Problem:


Score : 1200 points

Problem Statement

Snuke is playing with red and blue balls, placing them on a two-dimensional plane.

First, he performed N operations to place red balls. In the i-th of these operations, he placed RC_i red balls at coordinates (RX_i,RY_i).
Then, he performed another N operations to place blue balls. In the i-th of these operations, he placed BC_i blue balls at coordinates (BX_i,BY_i).
The total number of red balls placed and the total number of blue balls placed are equal, that is, \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i. Let this value be S.

Snuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair.
Let us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by|.

Snuke wants to maximize the sum of the scores of the pairs.
Help him by finding the maximum possible sum of the scores of the pairs.

Constraints

1 \leq N \leq 1000

0 \leq RX_i,RY_i,BX_i,BY_i \leq 10^9

1 \leq RC_i,BC_i \leq 10

\sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
RX_1 RY_1 RC_1
RX_2 RY_2 RC_2
\vdots
RX_N RY_N RC_N
BX_1 BY_1 BC_1
BX_2 BY_2 BC_2
\vdots
BX_N BY_N BC_N

Output

Print the maximum possible sum of the scores of the pairs.

Sample Input 1

2
0 0 1
3 2 1
2 2 1
5 0 1

Sample Output 1

8

If we pair the red ball at coordinates (0,0) and the blue ball at coordinates (2,2), the score of this pair is |0-2| + |0-2|=4.
Then, if we pair the red ball at coordinates (3,2) and the blue ball at coordinates (5,0), the score of this pair is |3-5| + |2-0|=4.
Making these two pairs results in the total score of 8, which is the maximum result.

Sample Input 2

3
0 0 1
2 2 1
0 0 2
1 1 1
1 1 1
3 3 2

Sample Output 2

16

Snuke may have performed multiple operations at the same coordinates.

Sample Input 3

10
582463373 690528069 8
621230322 318051944 4
356524296 974059503 6
372751381 111542460 9
392867214 581476334 6
606955458 513028121 5
882201596 791660614 9
250465517 91918758 3
618624774 406956634 6
426294747 736401096 5
974896051 888765942 5
726682138 336960821 3
715144179 82444709 6
599055841 501257806 6
390484433 962747856 4
912334580 219343832 8
570458984 648862300 6
638017635 572157978 10
435958984 585073520 7
445612658 234265014 6

Sample Output 3

45152033546



Sample input:
2
0 0 1
3 2 1
2 2 1
5 0 1


Sample output:
8

Submission status: Wrong Answer

Solution code:
import sys
from heapq import heappop, heappush


def min_cost_flow(links, s, t, flow, n2, INF, REV):
    remain = flow
    ans = 0
    REV2 = REV * 2
    potentials = [0] * n2  # to adjust negative edge for dijkstra
    predecessors_v = [0] * n2
    predecessors_i = [0] * n2

    while remain:
        distances = [INF] * n2
        distances[s] = 0
        q = [(0, s)]  # (cost, v, (p, v_idx_in_p))
        while q:
            cost, v = heappop(q)
            if cost > distances[v]:
                continue

            if v == t:
                break

            for i, (u, cap, uc, j) in enumerate(links[v]):
                if cap == 0:
                    continue
                new_cost = cost + uc + potentials[v] - potentials[u]
                if distances[u] <= new_cost:
                    continue
                distances[u] = new_cost
                predecessors_v[u] = v
                predecessors_i[u] = i
                heappush(q, (new_cost, u))

        # if distances[t] == INF:
        #     return -1

        for i in range(n + 1, n2):
            potentials[i] += distances[i]
        print(predecessors_v)

        min_cap = remain
        v = t
        while v != s:
            p = predecessors_v[v]
            i = predecessors_i[v]
            l = links[p][i]
            min_cap = min(min_cap, l[1])
            v = p
        v = t
        while v != s:
            p = predecessors_v[v]
            i = predecessors_i[v]
            l = links[p][i]
            if v != t:
                links[v][l[3]][1] += min_cap
            l[1] -= min_cap
            v = p
        remain -= min_cap
        ans += min_cap * (REV2 - potentials[t])
    return ans


