Problem:


Score : 800 points

Problem Statement

There are N cards placed on a grid with H rows and W columns of squares.

The i-th card has an integer A_i written on it, and it is placed on the square at the R_i-th row from the top and the C_i-th column from the left.

Multiple cards may be placed on the same square.

You will first pick up at most one card from each row.

Then, you will pick up at most one card from each column.

Find the maximum possible sum of the integers written on the picked cards.

Constraints

All values are integers.

1 \leq N \leq 10^5

1 \leq H, W \leq 10^5

1 \leq A_i \leq 10^5

1 \leq R_i \leq H

1 \leq C_i \leq W

Input

Input is given from Standard Input in the following format:

N H W
R_1 C_1 A_1
R_2 C_2 A_2
\vdots
R_N C_N A_N

Output

Print the maximum possible sum of the integers written on the picked cards.

Sample Input 1

6 2 2
2 2 2
1 1 8
1 1 5
1 2 9
1 2 7
2 1 4

Sample Output 1

28

The sum of the integers written on the picked cards will be 28, the maximum value possible, if you pick up cards as follows:

Pick up the fourth card from the first row.

Pick up the sixth card from the second row.

Pick up the second card from the first column.

Pick up the fifth card from the second column.

Sample Input 2

13 5 6
1 3 35902
4 6 19698
4 6 73389
3 6 3031
3 1 4771
1 4 4784
2 1 36357
2 1 24830
5 6 50219
4 6 22645
1 2 30739
1 4 68417
1 5 78537

Sample Output 2

430590

Sample Input 3

1 100000 100000
1 1 1

Sample Output 3

1



Sample input:
6 2 2
2 2 2
1 1 8
1 1 5
1 2 9
1 2 7
2 1 4


Sample output:
28

Submission status: Accepted

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

import operator

N,H,W = map(int,readline().split())
m = map(int,read().split())
RCA = sorted(zip(m,m,m),key=operator.itemgetter(2),reverse=True)

root = list(range(H+W))
size = [1] * (H+W)
no_cycle = [True] * (H+W)

def find_root(x):
    y = root[x]
    if x == y:
        return y
    z = find_root(y)
    root[x] = z
    return z

def merge(x,y):
    x,y = find_root(x),find_root(y)
    sx,sy = size[x],size[y]
    if sx < sy:
        sx,sy = sy,sx
        x,y = y,x
    root[y] = x
    size[x] += sy
    no_cycle[x] = no_cycle[x] and no_cycle[y]

answer = 0
for R,C,A in RCA:
    x,y = R-1,H+C-1
    rx,ry = find_root(x),find_root(y)
    if rx == ry:
        if not no_cycle[rx]:
            continue
        no_cycle[rx] = False
    else:
        if (not no_cycle[rx]) and (not no_cycle[ry]):
            continue
        merge(rx,ry)
    answer += A

print(answer)

Submission status: Accepted

Solution code:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10**7)

import operator

N,H,W = map(int,readline().split())
m = map(int,read().split())
RCA = sorted(zip(m,m,m),key=operator.itemgetter(2),reverse=True)

root = list(range(H+W))
size = [0] * (H+W)
no_cycle = [True] * (H+W)

def find_root(x):
    y = root[x]
    if x == y:
        return x
    path = [x]
    while y != root[y]:
        path.append(y)
        y = root[y]
    for p in path:
        root[p] = y
    return y

def merge(x,y):
    x,y = find_root(x),find_root(y)
    sx,sy = size[x],size[y]
    if sx < sy:
        sx,sy = sy,sx
        x,y = y,x
    root[y] = x
    size[x] += sy
    no_cycle[x] = no_cycle[x] and no_cycle[y]

answer = 0
for R,C,A in RCA:
    x,y = R-1,H+C-1
    rx,ry = find_root(x),find_root(y)
    if rx == ry:
        if not no_cycle[rx]:
            continue
        no_cycle[rx] = False
    else:
        if (not no_cycle[rx]) and (not no_cycle[ry]):
            continue
        merge(rx,ry)
    answer += A

print(answer)

