadonkorjuu

# test 1 succeeds
import math
import random


def I():
    return map(int, input().split())


a = """6
1 1 0 0 1 1
1 2 20
2 3 30
2 5 50
3 6 60
1 4 10
""".splitlines()
# print(a)


def generate_test(n: int):
    port_chance = 0.2

    def text_gen():
        yield str(n)
        random.seed(1001)
        yield " ".join(str(int(random.random() > port_chance)) for _ in range(n))
        for i in range(2, n + 1):
            yield " ".join(map(str, (i, random.randrange(1, i), random.randint(1, 100))))
    return text_gen().__next__


# input = iter(a).__next__
# input = generate_test(100)


def main():
    n, = I()
    cities = list(I())
    connections = [dict() for _ in range(n)]
    for i in range(n - 1):
        a, b, c = I()
        connections[a - 1][b - 1] = c
        connections[b - 1][a - 1] = c
    head = Node(None, 0, math.inf, cities[0])
    city = head
    head.form_children(cities, connections)
    while city is not None:
        new = city.next()
        if new is None:
            # city is the root, and has finished.
            break
        elif city.marker == 0:  # new is city's parent
            distance = city.distance
            if new.closest > city.closest + distance:
                new.closest = city.closest + distance
                new.marker = 0  # resetting the node
            city = new
        else:  # city is new's parent
            distance = new.distance
            if new.closest > city.closest + distance:
                new.closest = city.closest + distance
                city = new
            if not new.checked:
                city = new
                new.checked = True
                city.form_children(cities, connections)

    total = 0
    city = head
    while city is not None:
        new = city.next()
        if not city.marker:
            total += city.closest
        city = new
    # print(head.view())
    print(total)


class Node:
    def __init__(self, parent: "Node|None", id: int, distance: float, city_type: bool):
        self.parent = parent
        # if parent is not None:
        #     parent.children.append(self)
        self.children: list[Node] = []
        self.distance = distance
        self.city_type = city_type
        self.id = id
        self.closest = math.inf if city_type else 0
        self.formed_children = False
        self.checked = False

    def form_children(self, cities: "list[bool]", connections: "list[dict[int, float]]"):
        if self.formed_children:
            return
        for city_id, distance in connections[self.id].items():
            if (not self.parent) or city_id != self.parent.id:
                self.children.append(Node(self, city_id, distance, cities[city_id]))
        self.marker = 0
        self.formed_children = True

    def next(self):
        if self.marker < len(self.children):
            self.marker += 1
            return self.children[self.marker - 1]
        self.marker = 0
        return self.parent

    def confirm(self):
        assert all(self.closest <= c.closest + c.distance for c in self.children)
        assert self.parent is None or self.closest <= self.parent.closest + self.distance

    def view(self, indent: int = 0):
        out = ""
        out += " " * indent + f"{self.id}: {self.closest}, {self.distance}" + "\n"
        for c in self.children:
            out += c.view(indent + 4)
        return out


main()

Test 1

Group: 1, 2

Verdict: ACCEPTED

Test 2

Group: 1, 2

Verdict: ACCEPTED

Test 3

Group: 1, 2

Verdict: ACCEPTED

Test 4

Group: 1, 2

Verdict: ACCEPTED

Test 5

Group: 1, 2

Verdict: ACCEPTED

Test 6

Group: 1, 2

Verdict: ACCEPTED

Test 7

Group: 2

Verdict: ACCEPTED

Test 8

Group: 1, 2

Verdict: ACCEPTED

Test 9

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 10

Group: 1, 2

Verdict: ACCEPTED

Test 11

Group: 2

Verdict: ACCEPTED

Test 12

Group: 2

Verdict: ACCEPTED

Test 13

Group: 2

Verdict: ACCEPTED

Test 14

Group: 2

Verdict: ACCEPTED

Test 15

Group: 1, 2

Verdict: ACCEPTED

Test 16

Group: 1, 2

Verdict: ACCEPTED

Test 17

Group: 1, 2

Verdict: ACCEPTED

Test 18

Group: 1, 2

Verdict: ACCEPTED

Test 19

Group: 1, 2

Verdict: ACCEPTED

Test 20

Group: 1, 2

Verdict: ACCEPTED

Test 21

Group: 2

Verdict: ACCEPTED

Test 22

Group: 2

Verdict: ACCEPTED

Test 23

Group: 2

Verdict: ACCEPTED

Test 24

Group: 1, 2

Verdict: ACCEPTED

Test 25

Group: 2

Verdict: ACCEPTED

Test 26

Group: 1, 2

Verdict: ACCEPTED

Test 27

Group: 2

Verdict: ACCEPTED

Test 28

Group: 1, 2

Verdict: ACCEPTED

Test 29

Group: 2

Verdict: ACCEPTED

Test 30

Group: 1, 2

Verdict: ACCEPTED

Test 31

Group: 2

Verdict: ACCEPTED