Problem:


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Minimum Spanning Tree

  For a given weighted graph $G = (V, E)$, find the minimum spanning tree (MST) of $G$ and print total weight of edges belong to the MST.

Input

  In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, a $n \times n$ adjacency matrix $A$ which represents $G$ is given.
$a_{ij}$ denotes the weight of edge connecting vertex $i$ and vertex $j$. If there is no edge between $i$ and $j$, $a_{ij}$ is given by -1.

Output

Print the total weight of the minimum spanning tree of $G$.

Constraints

$1 \leq n \leq 100$

$0 \leq a_{ij} \leq 2,000$ (if $a_{ij} \neq -1$)

$a_{ij} = a_{ji}$

$G$ is a connected graph

Sample Input 1

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

Sample Output 1

5

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.



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


Sample output:
5

Submission status: Accepted

Solution code:
n = int(input())
G = [list(map(int, input().split())) for _ in range(n)]

color = ['White']*n
d = [10**6]*n # 移動コスト
d[0] = 0 # 0にはコストゼロ
p = [-1]*n # 親ノード
p[0] = -1 # 0には親なし

def prim():
    while True:
        mincost = 10**6
        u = -1
        # 最小コストを選ぶ
        for i in range(n):
            if color[i] != 'Black' and d[i] < mincost:
                mincost = d[i]
                u = i

        # 道がない
        if mincost == 10**6:
            break

        color[u] = 'Black'

        # 未訪問かつ道があるならコスト表を更新
        for v in range(n):
            if color[v] != 'Black' and G[u][v] != -1:
                if G[u][v] < d[v]:
                    d[v] = G[u][v]
                    p[v] = u
                    color[v] = 'Gray'
    return d

print(sum(prim()))

Submission status: Accepted

Solution code:
INF = float('inf')
N = int(input())
M = []
D = []
P = []
visited = []
for i in range(N):
    M.append([a if a != -1 else INF for a in map(int, input().split())])
    D.append(INF)
    P.append(-1)
    visited.append(False)

D[0] = 0
P[0] = None

while True:
    min_cost = INF
    u = -1
    for i in range(N):
        if not visited[i] and D[i] < min_cost:
            u = i
            min_cost = D[i]

    if u == -1:
        break

    visited[u] = True

    for i, m in enumerate(M[u]):
        if not visited[i] and m != INF and m < D[i]:
            D[i] = m
            P[i] = u

print(sum(D))

Submission status: Accepted

Solution code:
# 最小全域木 Minumum spannin tree

MAX_EDGE_COST = 2001
n = int(input())
A = [[0 for i in range(n)] for i in range(n)]
for i in range(n):
    A[i] = [int(i) for i in input().split()]

col = [-1 for i in range(n)]
d = [MAX_EDGE_COST for i in range(n)]
p = [-1 for i in range(n)]

d[0] = 0
while True:
    mincost = MAX_EDGE_COST;
    for i in range(n):
        if col[i] != 1 and d[i] < mincost:
            mincost = d[i]
            u = i
    
    if mincost == MAX_EDGE_COST:
        break;
    
    col[u] = 1
    
    for v in range(n):
        if col[v] != 1 and A[u][v] != -1:
            if A[u][v] < d[v]:
                d[v] = A[u][v]
                p[v] = u
                col[v] = 0

sum = 0
for i in range(n):
    if p[i] != -1:
        sum += A[i][p[i]]

print(sum)

Submission status: Accepted

Solution code:
def main():

    n = int(input())
    a_list = [list(map(int, input().split())) for _ in [0]*n]
    abc = []
    for i in range(n):
        for j in range(i+1, n):
            if a_list[i][j] > -1:
                abc.append((i, j, a_list[i][j]))

    def Kruskal(n, abc, weight=True):
        class unionfind():
            # size:要素数,tree：unionfind木
            def __init__(self, size):  # self,要素数
                self.size = size
                self.tree_root = list(range(self.size))
                self.tree_depth = [1]*self.size

            # rootを探す
            def root(self, index):
                temp_list = []
                temp = self.tree_root[index]
                while index != temp:
                    temp_list.append(index)
                    index = temp
                    temp = self.tree_root[index]
                for i in temp_list:
                    self.tree_root[i] = index
                return index