n = int(input())
lines = sys.stdin.readlines()
INF = 10 ** 18
REV = 10 ** 9
n2 = 2 * n + 6
t = 2 * n + 1
balls = 0
links = [[] for _ in range(n2)]  # [[tgt_node, capacity, unit_cost, idx_in_tgt], ]
for i in range(n):
    ri = i + 1
    rx, ry, rc = map(int, lines[i].split())
    balls += rc
    links[0].append([ri, rc, 0, len(links[ri])])
    ki = n2 - 4
    kc = REV - (rx + ry)
    links[ri].append([ki, INF, kc, len(links[ki])])
    links[ki].append([ri, 0, -kc, len(links[ri]) - 1])
    ki = n2 - 3
    kc = REV - (-rx + ry)
    links[ri].append([ki, INF, kc, len(links[ki])])
    links[ki].append([ri, 0, -kc, len(links[ri]) - 1])
    ki = n2 - 2
    kc = REV - (rx - ry)
    links[ri].append([ki, INF, kc, len(links[ki])])
    links[ki].append([ri, 0, -kc, len(links[ri]) - 1])
    ki = n2 - 1
    kc = REV - (-rx - ry)
    links[ri].append([ki, INF, kc, len(links[ki])])
    links[ki].append([ri, 0, -kc, len(links[ri]) - 1])

for i in range(n):
    bi = i + n + 1
    bx, by, bc = map(int, lines[i + n].split())
    links[bi].append([t, bc, 0, 0])
    ki = n2 - 4
    kc = REV - (-bx - by)
    links[ki].append([bi, INF, kc, len(links[bi])])
    links[bi].append([ki, 0, -kc, len(links[ki]) - 1])
    ki = n2 - 3
    kc = REV - (bx - by)
    links[ki].append([bi, INF, kc, len(links[bi])])
    links[bi].append([ki, 0, -kc, len(links[ki]) - 1])
    ki = n2 - 2
    kc = REV - (-bx + by)
    links[ki].append([bi, INF, kc, len(links[bi])])
    links[bi].append([ki, 0, -kc, len(links[ki]) - 1])
    ki = n2 - 1
    kc = REV - (bx + by)
    links[ki].append([bi, INF, kc, len(links[bi])])
    links[bi].append([ki, 0, -kc, len(links[ki]) - 1])

print(min_cost_flow(links, 0, t, balls, n2, INF, REV))

Submission status: Wrong Answer

Solution code:
import sys
from heapq import heappop, heappush


def min_cost_flow(links, s, t, flow, n2, INF, REV, potentials, predecessors_v, predecessors_i):
    remain = flow
    ans = 0
    REV2 = REV * 2

    while remain:
        distances = [INF] * n2
        distances[s] = 0
        q = [(0, s)]  # (cost, v, (p, v_idx_in_p))
        while q:
            cost, v = heappop(q)
            if cost > distances[v]:
                continue

            if v == t:
                break

            for i, (u, cap, uc, j) in enumerate(links[v]):
                if cap == 0:
                    continue
                new_cost = cost + uc + potentials[v] - potentials[u]
                if distances[u] <= new_cost:
                    continue
                distances[u] = new_cost
                predecessors_v[u] = v
                predecessors_i[u] = i
                heappush(q, (new_cost, u))

        # if distances[t] == INF:
        #     return -1

        for i in range(n + 1, n2):
            potentials[i] += distances[i]

        min_cap = remain
        v = t
        forward_links = []
        backward_links = []
        while v != s:
            p = predecessors_v[v]
            i = predecessors_i[v]
            l = links[p][i]
            forward_links.append(l)
            if v != t:
                backward_links.append(links[v][l[3]])
            min_cap = min(min_cap, l[1])
            v = p
        for l in forward_links:
            l[1] -= min_cap
        for l in backward_links:
            l[1] += min_cap
        remain -= min_cap
        ans += min_cap * (REV2 - potentials[t])
    return ans