Submission status: Accepted

Solution code:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10**7)

import operator

N,H,W = map(int,readline().split())
m = map(int,read().split())
RCA = sorted(zip(m,m,m),key=operator.itemgetter(2),reverse=True)

root = list(range(H+W))
size = [0] * (H+W)
no_cycle = [True] * (H+W)

def find_root(root,x):
    y = root[x]
    if x == y:
        return x
    path = [x]
    while y != root[y]:
        path.append(y)
        y = root[y]
    for p in path:
        root[p] = y
    return y

def merge(root,size,x,y):
    x,y = find_root(root,x),find_root(root,y)
    if x == y:
        return
    sx,sy = size[x],size[y]
    if sx < sy:
        sx,sy = sy,sx
        x,y = y,x
    root[y] = x
    no_cycle[x] = no_cycle[x] and no_cycle[y]

answer = 0
for R,C,A in RCA:
    x,y = R-1,H+C-1
    rx,ry = find_root(root,x),find_root(root,y)
    if rx == ry:
        if not no_cycle[rx]:
            continue
        no_cycle[rx] = False
    else:
        if (not no_cycle[rx]) and (not no_cycle[ry]):
            continue
        merge(root,size,rx,ry)
    answer += A

print(answer)

Submission status: Accepted

Solution code:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10**7)

import operator

N,H,W = map(int,readline().split())
m = map(int,read().split())
RCA = sorted(zip(m,m,m),key=operator.itemgetter(2),reverse=True)

root = list(range(H+W))
size = [0] * (H+W)
no_cycle = [True] * (H+W)

def find_root(x):
    y = root[x]
    if x == y:
        return x
    path = [x]
    while y != root[y]:
        path.append(y)
        y = root[y]
    for p in path:
        root[p] = y
    return y

def merge(x,y):
    x,y = find_root(x),find_root(y)
    sx,sy = size[x],size[y]
    if sx < sy:
        sx,sy = sy,sx
        x,y = y,x
    root[y] = x
    no_cycle[x] = no_cycle[x] and no_cycle[y]

answer = 0
for R,C,A in RCA:
    x,y = R-1,H+C-1
    rx,ry = find_root(x),find_root(y)
    if rx == ry:
        if not no_cycle[rx]:
            continue
        no_cycle[rx] = False
    else:
        if (not no_cycle[rx]) and (not no_cycle[ry]):
            continue
        merge(rx,ry)
    answer += A

print(answer)

Submission status: Accepted

Solution code:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10**7)

import operator

N,H,W = map(int,readline().split())
m = map(int,read().split())
RCA = sorted(zip(m,m,m),key=operator.itemgetter(2),reverse=True)

root = list(range(H+W))
size = [0] * (H+W)
no_cycle = [True] * (H+W)

def find_root(x):
    if x == root[x]:
        return x
    path = []
    while True:
        y = root[x]
        if x == y:
            break
        path.append(x)
        x = y
    for p in path:
        root[p] = x
    return root[x]

def merge(x,y):
    x,y = find_root(x),find_root(y)
    sx,sy = size[x],size[y]
    if sx < sy:
        sx,sy = sy,sx
        x,y = y,x
    root[y] = x
    no_cycle[x] = no_cycle[x] and no_cycle[y]

answer = 0
for R,C,A in RCA:
    x,y = R-1,H+C-1
    rx,ry = find_root(x),find_root(y)
    if rx == ry:
        if not no_cycle[rx]:
            continue
        no_cycle[rx] = False
    else:
        if (not no_cycle[rx]) and (not no_cycle[ry]):
            continue
        merge(rx,ry)
    answer += A

print(answer)

Submission status: Accepted

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

import operator

N,H,W = map(int,readline().split())
m = map(int,read().split())
RCA = sorted(zip(m,m,m),key=operator.itemgetter(2),reverse=True)

root = list(range(H+W))
size = [0] * (H+W)
no_cycle = [True] * (H+W)

def find_root(x):
    path = []
    while True:
        y = root[x]
        if x == y:
            break
        path.append(x)
        x = y
    for p in path:
        root[p] = x
    return root[x]

def merge(x,y):
    x,y = find_root(x),find_root(y)
    sx,sy = size[x],size[y]
    if sx < sy:
        sx,sy = sy,sx
        x,y = y,x
    root[y] = x
    no_cycle[x] = no_cycle[x] and no_cycle[y]

answer = 0
for R,C,A in RCA:
    x,y = R-1,H+C-1
    rx,ry = find_root(x),find_root(y)
    if rx == ry:
        if not no_cycle[rx]:
            continue
        no_cycle[rx] = False
    else:
        if (not no_cycle[rx]) and (not no_cycle[ry]):
            continue
        merge(rx,ry)
    answer += A

print(answer)