            # 結合
            def unite(self, index1, index2):
                r1 = self.root(index1)
                r2 = self.root(index2)
                if r1 != r2:
                    d1, d2 = self.tree_depth[r1], self.tree_depth[r2]
                    if d1 <= d2:
                        self.tree_root[r1] = r2
                        self.tree_depth[r2] = max(d1+1, d2)
                    else:
                        self.tree_root[r2] = r1
                        self.tree_depth[r1] = max(d2+1, d1)

            # 同じか判定
            def same(self, index1, index2):
                r1 = self.root(index1)
                r2 = self.root(index2)
                return r1 == r2

        uf = unionfind(n)
        ret = 0
        if weight:
            abc.sort(key=lambda x: x[2])
        for a, b, c in abc:
            if not uf.same(a, b):
                ret += c
                uf.unite(a, b)
        return ret

    print(Kruskal(n, abc))


main()

Submission status: Accepted

Solution code:
#0オリジンで行うので注意
import sys
input = sys.stdin.buffer.readline

INF = 10 ** 9


#隣接行列
n = int(input())
G = []
for _ in range(n):
    G.append(list(map(int, input().split())))
for i in range(n):
    for j in range(n):
        if G[i][j] == -1:
            G[i][j] = INF

#到着してない：white,　到着後:gray, 確定:black
white, gray, black = 1, 2, 3
color = [white] * n #初期条件

d = [INF] * n #d[m]にTに属する頂点とT-Vに属する頂点を繋ぐ辺の中で重みが最小の物を記録
p = [INF] * n #p[m]にMSTにおける頂点mの親を記録


def prim():
    d[0] = 0
    p[0] = -1
    
    while True:
        mincost = INF
        for i in range(n):
            if color[i] != black and d[i] < mincost:
                mincost = d[i]
                u = i #次に伸ばす頂点の候補として記録
                
                
        if mincost == INF: #次の頂点がなかったらbreak
            break
                
        color[u] = black #最小全域木の頂点として決定
            
        for v in range(n):
            if color[v] != black and G[u][v] != INF:
                if G[u][v] < d[v]:
                    d[v] = G[u][v] #d[n]を更新を更新する
                    p[v] = u #uをvの親候補として記録
                    color[v] = gray
    
    S = 0#合計
    for i in range(n):
        if p[i] != -1:
            S += G[i][p[i]]
    return S

print(prim())

Submission status: Accepted

Solution code:
def prim():
    mindist[0] = 0
    parent[0] = -1 

    while True:
        #MSTに追加する頂点を決定
        mincost = INF
        u = -1
        for i in range(n):
            if color[i] != black and mindist[i] < mincost:
                mincost = mindist[i]
                u = i
        if u == -1: break
        color[u] = black
        # MSTに含まれていないMSTとつながる隣接頂点の最小コストを探索
        for v in range(n):
            if color[v] == black: continue
            if M[u][v] == INF: continue
            if M[u][v] >= mindist[v]: continue
            mindist[v] = M[u][v] 
            parent[v] = u
            color[v] = gray
        
    sumcost = 0
    for i in range(n):
        if parent[i] == -1: continue
        sumcost += M[i][parent[i]]

    return sumcost

if __name__ == "__main__":
    n = int(input())
    INF = float("inf")
    M = [list(map(lambda x: INF if x == "-1" else int(x), input().split())) for _ in range(n)]
    white = 0; gray = 1; black =2
    color = [white]*n #各頂点の訪問状態 （white:未訪問 gray:暫定 black:確定）
    mindist = [INF]*n # 各頂点のMSTとつながる辺の最小コスト
    parent = [-1]*n #各頂点の親

    print(prim())

Submission status: Accepted

Solution code:
import heapq


def prim(G):
    n = len(G)
    is_visited = [False for _ in range(n)]
    que = []
    heapq.heappush(que, (0, 0))

    ret = 0
    while que:
        cost, cur_v = heapq.heappop(que)
        if is_visited[cur_v]:
            continue

        is_visited[cur_v] = True
        ret += cost
        for (adj_dst, adj_cost) in G[cur_v]:
            heapq.heappush(que, (adj_cost, adj_dst))

    return ret


def main():
    n = int(input())
    g = [[] for _ in range(n)]
    a = [[int(x) for x in input().split()] for _ in range(n)]

    for i in range(n):
        for j in range(n):
            if a[i][j] == -1:
                continue
            g[i].append((j, a[i][j]))
            g[j].append((i, a[i][j]))

    print(prim(g))


main()

