Problem:


Score : 700 points

Problem Statement

We have a rooted binary tree with N vertices, where the vertices are numbered 1 to N.
Vertex 1 is the root, and the parent of Vertex i (i \geq 2) is Vertex \left[ \frac{i}{2} \right].

Each vertex has one item in it. The item in Vertex i has a value of V_i and a weight of W_i.
Now, process the following query Q times:

Given are a vertex v of the tree and a positive integer L.
  Let us choose some (possibly none) of the items in v and the ancestors of v so that their total weight is at most L.
  Find the maximum possible total value of the chosen items.

Here, Vertex u is said to be an ancestor of Vertex v when u is an indirect parent of v, that is, there exists a sequence of vertices w_1,w_2,\ldots,w_k (k\geq 2) where w_1=v, w_k=u, and w_{i+1} is the parent of w_i for each i.

Constraints

All values in input are integers.

1 \leq N < 2^{18}

1 \leq Q \leq 10^5

1 \leq V_i \leq 10^5

1 \leq W_i \leq 10^5

For the values v and L given in each query, 1 \leq v \leq N and 1 \leq L \leq 10^5.

Input

Let v_i and L_i be the values v and L given in the i-th query.
Then, Input is given from Standard Input in the following format:

N
V_1 W_1
:
V_N W_N
Q
v_1 L_1
:
v_Q L_Q

Output

For each integer i from 1 through Q,
the i-th line should contain the response to the i-th query.

Sample Input 1

3
1 2
2 3
3 4
3
1 1
2 5
3 5

Sample Output 1

0
3
3

In the first query, we are given only one choice: the item with (V, W)=(1,2). Since L = 1, we cannot actually choose it, so our response should be 0.

In the second query, we are given two choices: the items with (V, W)=(1,2) and (V, W)=(2,3). Since L = 5, we can choose both of them, so our response should be 3.

Sample Input 2

15
123 119
129 120
132 112
126 109
118 103
115 109
102 100
130 120
105 105
132 115
104 102
107 107
127 116
121 104
121 115
8
8 234
9 244
10 226
11 227
12 240
13 237
14 206
15 227

Sample Output 2

256
255
250
247
255
259
223
253



Sample input:
3
1 2
2 3
3 4
3
1 1
2 5
3 5


Sample output:
0
3
3

Submission status: Time Limit Exceeded

Solution code:
import sys
MX = 10**5
def main():
    data = map(int, sys.stdin.buffer.read().split())
    N = next(data)
    IV, IW = [], []

    H = min(N + 1, 1 << 10)
    Hb = (H - 1).bit_length()
    dp = [[0] * (MX + 1) for _ in range(H)]
    i = 1
    for v, w in zip(data, data):
        if i < H:
            dpi = dp[i]
            dpip = dp[i >> 1]
            for j in range(w):
                dpi[j] = dpip[j]
            for j in range(w, MX + 1):
                dpi[j] = max(dpip[j], dpip[j - w] + v)
        else:
            IV.append(v)
            IW.append(w)
        i += 1
        if i > N:
            break

    Q = next(data)
    for v, L in zip(data, data):
        if v < H:
            print(dp[v][L])
            continue
        ans = []
        for i in range(1 << (v.bit_length() - Hb)):
            node = v
            value = weight = 0
            while node >= H:
                if i & 1:
                    value += IV[node - H]
                    weight += IW[node - H]
                    if weight > L:
                        break
                node >>= 1
                i >>= 1
            else:
                ans.append(value + dp[node][L - weight])
        print(max(ans))

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
import sys
MX = 10**5
def main():
    data = map(int, sys.stdin.buffer.read().split())
    N = next(data)
    IV, IW = [], []

    H = min(N + 1, 1 << 1)
    Hb = (H - 1).bit_length()
    dp = [[0] * (MX + 1) for _ in range(H)]
    i = 1
    for v, w in zip(data, data):
        if i < H:
            dpi = dp[i]
            dpip = dp[i >> 1]
            for j in range(w):
                dpi[j] = dpip[j]
            for j in range(w, MX + 1):
                dpi[j] = max(dpip[j], dpip[j - w] + v)
        else:
            IV.append(v)
            IW.append(w)
        i += 1
        if i > N:
            break