n = int(input())
lines = sys.stdin.readlines()
INF = 10 ** 18
REV = 10 ** 9
n2 = 2 * n + 6
t = 2 * n + 1
red_balls = []
links = [[] for _ in range(n2)]  # [[tgt_node, capacity, unit_cost, idx_in_tgt], ]
for i in range(n):
    ri = i + 1
    rx, ry, rc = map(int, lines[i].split())
    red_balls.append(rc)
    ki = n2 - 4
    kc = REV - (rx + ry)
    links[ri].append([ki, INF, kc, len(links[ki])])
    links[ki].append([ri, 0, -kc, len(links[ri]) - 1])
    ki = n2 - 3
    kc = REV - (-rx + ry)
    links[ri].append([ki, INF, kc, len(links[ki])])
    links[ki].append([ri, 0, -kc, len(links[ri]) - 1])
    ki = n2 - 2
    kc = REV - (rx - ry)
    links[ri].append([ki, INF, kc, len(links[ki])])
    links[ki].append([ri, 0, -kc, len(links[ri]) - 1])
    ki = n2 - 1
    kc = REV - (-rx - ry)
    links[ri].append([ki, INF, kc, len(links[ki])])
    links[ki].append([ri, 0, -kc, len(links[ri]) - 1])

for i in range(n):
    bi = i + n + 1
    bx, by, bc = map(int, lines[i + n].split())
    links[bi].append([t, bc, 0, 0])
    ki = n2 - 4
    kc = REV - (-bx - by)
    links[ki].append([bi, INF, kc, len(links[bi])])
    links[bi].append([ki, 0, -kc, len(links[ki]) - 1])
    ki = n2 - 3
    kc = REV - (bx - by)
    links[ki].append([bi, INF, kc, len(links[bi])])
    links[bi].append([ki, 0, -kc, len(links[ki]) - 1])
    ki = n2 - 2
    kc = REV - (-bx + by)
    links[ki].append([bi, INF, kc, len(links[bi])])
    links[bi].append([ki, 0, -kc, len(links[ki]) - 1])
    ki = n2 - 1
    kc = REV - (bx + by)
    links[ki].append([bi, INF, kc, len(links[bi])])
    links[bi].append([ki, 0, -kc, len(links[ki]) - 1])

potentials = [0] * n2  # to adjust negative edge for dijkstra
predecessors_v = [0] * n2
predecessors_i = [0] * n2

ans = 0
for i, flow in enumerate(red_balls, start=1):
    ans += min_cost_flow(links, i, t, flow, n2, INF, REV, potentials, predecessors_v, predecessors_i)
print(ans)

Submission status: Wrong Answer

Solution code:
print("wakaranai")

Submission status: Time Limit Exceeded

Solution code:
from networkx import*
N = int(input())
G = MultiDiGraph()
k = 0
for i in range(N):
    x, y, c = map(int, input().split())
    for _ in range(c):
        G.add_node(k, demand = -1)
        G.add_weighted_edges_from([(k, -1, x + y)], capacity = 1)
        G.add_weighted_edges_from([(k, -2, x - y)], capacity = 1)
        G.add_weighted_edges_from([(k, -3, -x + y)], capacity = 1)
        G.add_weighted_edges_from([(k, -4, -x - y)], capacity = 1)
        k += 1

for i in range(N):
    x, y, c = map(int, input().split())
    for _ in range(c):
        G.add_node(k, demand = 1)
        G.add_weighted_edges_from([(-1, k, -x - y)], capacity = 1)
        G.add_weighted_edges_from([(-2, k, -x + y)], capacity = 1)
        G.add_weighted_edges_from([(-3, k, x - y)], capacity = 1)
        G.add_weighted_edges_from([(-4, k, x + y)], capacity = 1)
        k += 1

print(-min_cost_flow_cost(G))

