Programming_2023/balanced_forest.py at main · Atan-D-RP4/Programming_2023 · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
#!/bin/python3

import math
import os
import random
import re
import sys

#
# Complete the 'balancedForest' function below.
#
# The function is expected to return an INTEGER.
# The function accepts following parameters:
#  1. INTEGER_ARRAY c
#  2. 2D_INTEGER_ARRAY edges
#

from operator import attrgetter
from itertools import groupby
from sys import stderr


class Node:
    def __init__(self, index, value):
        self.index = index
        self.value = value
        self.children = []


def readtree():
    size = int(input())
    values = readints()
    assert size == len(values)
    nodes = [Node(i, v) for i, v in enumerate(values)]
    for _ in range(size - 1):
        x, y = readints()
        nodes[x - 1].children.append(nodes[y - 1])
        nodes[y - 1].children.append(nodes[x - 1])
    return nodes


def readints():
    return [int(fld) for fld in input().strip().split()]


def balancedForest(nodes):
    if len(nodes) == 1:
        return -1
    rootify(nodes[0])
    #    print([(n.index, n.value, n.totalval) for n in nodes], file=stderr)
    best = total = nodes[0].totalval
    dummynode = Node(None, None)
    dummynode.totalval = 0
    sortnode = []
    for k, g in groupby(
        sorted([dummynode] + nodes, key=attrgetter("totalval")), attrgetter("totalval")
    ):
        sortnode.append(list(g))
    total = nodes[0].totalval
    for ihi, n in enumerate(sortnode):
        if 3 * n[0].totalval >= total:
            break
    else:
        assert False
    ilo = ihi - 1
    for ihi in range(ihi, len(sortnode)):
        hi = sortnode[ihi][0].totalval
        lo = sortnode[ilo][0].totalval
        while 2 * hi + lo > total:
            if lo == 0:
                return -1
            if (total - lo) % 2 == 0:
                x = (total - lo) // 2
                for lonode in sortnode[ilo]:
                    if uptototalval(lonode, x + lo):
                        return x - lo
            ilo -= 1
            lo = sortnode[ilo][0].totalval
        if len(sortnode[ihi]) > 1:
            return 3 * hi - total
        hinode = sortnode[ihi][0]
        if 2 * hi + lo == total:
            for lonode in sortnode[ilo]:
                if uptototalval(lonode, hi) != hinode:
                    return hi - lo
        y = total - 2 * hi
        if uptototalval(hinode, 2 * hi) or uptototalval(hinode, hi + y):
            return hi - y


def rootify(root):
    root.parent = root.jumpup = None
    root.depth = 0
    bfnode = [root]
    i = 0
    while i < len(bfnode):
        node = bfnode[i]
        depth = node.depth + 1
        jumpup = uptodepth(node, depth & (depth - 1))
        for child in node.children:
            child.parent = node
            child.children.remove(node)
            child.depth = depth
            child.jumpup = jumpup
            bfnode.append(child)
        i += 1
    for node in reversed(bfnode):
        node.totalval = node.value + sum(child.totalval for child in node.children)


def uptodepth(node, depth):
    while node.depth > depth:
        if node.jumpup.depth <= depth:
            node = node.jumpup
        else:
            node = node.parent
    return node


def uptototalval(node, totalval):
    try:
        #    print('uptototalval(%s,%s)' % (node.index, totalval), file=stderr)
        while node.totalval < totalval:
            if node.parent is None:
                return None
            if node.jumpup.totalval <= totalval:
                node = node.jumpup
            else:
                node = node.parent
        #        print((node.index, node.totalval), file=stderr)
        if node.totalval == totalval:
            return node
        else:
            return None
    except Exception:
        return None


ncases = int(input())
for _ in range(ncases):
    print(balancedForest(readtree()))