    Q = next(data)
    for v, L in zip(data, data):
        if v < H:
            print(dp[v][L])
            continue
        ans = []
        for i in range(1 << (v.bit_length() - Hb)):
            node = v
            value = weight = 0
            while node >= H:
                if i & 1:
                    value += IV[node - H]
                    weight += IW[node - H]
                    if weight > L:
                        break
                node >>= 1
                i >>= 1
            else:
                ans.append(value + dp[node][L - weight])
        print(max(ans))

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
import sys

import numpy as np
from itertools import product
from numba import njit


MASK = np.array([pat for pat in product(range(2), repeat=9)])
MASK *= np.arange(9, 0, -1)
INF = pow(10, 12)
HALF = pow(2, 9)
MAX = pow(10, 5)

readline = sys.stdin.buffer.readline
read = sys.stdin.buffer.read
n = int(readline())
Z = np.array(read().split(), np.int64)
V = np.zeros(n + 1, np.int64)
W = np.zeros(n + 1, np.int64)
V[1:] = Z[0:2 * n:2]
W[1:] = Z[1:2 * n:2]
U = Z[2 * n + 1::2]
L = Z[2 * n + 2::2]

N = min(n, HALF)


@njit
def f1():
    dp = np.zeros((N + 1, MAX + 1), np.int64)

    for i, (v, w) in enumerate(zip(V[1:N + 1], W[1:N + 1]), 1):
        i_prev = i // 2
        dp[i] = dp[i_prev]
        dp[i, w:] = np.maximum(dp[i, w:], dp[i_prev, :-w] + v)

    return dp


def main():
    dp = f1()

    for i in range(N):
        dp[i] = np.maximum.accumulate(dp[i])

    for u, l in zip(U, L):
        now = u
        li = [0]
        while now >= HALF:
            li.append(now)
            now //= 2
        li = np.array(li)

        size = li.size - 1
        MINI_MASK = MASK[:1 << size, -size:]
        IDX = li[MINI_MASK]
        W_SUM = W[IDX].sum(axis=1)
        V_SUM = V[IDX].sum(axis=1)

        V_SUM[W_SUM > l] = -INF
        W_SUM[W_SUM > l] = 0

        VV = dp[now][l - W_SUM] + V_SUM
        ans = VV.max()
        print(ans)


main()

Submission status: Time Limit Exceeded

Solution code:
import sys
MX = 10**5
def main():
    data = map(int, sys.stdin.buffer.read().split())
    N = next(data)
    IV, IW = [], []

    H = min(N + 1, 1 << 10)
    Hb = (H - 1).bit_length()
    dp = [[0] * (MX + 1) for _ in range(H)]
    i = 1
    for v, w in zip(data, data):
        IV.append(v)
        IW.append(w)
        if i < H:
            dpi = dp[i]
            dpip = dp[i >> 1]
            for j in range(w):
                dpi[j] = dpip[j]
            for j in range(w, MX + 1):
                dpi[j] = max(dpip[j], dpip[j - w] + v)
        i += 1
        if i > N:
            break

    Q = next(data)
    for v, L in zip(data, data):
        if v < H:
            print(dp[v][L])
            continue
        ans = []
        for i in range(1 << (v.bit_length() - Hb)):
            node = v
            value = weight = 0
            while node >= H:
                if i & 1:
                    value += IV[node - 1]
                    weight += IW[node - 1]
                    if weight > L:
                        break
                node >>= 1
                i >>= 1
            else:
                ans.append(value + dp[node][L - weight])
        print(max(ans))

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor, cos, radians, pi, sin
from operator import mul
from functools import reduce
from operator import mul
from decimal import Decimal