Submission status: Time Limit Exceeded

Solution code:
from heapq import heappush, heappop
def min_cost_flow_dijkstra(E, s, t, f):
    NN = 2 * N + 6
    LN = NN.bit_length()
    G = [[] for _ in range(NN)]
    for a, b, cap, c in E:
        G[a].append([b, cap, c, len(G[b])])
        G[b].append([a, 0, -c, len(G[a])-1])
    prevv = [-1] * NN
    preve = [-1] * NN
    res = 0
    h = [0] * NN
    while f > 0:
        dist = [-1] * NN
        dist[s] = 0
        Q = []
        heappush(Q, s)
        while len(Q):
            x = heappop(Q)
            d, v = (x>>LN), x % (1<<LN)
            if 0 <= dist[v] < d: continue
            for i, (w, _cap, c, r) in enumerate(G[v]):
                if _cap > 0 and (dist[w] < 0 or dist[w] > dist[v] + c + h[v] - h[w]):
                    dist[w] = dist[v] + c + h[v] - h[w]
                    prevv[w] = v
                    preve[w] = i
                    heappush(Q, (dist[w] << LN) + w)
        if dist[t] == -1:
            return -1
        
        for v in range(N):
            h[v] += dist[v]
        
        d = f
        v = t
        while v != s:
            d = min(d, G[prevv[v]][preve[v]][1])
            v = prevv[v]
        f -= d
        res += d * dist[t]
        v = t
        while v != s:
            G[prevv[v]][preve[v]][1] -= d
            G[v][G[prevv[v]][preve[v]][3]][1] += d
            v = prevv[v]
    return res

E = []
N = int(input())
su = 0
inf = 1 << 31
for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((2*N+4, i, cnt, 0))
    E.append((i, 2*N, cnt, x + y + inf))
    E.append((i, 2*N+1, cnt, x - y + inf))
    E.append((i, 2*N+2, cnt, - x + y + inf))
    E.append((i, 2*N+3, cnt, - x - y + inf))
    su += cnt

for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((i+N, 2*N+5, cnt, 0))
    E.append((2*N, i+N, cnt, - x - y + inf))
    E.append((2*N+1, i+N, cnt, - x + y + inf))
    E.append((2*N+2, i+N, cnt, x - y + inf))
    E.append((2*N+3, i+N, cnt, x + y + inf))

print(su * inf * 2 - min_cost_flow_dijkstra(E, 2*N+4, 2*N+5, su))

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline
from heapq import heappush, heappop
def min_cost_flow_dijkstra(E, s, t, f):
    INF = 1 << 100
    NN = 2 * N + 6
    LN = NN.bit_length()
    G = [[] for _ in range(NN)]
    for a, b, cap, c in E:
        G[a].append([b, cap, c, len(G[b])])
        G[b].append([a, 0, -c, len(G[a])-1])
    prevv = [-1] * NN
    preve = [-1] * NN
    res = 0
    h = [0] * NN
    while f > 0:
        dist = [INF] * NN
        dist[s] = 0
        Q = []
        heappush(Q, s)
        while len(Q):
            x = heappop(Q)
            d, v = (x>>LN), x % (1<<LN)
            if dist[v] < d: continue
            for i, (w, _cap, c, r) in enumerate(G[v]):
                if _cap > 0 and dist[w] > dist[v] + c + h[v] - h[w]:
                    dist[w] = dist[v] + c + h[v] - h[w]
                    prevv[w] = v
                    preve[w] = i
                    heappush(Q, (dist[w] << LN) + w)
        if dist[t] == INF:
            return -1
        
        for v in range(N):
            h[v] += dist[v]
        
        d = f
        v = t
        while v != s:
            d = min(d, G[prevv[v]][preve[v]][1])
            v = prevv[v]
        f -= d
        res += d * dist[t]
        v = t
        while v != s:
            G[prevv[v]][preve[v]][1] -= d
            G[v][G[prevv[v]][preve[v]][3]][1] += d
            v = prevv[v]
    return res

E = []
N = int(input())
su = 0
inf = 1 << 31
for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((2*N+4, i, cnt, 0))
    E.append((i, 2*N, cnt, x + y + inf))
    E.append((i, 2*N+1, cnt, x - y + inf))
    E.append((i, 2*N+2, cnt, - x + y + inf))
    E.append((i, 2*N+3, cnt, - x - y + inf))
    su += cnt

for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((i+N, 2*N+5, cnt, 0))
    E.append((2*N, i+N, cnt, - x - y + inf))
    E.append((2*N+1, i+N, cnt, - x + y + inf))
    E.append((2*N+2, i+N, cnt, x - y + inf))
    E.append((2*N+3, i+N, cnt, x + y + inf))

print(su * inf * 2 - min_cost_flow_dijkstra(E, 2*N+4, 2*N+5, su))