Submission status: Accepted

Solution code:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10**7)

import operator

N,H,W = map(int,readline().split())
m = map(int,read().split())
RCA = sorted(zip(m,m,m),key=operator.itemgetter(2),reverse=True)

root = list(range(H+W))
size = [0] * (H+W)
no_cycle = [True] * (H+W)

def find_root(x):
    y = root[x]
    if x == y:
        return y
    z = find_root(y)
    root[x] = z
    return z

def merge(x,y):
    x,y = find_root(x),find_root(y)
    sx,sy = size[x],size[y]
    if sx < sy:
        sx,sy = sy,sx
        x,y = y,x
    root[y] = x
    no_cycle[x] = no_cycle[x] and no_cycle[y]

answer = 0
for R,C,A in RCA:
    x,y = R-1,H+C-1
    rx,ry = find_root(x),find_root(y)
    if rx == ry:
        if not no_cycle[rx]:
            continue
        no_cycle[rx] = False
    else:
        if (not no_cycle[rx]) and (not no_cycle[ry]):
            continue
        merge(rx,ry)
    answer += A

print(answer)

Submission status: Accepted

Solution code:
import sys
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10 ** 7)
import operator

N,H,W = map(int,readline().split())
RCA = [tuple(int(x) for x in line.split()) for line in readlines()]

RCA.sort(key = operator.itemgetter(2), reverse=True)

root = list(range(H+W))
size = [0] * (H+W)
no_cycle = [True] * (H+W)

def find_root(x):
    y = root[x]
    if x == y:
        return y
    z = find_root(y)
    root[x] = z
    return z

def merge(x,y):
    x,y = find_root(x),find_root(y)
    sx,sy = size[x],size[y]
    if sx < sy:
        sx,sy = sy,sx
        x,y = y,x
    root[y] = x
    no_cycle[x] = no_cycle[x] and no_cycle[y]

answer = 0
for R,C,A in RCA:
    x,y = R-1,H+C-1
    rx,ry = find_root(x),find_root(y)
    if rx == ry:
        if not no_cycle[rx]:
            continue
        no_cycle[rx] = False
    else:
        if (not no_cycle[rx]) and (not no_cycle[ry]):
            continue
        merge(rx,ry)
    answer += A

print(answer)

Submission status: Accepted

Solution code:
import sys
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10 ** 7)

N,H,W = map(int,readline().split())
RCA = [tuple(int(x) for x in line.split()) for line in readlines()]

RCA.sort(key = lambda x: -x[2])

RCA

root = list(range(H+W))
size = [0] * (H+W)
no_cycle = [True] * (H+W)

def find_root(x):
    y = root[x]
    if x == y:
        return y
    z = find_root(y)
    root[x] = z
    return z

def merge(x,y):
    x,y = find_root(x),find_root(y)
    sx,sy = size[x],size[y]
    if sx < sy:
        sx,sy = sy,sx
        x,y = y,x
    root[y] = x
    no_cycle[x] = no_cycle[x] and no_cycle[y]

answer = 0
for R,C,A in RCA:
    x,y = R-1,H+C-1
    rx,ry = find_root(x),find_root(y)
    if rx == ry:
        if not no_cycle[rx]:
            continue
        no_cycle[rx] = False
    else:
        if (not no_cycle[rx]) and (not no_cycle[ry]):
            continue
        merge(rx,ry)
    answer += A

print(answer)

Submission status: Accepted

Solution code:
import sys
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 7)

N,H,W = map(int,readline().split())
RCA = [tuple(int(x) for x in line.split()) for line in readlines()]

RCA.sort(key = lambda x: -x[2])