Submission status: Accepted

Solution code:
def minimum_spanning_tree(adj_mat, cost, color, parent):
    N = len(cost)
    cost[0] = 0
    parent[0] = -1

    while True:
        mincost = 2000000

        for i in range(N):
            if color[i] != "B" and cost[i] < mincost:
                mincost = cost[i]
                cur = i

        if mincost == 2000000:
            break

        color[cur] = "B"

        for v in range(N):
            if color[v] != "B" and adj_mat[cur][v] >= 0:
                if adj_mat[cur][v] < cost[v]:
                    cost[v] = adj_mat[cur][v]
                    parent[v] = cur
                    color[v] = "G"

def Main():
    N = int(input())
    adj_mat = list()
    cost  = [ 2000000 for n in range(N)]
    color = ["W" for n in range(N)]
    parent = [None for n in range(N)]

    for n in range(N):
        adj_mat.append([int(a) for a in input().split()])

    minimum_spanning_tree(adj_mat, cost, color, parent)
    print(sum(cost))

Main()

Submission status: Accepted

Solution code:
# Minimum Spanning Tree

INF = 10**5
N, *W = map(int, open(0).read().split())
W = tuple(zip(*[iter(INF if w < 0 else w for w in W)]*N))

S = set([0])
ans = 0
while len(S) < N:
    min_w = INF
    u = -1
    for v in S:
        for j, w in enumerate(W[v]):
            if j not in S and w < min_w:
                min_w = w
                u = j

    ans += min_w
    S.add(u)
    
print(ans)

Submission status: Accepted

Solution code:

import heapq

def main():

    INF = 1000000009
    n = int(input())
    e = [[] for _ in range(n)]
    for i in range(n):
        inf = list(map(int,input().split()))
        for j in range(n):
            if inf[j]!=-1:e[i].append([j,inf[j]])

    dp = [INF]*n
    finished = [False]*n
    dp[0] = 0
    pq = [[0,0]]
    heapq.heapify(pq)
    while pq:
        cost,v = heapq.heappop(pq)
        if dp[v]<cost:continue
        finished[v] = True
        for i in range(len(e[v])):
            u = e[v][i][0]
            ncost = e[v][i][1]
            if ncost < dp[u] and not finished[u]:
                dp[u] = ncost
                heapq.heappush(pq,[ncost,u])
    res = 0
    for i in range(n):res+=dp[i]
    print(res)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import queue

INFTY=1<<21

#プリム法
def prim(n,EdgeMatrix):

    EdgeList=queue.PriorityQueue() #探索対象の辺
    used=[False]*n #頂点の使用情報

    used[0]=True #0から探索を始める
    LastNode=0 #最新の頂点
    count=1 #つないだ頂点の数
    EdgeSum=0 #重みの合計

    while count<n:

        for i in range(len(EdgeMatrix[LastNode])):
            #探索していない頂点へ辺があればキューに追加
            Edge=EdgeMatrix[LastNode][i]
            if used[Edge[0]]==False:
                EdgeList.put([Edge[1],Edge[0]])

        #探索していない頂点への最も重みの小さい辺を取り出す
        while True:
            minEdge=EdgeList.get()
            if used[minEdge[1]]==False:
                break

        EdgeSum+=minEdge[0] #辺の合計を増やす
        LastNode=minEdge[1] #最新の頂点を更新
        used[minEdge[1]]=True #頂点の使用情報を更新
        count+=1 #つないだ頂点の数を更新

    return EdgeSum


#入力
n=int(input())

#辺の隣接行列
EdgeMatrix=[[] for i in range(n)]
for i in range(n):
    l=list(map(int,input().split()))
    for j in range(n):
        if l[j]!=-1:
            EdgeMatrix[i].append([j,l[j]])
            EdgeMatrix[j].append([i,l[j]])

#最小全域木の重みの総和
print(prim(n,EdgeMatrix))