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline
from heapq import heappush, heappop
def min_cost_flow_dijkstra(E, s, t, f):
    INF = 1 << 100
    NN = 2 * N + 6
    LN = NN.bit_length()
    G = [[] for _ in range(NN)]
    for a, b, cap, c in E:
        G[a].append([b, cap, c, len(G[b])])
        G[b].append([a, 0, -c, len(G[a])-1])
    prevv = [-1] * NN
    preve = [-1] * NN
    res = 0
    h = [0] * NN
    while f > 0:
        dist = [INF] * NN
        dist[s] = 0
        Q = []
        heappush(Q, s)
        while len(Q):
            x = heappop(Q)
            d, v = (x>>LN), x % (1<<LN)
            if dist[v] < d: continue
            for i, (w, _cap, c, r) in enumerate(G[v]):
                if _cap > 0 and dist[w] > dist[v] + c + h[v] - h[w]:
                    dist[w] = dist[v] + c + h[v] - h[w]
                    prevv[w] = v
                    preve[w] = i
                    heappush(Q, (dist[w] << LN) + w)
        if dist[t] == INF:
            return -1
        h = [0] * NN
        for v in range(N):
            h[v] += dist[v]
        
        d = f
        v = t
        while v != s:
            d = min(d, G[prevv[v]][preve[v]][1])
            v = prevv[v]
        f -= d
        res += d * dist[t]
        v = t
        while v != s:
            G[prevv[v]][preve[v]][1] -= d
            G[v][G[prevv[v]][preve[v]][3]][1] += d
            v = prevv[v]
    return res

E = []
N = int(input())
su = 0
inf = 1 << 31
for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((2*N+4, i, cnt, 0))
    E.append((i, 2*N, cnt, x + y + inf))
    E.append((i, 2*N+1, cnt, x - y + inf))
    E.append((i, 2*N+2, cnt, - x + y + inf))
    E.append((i, 2*N+3, cnt, - x - y + inf))
    su += cnt

for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((i+N, 2*N+5, cnt, 0))
    E.append((2*N, i+N, cnt, - x - y + inf))
    E.append((2*N+1, i+N, cnt, - x + y + inf))
    E.append((2*N+2, i+N, cnt, x - y + inf))
    E.append((2*N+3, i+N, cnt, x + y + inf))

print(su * inf * 2 - min_cost_flow_dijkstra(E, 2*N+4, 2*N+5, su))

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline
from heapq import heappush, heappop
def min_cost_flow_dijkstra(E, s, t, f):
    INF = 1 << 100
    NN = 2 * N + 6
    LN = NN.bit_length()
    G = [[] for _ in range(NN)]
    for a, b, cap, c in E:
        G[a].append([b, cap, c, len(G[b])])
        G[b].append([a, 0, -c, len(G[a])-1])
    prevv = [-1] * NN
    preve = [-1] * NN
    res = 0
    while f > 0:
        h = [0] * NN
        dist = [INF] * NN
        dist[s] = 0
        Q = []
        heappush(Q, s)
        while len(Q):
            x = heappop(Q)
            d, v = (x>>LN), x % (1<<LN)
            if dist[v] < d: continue
            for i, (w, _cap, c, r) in enumerate(G[v]):
                if _cap > 0 and dist[w] > dist[v] + c + h[v] - h[w]:
                    dist[w] = dist[v] + c + h[v] - h[w]
                    prevv[w] = v
                    preve[w] = i
                    heappush(Q, (dist[w] << LN) + w)
        if dist[t] == INF:
            return -1
        for v in range(N):
            h[v] += dist[v]
        
        d = f
        v = t
        while v != s:
            d = min(d, G[prevv[v]][preve[v]][1])
            v = prevv[v]
        f -= d
        res += d * dist[t]
        v = t
        while v != s:
            G[prevv[v]][preve[v]][1] -= d
            G[v][G[prevv[v]][preve[v]][3]][1] += d
            v = prevv[v]
    return res