INF = 10 ** 13
sys.setrecursionlimit(2147483647)
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def I(): return int(sys.stdin.buffer.readline())
def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()
def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]


def merge(a, b):
    res = []
    i, j = 0, 0
    while i < len(a) or j < len(b):
        if j >= len(b) or (i < len(a) and a[i][0] < b[j][0]):
            w, v = a[i]
            i += 1
        else:
            w, v = b[j]
            j += 1
        if not res or res[-1][1] < v:
            res.append((w, v))
        elif res[-1][0] == w and res[-1][1] < v:
            res[-1] = (w, v)
    return res


def best(L, a, b):
    res = 0
    i = 0
    j = len(b) - 1
    while i < len(a):
        w, v = a[i]
        if j < 0:
            break
        if b[j][0] + w > L:
            j -= 1
            continue
        res = max(res, v + b[j][1])
        i += 1
    return res


def main():
    N = int(input())
    VW = [(-1, -1)] + [list(map(int, input().split())) for _ in range(N)]
    Q = int(input())
    query = tuple(tuple(map(int, input().split())) for _ in range(Q))

    dp = [[] for _ in range(1024)]
    dp[0] = [(0, 0)]
    for i in range(1, min(N + 1, 1024)):
        vi, wi = VW[i]
        a1 = dp[i // 2]
        a2 = [(w + wi, v + vi) for w, v in a1]
        dp[i] = merge(a1, a2)

    for n, L in query:
        a = [(0, 0)]
        while n >= 1024:
            vi, wi = VW[n]
            b = [(w + wi, v + vi) for w, v in a]
            a = merge(a, b)
            n //= 2
        print(best(L, a, dp[n]))


if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
import sys
readline = sys.stdin.buffer.readline
read = sys.stdin.buffer.read

import numpy as np
from itertools import product

MASK = np.array([pat for pat in product(range(2), repeat=9)])
MASK *= np.arange(9, 0, -1)

INF = pow(10, 12)

n = int(readline())
Z = np.array(read().split(), np.int64)
V = np.zeros(n + 1, np.int64)
W = np.zeros(n + 1, np.int64)
V[1:] = Z[0:2*n:2]
W[1:] = Z[1:2*n:2]
U = Z[2*n+1::2]
L = Z[2*n+2::2]

HALF = pow(2, 9)
MAX = pow(10, 5)

N = min(n, HALF)

dp = np.zeros((N + 1, MAX + 1), np.int64)

for i, (v, w) in enumerate(zip(V[1:N+1], W[1:N+1]), 1):
    i_prev = i // 2
    dp[i] = dp[i_prev]
    dp[i, w:] = np.maximum(dp[i, w:], dp[i_prev, :-w] + v)

for i in range(N):
    dp[i] = np.maximum.accumulate(dp[i])

for u, l in zip(U, L):
    now = u
    li = [0]
    while now >= HALF:
        li.append(now)
        now //= 2
    li = np.array(li)

    size = li.size - 1
    MINI_MASK = MASK[:1 << size, -size:]
    IDX = li[MINI_MASK]
    W_SUM = W[IDX].sum(axis=1)
    V_SUM = V[IDX].sum(axis=1)

    V_SUM[W_SUM>l] = -INF
    W_SUM[W_SUM>l] = 0

    VV = dp[now][l-W_SUM] + V_SUM
    ans = VV.max()
    print(ans)

Submission status: Time Limit Exceeded

Solution code:
import sys
MX = 10**5
def main():
    data = map(int, sys.stdin.buffer.read().split())
    N = next(data)
    items = [(next(data), next(data)) for _ in range(N)]
    Q = next(data)

    H = min(N + 1, 1 << 10)
    Hb = (H - 1).bit_length()
    dp = [[0] * (MX + 1) for _ in range(H)]
    for i in range(1, H):
        v, w = items[i - 1]
        dpi = dp[i]
        dpip = dp[i >> 1]
        for j in range(w):
            dpi[j] = dpip[j]
        for j in range(w, MX + 1):
            dpi[j] = max(dpip[j], dpip[j - w] + v)

    for v, L in zip(data, data):
        if v < H:
            print(dp[v][L])
            continue
        ans = []
        for i in range(1 << (v.bit_length() - Hb)):
            node = v
            value = weight = 0
            while node >= H:
                if i & 1:
                    iv, iw = items[node - 1]
                    value += iv
                    weight += iw
                node >>= 1
                i >>= 1
            if weight > L:
                continue
            ans.append(value + dp[node][L - weight])
        print(max(ans))

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor, cos, radians, pi, sin
from operator import mul
from functools import reduce
from operator import mul
from decimal import Decimal