RCA

root = list(range(H+W))
size = [0] * (H+W)
no_cycle = [True] * (H+W)

def find_root(x):
    y = root[x]
    if x == y:
        return y
    z = find_root(y)
    root[x] = z
    return z

def merge(x,y):
    x,y = find_root(x),find_root(y)
    sx,sy = size[x],size[y]
    if sx < sy:
        sx,sy = sy,sx
        x,y = y,x
    root[y] = x
    no_cycle[x] = no_cycle[x] and no_cycle[y]

answer = 0
for R,C,A in RCA:
    x,y = R-1,H+C-1
    rx,ry = find_root(x),find_root(y)
    if rx == ry:
        if not no_cycle[rx]:
            continue
        no_cycle[rx] = False
    else:
        if (not no_cycle[rx]) and (not no_cycle[ry]):
            continue
        merge(rx,ry)
    answer += A

print(answer)

Submission status: Accepted

Solution code:
class UnionFindNode:
    def __init__(self, group_id, parent=None, value=None):
        self.group_id_ = group_id
        self.parent_ = parent
        self.value = value
        self.rank_ = 1
        self.member_num_ = 1
        self.enum = 0

    def is_root(self):
        return not self.parent_

    def root(self):
        parent = self
        while not parent.is_root():
            parent = parent.parent_
            self.parent_ = parent
        return parent

    def find(self):
        root = self.root()
        return root.group_id_

    def rank(self):
        root = self.root()
        return root.rank_

    def unite(self, unite_node):
        root = self.root()
        unite_root = unite_node.root()
        if not self.check(unite_node):
            return False
        if root.group_id_ != unite_root.group_id_:
            if root.rank() > unite_root.rank():
                unite_root.parent_ = root
                root.rank_ = max(root.rank_, unite_root.rank_ + 1)
                root.member_num_ = root.member_num_ + unite_root.member_num_
                root.enum = root.enum + unite_root.enum + 1
            else:
                root.parent_ = unite_root
                unite_root.rank_ = max(root.rank_ + 1, unite_root.rank_)
                unite_root.member_num_ = root.member_num_ + unite_root.member_num_
                unite_root.enum = root.enum + unite_root.enum + 1
        else:
            root.enum += 1
        return True


    def check(self, unite_node):
        root = self.root()
        unite_root = unite_node.root()
        if root.group_id_ == unite_root.group_id_:
            if root.enum < root.member_num_:
                return True
        else:
            if root.member_num_ + unite_root.member_num_ > root.enum + unite_root.enum:
                return True
        return False


if __name__ == "__main__":
    N,H,W=[int(i) for i in input().strip().split(" ")]
    node_list = [UnionFindNode(i) for i in range(H+W)]
    import sys
    es = []
    for line in sys.stdin:
        es.append(tuple(int(i) for i in line.strip().split(" ")))
    es = sorted(es, key=lambda x:x[2])
    r = 0
    for e in es[::-1]:
        if node_list[e[0]-1].unite(node_list[e[1]+H-1]):
            r += e[2]
    print(r)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**6)
N, H, W = map(int, input().split())
P = [-1 for i in range(H+W)]
C = [1] * (H+W)
arr = []
for _ in range(N):
    r, c, a = map(int, input().split())
    arr.append((a, r-1, c+H-1))
arr = sorted(arr)

ans = 0
def find(a):
    if P[a] < 0: return a
    t = find(P[a])
    P[a] = t
    return t

def unite(r, c):
    fr, fc = find(r), find(c)
    if fr == fc:  return 0
    C[fr] = C[fc] = C[fr] + C[fc]
    if P[fr] == P[fc]:
        P[fc] = fr
        P[fr] -= 1
    elif P[fr] > P[fc]:
        P[fc] = fr
    else:
        P[fr] = fc
    
while arr:
    a, r, c = arr.pop()
    unite(r, c)
    fr = find(r)
    if C[fr]:
        ans += a
        C[fr] -= 1
print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**6)

def par(a):
    if P[a] < 0: return a
    t = par(P[a])
    P[a] = t
    return t
def unite(a, b):
    if par(a) == par(b): return 0
    C[par(a)], C[par(b)] = C[par(a)] + C[par(b)], C[par(a)] + C[par(b)]
    if P[par(b)] == P[par(a)]:
        P[par(b)] = par(a)
        P[par(a)] -= 1
    elif P[par(b)] > P[par(a)]:
        P[par(b)] = par(a)
    else:
        P[par(a)] = par(b)
N, H, W = map(int, input().split())
P = [-1 for i in range(H+W)]
C = [1] * (H+W)
X = []
for _ in range(N):
    r, c, a = map(int, input().split())
    X.append((a, r-1, c+H-1))
X = sorted(X)
ans = 0
while X:
    a, r, c = X.pop()
    unite(r, c)
    if C[par(r)]:
        ans += a
        C[par(r)] -= 1
print(ans)