E = []
N = int(input())
su = 0
inf = 1 << 31
for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((2*N+4, i, cnt, 0))
    E.append((i, 2*N, cnt, x + y + inf))
    E.append((i, 2*N+1, cnt, x - y + inf))
    E.append((i, 2*N+2, cnt, - x + y + inf))
    E.append((i, 2*N+3, cnt, - x - y + inf))
    su += cnt

for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((i+N, 2*N+5, cnt, 0))
    E.append((2*N, i+N, cnt, - x - y + inf))
    E.append((2*N+1, i+N, cnt, - x + y + inf))
    E.append((2*N+2, i+N, cnt, x - y + inf))
    E.append((2*N+3, i+N, cnt, x + y + inf))

print(su * inf * 2 - min_cost_flow_dijkstra(E, 2*N+4, 2*N+5, su))

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline
from heapq import heappush, heappop
def min_cost_flow_dijkstra(E, s, t, f):
    INF = 1 << 100
    NN = 2 * N + 6
    LN = NN.bit_length()
    G = [[] for _ in range(NN)]
    for a, b, cap, c in E:
        G[a].append([b, cap, c, len(G[b])])
        G[b].append([a, 0, -c, len(G[a])-1])
    prevv = [-1] * NN
    preve = [-1] * NN
    res = 0
    while f > 0:
        h = [0] * NN
        dist = [INF] * NN
        dist[s] = 0
        Q = []
        heappush(Q, s)
        while len(Q):
            x = heappop(Q)
            d, v = -(x>>LN), x % (1<<LN)
            if dist[v] < d: continue
            for i, (w, _cap, c, r) in enumerate(G[v]):
                if _cap > 0 and dist[w] > dist[v] + c + h[v] - h[w]:
                    dist[w] = dist[v] + c + h[v] - h[w]
                    prevv[w] = v
                    preve[w] = i
                    heappush(Q, (-dist[w] << LN) + w)
        if dist[t] == INF:
            return -1
        for v in range(N):
            h[v] += dist[v]
        
        d = f
        v = t
        while v != s:
            d = min(d, G[prevv[v]][preve[v]][1])
            v = prevv[v]
        f -= d
        res += d * dist[t]
        v = t
        while v != s:
            G[prevv[v]][preve[v]][1] -= d
            G[v][G[prevv[v]][preve[v]][3]][1] += d
            v = prevv[v]
    return res

E = []
N = int(input())
su = 0
inf = 1 << 31
for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((2*N+4, i, cnt, 0))
    E.append((i, 2*N, cnt, x + y + inf))
    E.append((i, 2*N+1, cnt, x - y + inf))
    E.append((i, 2*N+2, cnt, - x + y + inf))
    E.append((i, 2*N+3, cnt, - x - y + inf))
    su += cnt

for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((i+N, 2*N+5, cnt, 0))
    E.append((2*N, i+N, cnt, - x - y + inf))
    E.append((2*N+1, i+N, cnt, - x + y + inf))
    E.append((2*N+2, i+N, cnt, x - y + inf))
    E.append((2*N+3, i+N, cnt, x + y + inf))

print(su * inf * 2 - min_cost_flow_dijkstra(E, 2*N+4, 2*N+5, su))

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline
from heapq import heappush, heappop
def min_cost_flow_dijkstra(E, s, t, f):
    INF = 1 << 100
    NN = 2 * N + 6
    LN = NN.bit_length()
    G = [[] for _ in range(NN)]
    for a, b, cap, c in E:
        G[a].append([b, cap, c, len(G[b])])
        G[b].append([a, 0, -c, len(G[a])-1])
    prevv = [-1] * NN
    preve = [-1] * NN
    res = 0
    h = [0] * NN
    while f > 0:
        dist = [INF] * NN
        dist[s] = 0
        Q = []
        heappush(Q, s)
        while len(Q):
            x = heappop(Q)
            d, v = -(x>>LN), x % (1<<LN)
            if dist[v] < d: continue
            for i, (w, _cap, c, r) in enumerate(G[v]):
                if _cap > 0 and dist[w] > dist[v] + c + h[v] - h[w]:
                    dist[w] = dist[v] + c + h[v] - h[w]
                    prevv[w] = v
                    preve[w] = i
                    heappush(Q, (-dist[w] << LN) + w)
        if dist[t] == INF:
            return -1
        for v in range(N):
            h[v] += dist[v]
        
        d = f
        v = t
        while v != s:
            d = min(d, G[prevv[v]][preve[v]][1])
            v = prevv[v]
        f -= d
        res += d * dist[t]
        v = t
        while v != s:
            G[prevv[v]][preve[v]][1] -= d
            G[v][G[prevv[v]][preve[v]][3]][1] += d
            v = prevv[v]
    return res