INF = 10 ** 13
sys.setrecursionlimit(2147483647)
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def I(): return int(sys.stdin.buffer.readline())
def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()
def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]


def merge(a, b):
    res = []
    i, j = 0, 0
    while i < len(a) or j < len(b):
        if j >= len(b) or (i < len(a) and a[i][0] < b[j][0]):
            w, v = a[i]
            i += 1
        else:
            w, v = b[j]
            j += 1
        if not res or res[-1][1] < v:
            res.append((w, v))
        elif res[-1][0] == w and res[-1][1] < v:
            res[-1] = (w, v)
    return res


def best(L, a, b):
    res = 0
    i = 0
    j = len(b) - 1
    while i < len(a):
        w, v = a[i]
        if j < 0:
            break
        if b[j][0] + w > L:
            j -= 1
            continue
        res = max(res, v + b[j][1])
        i += 1
    return res


def main():
    N = int(input())
    VW = [(-1, -1)] + [list(map(int, input().split())) for _ in range(N)]
    Q = int(input())
    query = tuple(tuple(map(int, input().split())) for _ in range(Q))

    dp = [[] for _ in range(2048)]
    dp[0] = [(0, 0)]
    for i in range(1, min(N + 1, 2048)):
        vi, wi = VW[i]
        a1 = dp[i // 2]
        a2 = [(w + wi, v + vi) for w, v in a1]
        dp[i] = merge(a1, a2)

    for n, L in query:
        a = [(0, 0)]
        while n >= 2048:
            vi, wi = VW[n]
            b = [(w + wi, v + vi) for w, v in a]
            a = merge(a, b)
            n //= 2
        print(best(L, a, dp[n]))


if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
import sys
MX = 10**5
def main():
    data = map(int, sys.stdin.buffer.read().split())
    N = next(data)
    items = [(next(data), next(data)) for _ in range(N)]
    Q = next(data)

    H = min(N + 1, 1 << 10)
    Hb = (H - 1).bit_length()
    dp = [[0] * (MX + 1) for _ in range(H)]
    for i in range(1, H):
        v, w = items[i - 1]
        dpi = dp[i]
        dpip = dp[i >> 1]
        for j in range(w):
            dpi[j] = dpip[j]
        for j in range(w, MX + 1):
            dpi[j] = max(dpip[j], dpip[j - w] + v)

    for v, L in zip(data, data):
        if v < H:
            print(dp[v][L])
            continue
        ans = []
        for i in range(1 << (v.bit_length() - Hb)):
            node = v
            value = weight = 0
            while node >= H:
                if i & 1:
                    iv, iw = items[node - 1]
                    value += iv
                    weight += iw
                    if weight > L:
                        break
                node >>= 1
                i >>= 1
            else:
                ans.append(value + dp[node][L - weight])
        print(max(ans))

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor, cos, radians, pi, sin
from operator import mul
from functools import reduce
from operator import mul
from decimal import Decimal


INF = 10 ** 13
sys.setrecursionlimit(2147483647)
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def I(): return int(sys.stdin.buffer.readline())
def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()
def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]


def merge(a, b):
    res = []
    i, j = 0, 0
    while i < len(a) or j < len(b):
        if j >= len(b) or (i < len(a) and a[i][0] < b[j][0]):
            w, v = a[i]
            i += 1
        else:
            w, v = b[j]
            j += 1
        if not res or res[-1][1] < v:
            res.append((w, v))
        elif res[-1][0] == w and res[-1][1] <= v:
            res.pop()
            res.append((w, v))
    return res


def best(L, a, b):
    res = 0
    i = 0
    j = len(b) - 1
    while i < len(a):
        w, v = a[i]
        if j < 0:
            break
        if b[j][0] + w > L:
            j -= 1
            continue
        res = max(res, v + b[j][1])
        i += 1
    return res


def main():
    N = int(input())
    VW = [(-1, -1)] + [list(map(int, input().split())) for _ in range(N)]
    Q = int(input())
    query = tuple(tuple(map(int, input().split())) for _ in range(Q))

    dp = [[] for _ in range(2048)]
    dp[0] = [(0, 0)]
    for i in range(1, min(N + 1, 2048)):
        vi, wi = VW[i]
        a1 = dp[i // 2]
        a2 = [(w + wi, v + vi) for w, v in a1]
        dp[i] = merge(a1, a2)

    for n, L in query:
        a = [(0, 0)]
        while n >= 2048:
            vi, wi = VW[n]
            b = [(w + wi, v + vi) for w, v in a]
            a = merge(a, b)
            n //= 2
        print(best(L, a, dp[n]))


if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor, cos, radians, pi, sin
from operator import mul
from functools import reduce
from operator import mul
from decimal import Decimal