Submission status: Accepted

Solution code:
class UnionFind:
    def __init__(self, n):
        self.par = [i for i in range(n)]
        self.size = [1] * n
        self.rank = [0] * n
        self.edge = [0] * n

    def find(self, x):
        if self.par[x] == x:
            return x
        else:
            self.par[x] = self.find(self.par[x])
            return self.par[x]

    def is_saturated(self, x):
        x = self.find(x)
        return self.edge[x] == self.size[x]

    def get_size(self, x):
        return self.size[self.find(x)]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        self.edge[x] += 1
        if x == y:
            return

        if self.rank[x] < self.rank[y]:
            self.par[x] = y
            self.size[y] += self.size[x]
            self.edge[y] += self.edge[x]
        else:
            self.par[y] = x
            self.size[x] += self.size[y]
            self.edge[x] += self.edge[y]
            if self.rank[x] == self.rank[y]:
                self.rank[x] += 1

n, h, w = [int(item) for item in input().split()]

UF = UnionFind(h+w)
arc = []
for i in range(n):
    r, c, a = [int(item) for item in input().split()]
    r -= 1; c -= 1
    c += h
    arc.append([a, r, c])
arc.sort(reverse=True)

ans = 0
for a, r, c in arc:
    if not UF.is_saturated(r) or not UF.is_saturated(c):
        UF.union(r, c)
        ans += a

print(ans)

Submission status: Accepted

Solution code:
class UnionFind:
    def __init__(self, n):
        self.par = [i for i in range(n)]
        self.size = [1] * n
        self.rank = [0] * n
        self.edge = [0] * n

    def find(self, x):
        if self.par[x] == x:
            return x
        else:
            self.par[x] = self.find(self.par[x])
            return self.par[x]

    def is_saturated(self, x):
        x = self.find(x)
        return self.edge[x] == self.size[x]

    def get_size(self, x):
        return self.size[self.find(x)]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        self.edge[x] += 1
        if x == y:
            return

        if self.rank[x] < self.rank[y]:
            self.par[x] = y
            self.size[y] += self.size[x]
            self.edge[y] += self.edge[x]
        else:
            self.par[y] = x
            self.size[x] += self.size[y]
            self.edge[x] += self.edge[y]
            if self.rank[x] == self.rank[y]:
                self.rank[x] += 1

n, h, w = [int(item) for item in input().split()]

UF = UnionFind(h+w)
arc = []
for i in range(n):
    r, c, a = [int(item) for item in input().split()]
    r -= 1; c -= 1
    c += h
    arc.append([a, r, c])
arc.sort(reverse=True)

ans = 0
for a, r, c in arc:
    if not UF.is_saturated(r) or not UF.is_saturated(c):
        UF.union(r, c)
        ans += a

print(ans)

Submission status: Accepted

Solution code:
import sys
from collections import deque
input = sys.stdin.readline
sys.setrecursionlimit(10**5)
N, H, W = map(int, input().split())
RCA = []

class UF(object):
    def __init__(self, n):
        self.parent = [i for i in range(n)]

    def root(self, v):
        if v == self.parent[v]:
            return v
        else:
            self.parent[v] = self.root(self.parent[v])
            return self.parent[v]
    
    def unite(self, u, v):
        u, v = self.root(u), self.root(v)
        if (u == v):
            return
        self.parent[u] = v

for _ in range(N):
    r, c, a = map(int, input().split())
    r, c = r-1, c-1
    RCA.append((a, r, c))

RCA.sort(reverse=True)
RCA = deque(RCA)

uf = UF(H+W+1)  # r0, r1, ..., rH, c0, c1, ..., cW, loopflag

cnt, ans = 0, 0
while RCA and cnt < H+W:
    a, r, c = RCA.popleft()
    c += H
    if uf.root(r) == uf.root(c):
        if uf.root(r) == uf.root(H+W):  # loop?
            continue
        uf.unite(r, H+W)
    ans += a
    cnt += 1
    uf.unite(r, c)

print(ans)