E = []
N = int(input())
su = 0
inf = 1 << 31
for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((2*N+4, i, cnt, 0))
    E.append((i, 2*N, cnt, x + y + inf))
    E.append((i, 2*N+1, cnt, x - y + inf))
    E.append((i, 2*N+2, cnt, - x + y + inf))
    E.append((i, 2*N+3, cnt, - x - y + inf))
    su += cnt

for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((i+N, 2*N+5, cnt, 0))
    E.append((2*N, i+N, cnt, - x - y + inf))
    E.append((2*N+1, i+N, cnt, - x + y + inf))
    E.append((2*N+2, i+N, cnt, x - y + inf))
    E.append((2*N+3, i+N, cnt, x + y + inf))

print(su * inf * 2 - min_cost_flow_dijkstra(E, 2*N+4, 2*N+5, su))

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline
from heapq import heappush, heappop
def min_cost_flow_dijkstra(E, s, t, f):
    INF = 1 << 100
    NN = 2 * N + 6
    LN = NN.bit_length()
    G = [[] for _ in range(NN)]
    for a, b, cap, c in E:
        G[a].append([b, cap, c, len(G[b])])
        G[b].append([a, 0, -c, len(G[a])-1])
    prevv = [-1] * NN
    preve = [-1] * NN
    res = 0
    h = [0] * NN
    while f > 0:
        dist = [INF] * NN
        dist[s] = 0
        update = 1
        Q = []
        heappush(Q, s)
        while len(Q):
            x = heappop(Q)
            d, v = -(x>>LN), x % (1<<LN)
            if dist[v] < d: continue
            for i, (w, _cap, c, r) in enumerate(G[v]):
                if _cap > 0 and dist[w] > dist[v] + c + h[v] - h[w]:
                    dist[w] = dist[v] + c + h[v] - h[w]
                    prevv[w] = v
                    preve[w] = i
                    heappush(Q, (-dist[w] << LN) + w)
        if dist[t] == INF:
            return -1
        d = f
        v = t
        while v != s:
            d = min(d, G[prevv[v]][preve[v]][1])
            v = prevv[v]
        f -= d
        res += d * dist[t]
        v = t
        while v != s:
            G[prevv[v]][preve[v]][1] -= d
            G[v][G[prevv[v]][preve[v]][3]][1] += d
            v = prevv[v]
    return res

E = []
N = int(input())
su = 0
inf = 1 << 31
for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((2*N+4, i, cnt, 0))
    E.append((i, 2*N, cnt, x + y + inf))
    E.append((i, 2*N+1, cnt, x - y + inf))
    E.append((i, 2*N+2, cnt, - x + y + inf))
    E.append((i, 2*N+3, cnt, - x - y + inf))
    su += cnt

for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((i+N, 2*N+5, cnt, 0))
    E.append((2*N, i+N, cnt, - x - y + inf))
    E.append((2*N+1, i+N, cnt, - x + y + inf))
    E.append((2*N+2, i+N, cnt, x - y + inf))
    E.append((2*N+3, i+N, cnt, x + y + inf))

print(su * inf * 2 - min_cost_flow_dijkstra(E, 2*N+4, 2*N+5, su))