INF = 10 ** 13
sys.setrecursionlimit(2147483647)
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def I(): return int(sys.stdin.buffer.readline())
def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()
def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]


def merge(a, b):
    res = []
    i, j = 0, 0
    while i < len(a) or j < len(b):
        if j >= len(b) or (i < len(a) and a[i][0] < b[j][0]):
            w, v = a[i]
            i += 1
        else:
            w, v = b[j]
            j += 1
        if not res or res[-1][1] < v:
            res.append((w, v))
        elif res[-1][0] == w and res[-1][1] < v:
            res.pop()
            res.append((w, v))
    return res


def best(L, a, b):
    res = 0
    i = 0
    j = len(b) - 1
    while i < len(a):
        w, v = a[i]
        if j < 0:
            break
        if b[j][0] + w > L:
            j -= 1
            continue
        res = max(res, v + b[j][1])
        i += 1
    return res


def main():
    N = int(input())
    VW = [(-1, -1)] + [list(map(int, input().split())) for _ in range(N)]
    Q = int(input())
    query = tuple(tuple(map(int, input().split())) for _ in range(Q))

    dp = [[] for _ in range(2048)]
    dp[0] = [(0, 0)]
    for i in range(1, min(N + 1, 2048)):
        vi, wi = VW[i]
        a1 = dp[i // 2]
        a2 = [(w + wi, v + vi) for w, v in a1]
        dp[i] = merge(a1, a2)

    for n, L in query:
        a = [(0, 0)]
        while n >= 2048:
            vi, wi = VW[n]
            b = [(w + wi, v + vi) for w, v in a]
            a = merge(a, b)
            n //= 2
        print(best(L, a, dp[n]))


if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
import sys
MX = 10**5
def main():
    data = map(int, sys.stdin.buffer.read().split())
    N = next(data)
    items = [(next(data), next(data)) for _ in range(N)]
    Q = next(data)

    H = min(N + 1, 1 << 9)
    Hb = (H - 1).bit_length()
    dp = [[0] * (MX + 1) for _ in range(H)]
    for i in range(1, H):
        v, w = items[i - 1]
        dpi = dp[i]
        dpip = dp[i >> 1]
        for j in range(w):
            dpi[j] = dpip[j]
        for j in range(w, MX + 1):
            dpi[j] = max(dpip[j], dpip[j - w] + v)

    for v, L in zip(data, data):
        if v < H:
            print(dp[v][L])
            continue
        ans = []
        for i in range(1 << (v.bit_length() - Hb)):
            node = v
            value = weight = 0
            while node >= H:
                if i & 1:
                    iv, iw = items[node - 1]
                    value += iv
                    weight += iw
                    if weight > L:
                        break
                node >>= 1
                i >>= 1
            else:
                ans.append(value + dp[node][L - weight])
        print(max(ans))

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
import sys
MX = 10**5
def main():
    input = sys.stdin.readline
    N = int(input())
    items = [tuple(map(int, input().split())) for _ in range(N)]
    Q = int(input())
    vL = [tuple(map(int, input().split())) for _ in range(Q)]

    H = min(N + 1, 1 << 9)
    Hb = (H - 1).bit_length()
    dp = [[0] * (MX + 1) for _ in range(H)]
    for i in range(1, H):
        v, w = items[i - 1]
        dpi = dp[i]
        dpip = dp[i >> 1]
        for j in range(w):
            dpi[j] = dpip[j]
        for j in range(w, MX + 1):
            dpi[j] = max(dpip[j], dpip[j - w] + v)
    for v, L in vL:
        if v < H:
            print(dp[v][L])
            continue
        ans = 0
        for i in range(1 << (v.bit_length() - Hb)):
            node = v
            value = weight = 0
            while node >= H:
                if i & 1:
                    iv, iw = items[node - 1]
                    value += iv
                    weight += iw
                    if weight > L:
                        break
                node >>= 1
                i >>= 1
            else:
                ans = max(ans, value + dp[node][L - weight])
        print(ans)