Submission status: Accepted

Solution code:
import sys

sys.setrecursionlimit(10 ** 5)


class UnionFind:
    def __init__(self, n):
        self.table = [-1] * n
        self.taken = [0] * n

    def _root(self, x):
        if self.table[x] < 0:
            return x
        else:
            self.table[x] = self._root(self.table[x])
            return self.table[x]

    def union(self, x, y):
        r1 = self._root(x)
        r2 = self._root(y)
        if r1 == r2:
            new_root = r1
        else:
            d1 = self.table[r1]
            d2 = self.table[r2]
            if d1 <= d2:
                self.table[r2] = r1
                self.table[r1] += d2
                self.taken[r1] += self.taken[r2]
                new_root = r1
            else:
                self.table[r1] = r2
                self.table[r2] += d1
                self.taken[r2] += self.taken[r1]
                new_root = r2

        cells = -self.table[new_root]
        taken = self.taken[new_root]
        if cells > taken:
            self.taken[new_root] += 1
            return True
        return False


n, h, w = map(int, input().split())
hw = h + w
cards = []
for line in sys.stdin:
    r, c, a = map(int, line.split())
    cards.append((a, r - 1, h + c - 1))
cards.sort(reverse=True)

uft = UnionFind(hw)
ans = 0

for a, r, c in cards:
    if uft.union(r, c):
        ans += a
print(ans)

Submission status: Accepted

Solution code:
import sys
from heapq import *

sys.setrecursionlimit(10 ** 6)
input = sys.stdin.readline

def main():
    def get_group(k):
        g = pd[k]
        if g < 0:
            return k
        gg = get_group(g)
        pd[k] = gg
        return gg

    def merge(j, k):
        g1 = get_group(j)
        g2 = get_group(k)
        if g1 != g2:
            d1 = -pd[g1]
            d2 = -pd[g2]
            if d2 > d1:
                g1, g2 = g2, g1
            pd[g2] = g1
            if d1 == d2:
                pd[g1] -= 1

    hp = []
    n, h, w = map(int, input().split())
    pd = [-1] * (h + w + 2)  # 親(parent)と深さ(depth)。0以上は親。負の場合、そのノードが根で絶対値が深さ。
    pd[0] = -(h + w + 2)
    for _ in range(n):
        r, c, a = map(int, input().split())
        heappush(hp, [-a, r, h + c])
    cnt = h + w
    ans = 0
    while cnt and hp:
        a, r, c = heappop(hp)
        gr = get_group(r)
        gc = get_group(c)
        if gr + gc == 0: continue
        if gr == gc:
            merge(gr, 0)
        else:
            merge(gr, gc)
        ans -= a
        cnt -= 1
    print(ans)

main()

Submission status: Accepted

Solution code:
class UnionFind():
	def __init__(self, n):
		self.n = n
		self.root = [-1]*n
		self.rank = [0]*n
		self.cycle = [False]*n

	def find(self, x):
		if(self.root[x] < 0):
			return x
		else:
			self.root[x] = self.find(self.root[x])
			return self.root[x]
			
	def unite(self, x, y):
		x = self.find(x)
		y = self.find(y)
		if(x == y):
			self.cycle[x] = True
		elif(self.rank[x] > self.rank[y]):
			self.root[x] += self.root[y]
			self.cycle[x] |= self.cycle[y]
			self.root[y] = x
		else:
			self.root[y] += self.root[x]
			self.cycle[y] |= self.cycle[x]
			self.root[x] = y
			if(self.rank[x] == self.rank[y]):
				self.rank[y] += 1

	def isSame(self, x, y):
		return self.find(x) == self.find(y)
	
	#サイクルは各連結成分に一つまで
	def isSafe(self, x, y):
		cx = self.cycle[self.find(x)] 
		cy = self.cycle[self.find(y)]
		return not((self.isSame(x,y) and (cx or cy)) or (cx and cy))

n,h,w,*l = map(int,open(0).read().split())
cards = sorted([(a,r-1,c-1) for r,c,a in zip(*[iter(l)]*3)])[::-1]
uf = UnionFind(h+w)
ans = 0

for a,r,c in cards:
	c += h
	if uf.isSafe(r,c):
		uf.unite(r,c)
		ans += a
print(ans)