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline
from heapq import heappush, heappop
def min_cost_flow_dijkstra(E, s, t, f):
    INF = 1 << 100
    NN = 2 * N + 6
    LN = NN.bit_length()
    G = [[] for _ in range(NN)]
    for a, b, cap, c in E:
        G[a].append([b, cap, c, len(G[b])])
        G[b].append([a, 0, -c, len(G[a])-1])
    prevv = [-1] * NN
    preve = [-1] * NN
    res = 0
    h = [0] * NN
    Q = []
    while f > 0:
        dist = [INF] * NN
        dist[s] = 0
        update = 1
        heappush(Q, s)
        while len(Q):
            x = heappop(Q)
            d, v = -(x>>LN), x % (1<<LN)
            if dist[v] < d: continue
            for i, (w, _cap, c, r) in enumerate(G[v]):
                if _cap > 0 and dist[w] > dist[v] + c + h[v] - h[w]:
                    dist[w] = dist[v] + c + h[v] - h[w]
                    prevv[w] = v
                    preve[w] = i
                    heappush(Q, (-dist[w] << LN) + w)
        if dist[t] == INF:
            return -1
        d = f
        v = t
        while v != s:
            d = min(d, G[prevv[v]][preve[v]][1])
            v = prevv[v]
        f -= d
        res += d * dist[t]
        v = t
        while v != s:
            G[prevv[v]][preve[v]][1] -= d
            G[v][G[prevv[v]][preve[v]][3]][1] += d
            v = prevv[v]
    return res

E = []
N = int(input())
su = 0
inf = 1 << 31
for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((2*N+4, i, cnt, 0))
    E.append((i, 2*N, cnt, x + y + inf))
    E.append((i, 2*N+1, cnt, x - y + inf))
    E.append((i, 2*N+2, cnt, - x + y + inf))
    E.append((i, 2*N+3, cnt, - x - y + inf))
    su += cnt

for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((i+N, 2*N+5, cnt, 0))
    E.append((2*N, i+N, cnt, - x - y + inf))
    E.append((2*N+1, i+N, cnt, - x + y + inf))
    E.append((2*N+2, i+N, cnt, x - y + inf))
    E.append((2*N+3, i+N, cnt, x + y + inf))

print(su * inf * 2 - min_cost_flow_dijkstra(E, 2*N+4, 2*N+5, su))

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline
from heapq import heappush, heappop
def min_cost_flow_dijkstra(E, s, t, f):
    INF = 1 << 100
    NN = 2 * N + 6
    G = [[] for _ in range(NN)]
    for a, b, cap, c in E:
        G[a].append([b, cap, c, len(G[b])])
        G[b].append([a, 0, -c, len(G[a])-1])
    prevv = [-1] * NN
    preve = [-1] * NN
    res = 0
    h = [0] * NN
    Q = []
    while f > 0:
        dist = [INF] * NN
        dist[s] = 0
        update = 1
        heappush(Q, (0, s))
        while len(Q):
            d, v = heappop(Q)
            d = -d
            if dist[v] < d: continue
            for i, (w, _cap, c, r) in enumerate(G[v]):
                if _cap > 0 and dist[w] > dist[v] + c + h[v] - h[w]:
                    dist[w] = dist[v] + c + h[v] - h[w]
                    prevv[w] = v
                    preve[w] = i
                    heappush(Q, (-dist[w], w))
        if dist[t] == INF:
            return -1
        d = f
        v = t
        while v != s:
            d = min(d, G[prevv[v]][preve[v]][1])
            v = prevv[v]
        f -= d
        res += d * dist[t]
        v = t
        while v != s:
            G[prevv[v]][preve[v]][1] -= d
            G[v][G[prevv[v]][preve[v]][3]][1] += d
            v = prevv[v]
    return res

E = []
N = int(input())
su = 0
inf = 1 << 31
for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((2*N+4, i, cnt, 0))
    E.append((i, 2*N, cnt, x + y + inf))
    E.append((i, 2*N+1, cnt, x - y + inf))
    E.append((i, 2*N+2, cnt, - x + y + inf))
    E.append((i, 2*N+3, cnt, - x - y + inf))
    su += cnt

for i in range(N):
    x, y, cnt = map(int, input().split())
    E.append((i+N, 2*N+5, cnt, 0))
    E.append((2*N, i+N, cnt, - x - y + inf))
    E.append((2*N+1, i+N, cnt, - x + y + inf))
    E.append((2*N+2, i+N, cnt, x - y + inf))
    E.append((2*N+3, i+N, cnt, x + y + inf))

print(su * inf * 2 - min_cost_flow_dijkstra(E, 2*N+4, 2*N+5, su))