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
import sys
MX = 10**5
def main():
    data = map(int, sys.stdin.buffer.read().split())
    N = next(data)
    items = [(next(data), next(data)) for _ in range(N)]
    Q = next(data)

    H = min(N + 1, 1 << 9)
    Hb = (H - 1).bit_length()
    dp = [[0] * (MX + 1) for _ in range(H)]
    for i in range(1, H):
        v, w = items[i - 1]
        dpi = dp[i]
        dpip = dp[i >> 1]
        for j in range(w):
            dpi[j] = dpip[j]
        for j in range(w, MX + 1):
            dpi[j] = max(dpip[j], dpip[j - w] + v)
    for v, L in zip(data, data):
        if v < H:
            print(dp[v][L])
            continue
        ans = 0
        for i in range(1 << (v.bit_length() - Hb)):
            node = v
            value = weight = 0
            while node >= H:
                if i & 1:
                    iv, iw = items[node - 1]
                    value += iv
                    weight += iw
                    if weight > L:
                        break
                node >>= 1
                i >>= 1
            else:
                ans = max(ans, value + dp[node][L - weight])
        print(ans)

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
import sys
import math
from collections import deque

sys.setrecursionlimit(1000000)
MOD = 10 ** 9 + 7
input = lambda: sys.stdin.readline().strip()
NI = lambda: int(input())
NMI = lambda: map(int, input().split())
NLI = lambda: list(NMI())
SI = lambda: input()


def make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]


def main():
    N = NI()
    tree = [[0,0]] + [NLI() for _ in range(N)]
    Q = NI()
    querys = [NLI() for _ in range(Q)]

    def indexes(node):
        res = []
        for _ in range(20):
            res.append(node)
            node = node // 2
            if node == 0:
                break
        return res

    for node, limit in querys:
        idxes = indexes(node)
        items = [tree[idx] for idx in idxes]
        dp = make_grid(len(items)+1, limit+1, 0)
        for i, item in enumerate(items):
            i += 1
            for w in range(limit+1):
                if w >= item[1]:
                    dp[i][w] = max(dp[i-1][w], dp[i-1][w-item[1]] + item[0])
                else:
                    dp[i][w] = dp[i-1][w]
        print(dp[len(items)][limit])


if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
import sys
MX = 10**5
def main():
    data = map(int, sys.stdin.buffer.read().split())
    N = next(data)
    items = [(next(data), next(data)) for _ in range(N)]
    Q = next(data)

    H = min(N + 1, 1 << 9)
    Hb = (H - 1).bit_length()
    dp = [None for _ in range(H)]
    dp[0] = [0] * (MX + 1)
    for i in range(1, H):
        v, w = items[i - 1]
        dpip = dp[i >> 1]
        dpi = dpip[:]
        dp[i] = dpi
        for j in range(w, MX + 1):
            dpi[j] = max(dpi[j], dpip[j - w] + v)
    for v, L in zip(data, data):
        if v < H:
            print(dp[v][L])
            continue
        ans = 0
        for i in range(1 << (v.bit_length() - Hb)):
            node = v
            value = weight = 0
            while node >= H:
                if i & 1:
                    iv, iw = items[node - 1]
                    value += iv
                    weight += iw
                node >>= 1
                i >>= 1
            if weight > L:
                continue
            ans = max(ans, value + dp[node][L - weight])
        print(ans)

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
def main():
    import sys
    input = sys.stdin.readline

    N = int(input())
    half = min(2 ** 11, N)

    VW = [tuple(map(int, input().split())) for _ in range(N)]