Submission status: Accepted

Solution code:
class UnionFind():
	def __init__(self, n):
		self.n = n
		self.root = [-1]*(n+1)
		self.rank = [0]*(n+1)
		self.cycle = [False]*(n+1)

	def find(self, x):
		if(self.root[x] < 0):
			return x
		else:
			self.root[x] = self.find(self.root[x])
			return self.root[x]
			
	def unite(self, x, y):
		x = self.find(x)
		y = self.find(y)
		if(x == y):
			self.cycle[x] = True
		elif(self.rank[x] > self.rank[y]):
			self.root[x] += self.root[y]
			self.cycle[x] |= self.cycle[y]
			self.root[y] = x
		else:
			self.root[y] += self.root[x]
			self.cycle[y] |= self.cycle[x]
			self.root[x] = y
			if(self.rank[x] == self.rank[y]):
				self.rank[y] += 1

	def isSame(self, x, y):
		return self.find(x) == self.find(y)
		
	def isCycle(self, x, y):
		cx = self.cycle[self.find(x)]
		cy = self.cycle[self.find(y)]
		if cx == cy == False:
			return False
		elif cx ^ cy:
			return True
		else:
			return 2

	def size(self, x):
		return -self.root[self.find(x)]

n,h,w,*l = map(int,open(0).read().split())
cards = sorted([(a,r,c) for r,c,a in zip(*[iter(l)]*3)])[::-1]

uf = UnionFind(h+w)
ans = 0

for a,r,c in cards:
	c += h
	if not ( (uf.isSame(r,c) and uf.isCycle(r,c)) or uf.isCycle(r,c)==2 ):
		uf.unite(r,c)
		ans += a
print(ans)

Submission status: Accepted

Solution code:
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
    res = list(sys.stdin.readline())
    if res[-1] == "\n":
        return res[:-1]
    return res
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)]

sys.setrecursionlimit(1000000)
mod = 1000000007

#A
def A():
    m,d = LI()
    ans = 0
    for i in range(1,m+1):
        for j in range(1,d+1):
            d1 = j%10
            d2 = j//10
            if d1 >= 2 and d2 >= 2 and d1*d2 == i:
                ans += 1
    print(ans)
    return

#B
def B():
    def add(i):
        while i <= m:
            bit[i] += 1
            i += i&-i

    def sum(i):
        res = 0
        while i > 0:
            res += bit[i]
            i -= i&-i
        return res

    n,k = LI()
    m = 2000
    a = LI()
    bit = [0]*(m+1)
    ans = 0
    for i in range(n):
        ans += (i-sum(a[i]))*k
        add(a[i])
    inv = pow(2,mod-2,mod)
    for i in range(n):
        ans += sum(a[i]-1)*k*(k-1)*inv%mod
    print(ans%mod)
    return

#C
def C():
    n = I()
    s = S()
    if "W" in (s[0],s[-1]):
        print(0)
        return
    d = [0]
    for i in range(1,2*n):
        if s[i] == s[i-1]:
            d.append(1-d[-1])
        else:
            d.append(d[-1])
    if sum(d) != n:
        print(0)
        return
    ans = 1
    s = 0
    for i in d:
        if not i:
            s += 1
        else:
            ans *= s
            s -= 1
            ans %= mod
    for i in range(1,n+1):
        ans *= i
        ans %= mod
    print(ans)
    return

#D
def D():
    n = I()
    m = n.bit_length()
    v = [[0]*n for i in range(n)]
    for i in range(n):
        for j in range(n):
            k = i^j
            for l in range(m):
                if k&(1<<l):
                    v[i][j] = l+1
                    break
    for i in range(n-1):
        print(*v[i][i+1:])
    return

#E
def E():
    def root(x):
        if par[x] == x:
            return x
        par[x] = root(par[x])
        return par[x]

    def unite(x,y):
        x = root(x)
        y = root(y)
        if rank[x] < rank[y]:
            par[x] = y
            s[y] += s[x]
            e[y] += e[x]+1
        else:
            par[y] = x
            s[x] += s[y]
            e[x] += e[y]+1
            if rank[x] == rank[y]:
                rank[x] += 1

    n,h,w = LI()
    v = []
    m = h+w
    for i in range(n):
        r,c,a = LI()
        r -= 1
        c += h-1
        v.append((a,r,c))
    v.sort(key = lambda x:-x[0])
    par = [i for i in range(m)]
    rank = [0]*m
    s = [1]*m
    e = [0]*m
    ans = 0
    for a,x,y in v:
        rx,ry = root(x), root(y)
        if rx == ry:
            if e[rx]+1 <= s[rx]:
                ans += a
                e[rx] += 1
        else:
            if e[rx]+e[ry]+1 <= s[rx]+s[ry]:
                ans += a
                unite(x,y)
    print(ans)
    return

#F
def F():

    return

#Solve
if __name__ == "__main__":
    E()

Submission status: Accepted

Solution code:
import sys
input=sys.stdin.readline
class UnionFind:
    def __init__(self,n):
        self.par=[i for i in range(n)]
        self.rank=[0]*n
        self.size=[1]*n
        self.Ecnt=[0]*n
    def root(self,x):
        if self.par[x]==x:
            return x
        else:
            self.par[x]=self.root(self.par[x])
            return self.par[x]
    def union(self,x,y):
        px=self.root(x); py=self.root(y)
        if px!=py:
            if self.rank[px]==self.rank[py]:
                self.rank[px]+=1
            elif self.rank[px]<self.rank[py]:
                px,py=py,px
            self.par[py]=px
            self.size[px]+=self.size[py]
            self.Ecnt[px]+=self.Ecnt[py]+1
        else:
            self.Ecnt[px]+=1
    def same_check(self,x,y):
        return self.root(x)==self.root(y)

n,h,w=map(int,input().split())
RCA=[]
for _ in range(n):
    r,c,a=map(int,input().split())
    r-=1
    c+=h-1
    RCA.append((r,c,a))
RCA.sort(lambda x:x[2],reverse=True)
uf=UnionFind(h+w)
ans=0
for r,c,a in RCA:
    if uf.same_check(r,c):
        if uf.size[uf.par[r]]>uf.Ecnt[uf.par[r]]:
            uf.union(r,c)
            ans+=a
    else:
        if (uf.size[uf.par[r]]+uf.size[uf.par[c]])>(uf.Ecnt[uf.par[r]]+uf.Ecnt[uf.par[c]]):
            uf.union(r,c)
            ans+=a
print(ans)

Submission status: Accepted

Solution code:
# coding: utf-8
# Your code here!
class UnionFind:
    def __init__(self, n):
        self.parent = list(range(n)) #親ノード
        self.size = [1]*n #グループの要素数
        self.cycle = [0]*n
 
    def root(self, x): #root(x): xの根ノードを返す．
        while self.parent[x] != x:
            self.parent[x] = self.parent[self.parent[x]]
            x = self.parent[x]
        return x 
 
    def merge(self, x, y): #merge(x,y): xのいる組とyのいる組をまとめる
        x, y = self.root(x), self.root(y)
        if x == y: return False
        if self.size[x] < self.size[y]: x,y=y,x #xの要素数が大きいように
        self.size[x] += self.size[y] #xの要素数を更新
        self.parent[y] = x #yをxにつなぐ
        self.cycle[x] = self.cycle[x]+self.cycle[y]
        return True
 
    def issame(self, x, y): #same(x,y): xとyが同じ組ならTrue
        return self.root(x) == self.root(y)
        
    def getsize(self,x): #size(x): xのいるグループの要素数を返す
        return self.size[self.root(x)]

    def getcycle(self,x): #size(x): xのいるグループの要素数を返す
        return self.cycle[self.root(x)]

    def addcycle(self,x): #size(x): xのいるグループの要素数を返す
        self.cycle[self.root(x)]+=1
        return 

import sys
sys.setrecursionlimit(10**6)
readline = sys.stdin.readline #文字列入力のときは注意
 
#n = int(input())
n,h,w = [int(i) for i in readline().split()]
#a = [int(i) for i in readline().split()]

uf = UnionFind(h+w)

rca = [[int(i)-1 for i in readline().split()] for i in range(n)]

from operator import itemgetter
rca.sort(key = itemgetter(2), reverse=True)

ans = 0
#print(rca)
for r,c,a in rca:
    c += h
    a += 1
    if uf.issame(r,c):
        if uf.getcycle(r): continue
        ans += a
        uf.addcycle(r)
    else:
        if uf.getcycle(r)+uf.getcycle(c) >= 2: continue
        uf.merge(r,c)
        ans += a

print(ans)