    MAX_W = 10 ** 5 + 1

    dp = [[0] * (MAX_W) for _ in range(half + 1)]

    for i in range(1, half + 1):
        V, W = VW[i - 1][0], VW[i - 1][1]
        for j in range(W):
            dp[i][j] = dp[i // 2][j]
        for j in range(W, MAX_W):
            dp[i][j] = max(dp[i // 2][j], dp[i // 2][j - W] + V)


    def calc(n, L):
        ans = 0
        lst = []
        lst_append = lst.append
        while n > half:
            lst_append(n)
            n //= 2
        # print (lst)
        length = len(lst)
        for i in range(2 ** length):
            v = 0
            w = 0
            for j in range(length):
                if ((i >> j) & 1):
                    v += VW[lst[j] - 1][0]
                    w += VW[lst[j] - 1][1]
            if L >= w:
                ans = max(ans, dp[n][L - w] + v) 
        return ans

    Q = int(input())
    for _ in range(Q):
        v, L = map(int, input().split())
        if v > half:
            print (calc(v, L))
        else: #こっち側はOK(当然)
            print (dp[v][L])

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
import sys
MX = 10**5
def main():
    data = map(int, sys.stdin.buffer.read().split())
    N = next(data)
    items = [(next(data), next(data)) for _ in range(N)]
    Q = next(data)

    H = min(N + 1, 1 << 10)
    Hb = (H - 1).bit_length()
    dp = [[0] * (MX + 1) for _ in range(H)]
    for i in range(1, H):
        v, w = items[i - 1]
        dpi = dp[i]
        dpip = dp[i >> 1]
        for j in range(MX + 1):
            t = dpip[j]
            if j >= w:
                t = max(t, dpip[j - w] + v)
            dpi[j] = t
    for v, L in zip(data, data):
        if v < H:
            print(dp[v][L])
            continue
        ans = 0
        for i in range(1 << (v.bit_length() - Hb)):
            node = v
            value = weight = 0
            while node >= H:
                if i & 1:
                    iv, iw = items[node - 1]
                    value += iv
                    weight += iw
                node >>= 1
                i >>= 1
            if weight > L:
                continue
            ans = max(ans, value + dp[node][L - weight])
        print(ans)

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
import sys
MX = 10**5
def main():
    data = map(int, sys.stdin.buffer.read().split())
    N = next(data)
    items = [(next(data), next(data)) for _ in range(N)]
    Q = next(data)

    H = min(N + 1, 1 << 9)
    Hb = (H - 1).bit_length()
    dp = [[0] * (MX + 1) for _ in range(H)]
    for i in range(1, H):
        v, w = items[i - 1]
        dpi = dp[i]
        dpip = dp[i >> 1]
        for j in range(MX + 1):
            t = dpip[j]
            if j >= w:
                t = max(t, dpip[j - w] + v)
            dpi[j] = t
    for v, L in zip(data, data):
        if v < H:
            print(dp[v][L])
            continue
        ans = 0
        for i in range(1 << (v.bit_length() - Hb)):
            node = v
            value = weight = 0
            while node >= H:
                if i & 1:
                    iv, iw = items[node - 1]
                    value += iv
                    weight += iw
                node >>= 1
                i >>= 1
            if weight > L:
                continue
            ans = max(ans, value + dp[node][L - weight])
        print(ans)

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
n = int(input())
vw = [tuple(map(int, input().split())) for _ in range(n)]
q = int(input())
ul = [map(int, input().split()) for _ in range(q)]

HALF = pow(2, 9)
MAX = pow(10, 5)

N = min(n, HALF)

dp = [[0] * (MAX + 1) for _ in range(N + 1)]

for i, (v, w) in enumerate(vw[:N], 1):
    i_prev = i // 2
    for j in range(1, MAX + 1):
        dp[i][j] = dp[i_prev][j]
        if j - w >= 0:
            dp[i][j] = max(dp[i][j], dp[i_prev][j-w] + v)

for i in range(N):
    for j in range(MAX):
        dp[i][j+1] = max(dp[i][j+1], dp[i][j])

for u, l in ul:
    now = u
    li = []
    while now >= HALF:
        li.append(now)
        now //= 2

    ans = dp[now][l]
    for i in range(1 << len(li)):
        bn = i
        v_sm = 0
        w_sm = 0
        for e in li:
            if bn & 1:
                v, w = vw[e-1]
                v_sm += v
                w_sm += w
            bn >>= 1

            if w_sm <= l:
                ans = max(ans, dp[now][l-w_sm] + v_sm)

    print(ans)