Submission status: Accepted

Solution code:
N = int(input())
G = [[] for i in range(N)]
for v in range(N):
    for w, c in enumerate(map(int, input().split())):
        if c != -1:
            G[v].append((w, c))

from heapq import heappush, heappop, heapify
used = [0]*N
que = [(c, w) for w, c in G[0]]
used[0] = 1
heapify(que)

ans = 0
while que:
    cv, v = heappop(que)
    if used[v]:
        continue
    used[v] = 1
    ans += cv
    for w, c in G[v]:
        if used[w]:
            continue
        heappush(que, (c, w))
print(ans)

Submission status: Accepted

Solution code:
import sys
# sys.stdin = open('input.txt')

def createMatrix():
  matrix = [[i for i in map(int, input().split())] for i in range(n)]
  return matrix

def prim():
    d[0] = 0
    p[0] = -1

    while True:
        mincost = INFTY
        for i in range(n):
            if status[i] != VISITED and d[i] < mincost:
                mincost = d[i]
                u = i

        if mincost == INFTY:
            break

        status[u] = VISITED

        for v in range(n):
            if status[v] != VISITED and matrix[u][v] != -1:
                if matrix[u][v] < d[v]:
                    d[v] = matrix[u][v]
                    p[v] = u
                    status[v] = VISITING

n = int(input())
NOT_VISITED = 0 # WHITE
VISITING = 1 # GRAY
VISITED = 2 # BLACK
INFTY = 10**21

matrix = createMatrix()
status =  [NOT_VISITED] * n
d = [INFTY] * n
p = [-1] * n

prim()
print(sum(d))

Submission status: Accepted

Solution code:
from sys import stdin
input = stdin.readline

INFTY = 2**21
WHITE = 0
GRAY = 1
BLACK = 2

n = int(input())

M = [[0]*n for _ in range(n)]

for i in range(n):
    ee = map(int, input().split())
    for j, e in enumerate(ee): # 先に1行分読み込んでから、eにわける
        if e == -1:
            M[i][j] = INFTY
        else:
            M[i][j] = e


def prim():
    d = [INFTY]*n
    p = [-1]*n
    color = [WHITE]*n

    d[0] = 0

    while True:
        minv = INFTY
        u = -1
        for i in range(n):
            if (minv > d[i]) and (color[i] != BLACK):
                u = i
                minv = d[i]

        if u == -1:
            break
        color[u] = BLACK
        for v in range(n):
            if (color[v] != BLACK) and (M[u][v] != INFTY):
                if d[v] > M[u][v]:
                    d[v] = M[u][v]
                    p[v] = u
                    color[v] = GRAY

    _sum = 0 # pythonは標準でsum関数があるので一応sumは使わないでおく
    for i in range(n):
        if p[i] != -1:
            _sum += M[i][p[i]]

    return _sum

print(prim())

Submission status: Accepted

Solution code:
def prim():
    INFTY = float('inf')
    color = ['WHITE' for _ in range(n)]
    d = [INFTY for _ in range(n)]
    p = [None for _ in range(n)]
    d[0] = 0
    p[0] = -1

    while True:
        mincost = INFTY
        for i in range(n):
            if color[i] != 'BLACK' and d[i] < mincost:
                mincost = d[i]
                u = i
        
        if mincost == INFTY:
            break

        color[u] = 'BLACK'

        for v in range(n):
            if color[v] != 'BLACK' and A[u][v] != -1:
                if A[u][v] < d[v]:
                    d[v] = A[u][v]
                    p[v] = u
                    color[v] = 'GRAY'
    return sum(d)

n = int(input())
A = []
for _ in range(n):
    l = list(map(int, input().split()))
    A.append(l)

print(prim())

Submission status: Accepted

Solution code:
class UnionFind:
  def __init__(self, v):
    # number of vertices
    self.v = v
    # parents of each node
    self.parents = [None] * v
    # heights of each node
    self.height = [None] * v

  def init(self):
    for i in range(self.v):
      self.parents[i] = i
      self.height[i] = 0

  def find(self, p):
    # finds the group containing p and return the position of its leader
    if self.parents[p] != p:
      self.parents[p] = self.find(self.parents[p])
    return self.parents[p]

  def union(self, p, q):
    parent_p = self.find(p)
    parent_q = self.find(q)

    if parent_p == parent_q: return

    if self.height[p] > self.height[q]:
      self.parents[q] = parent_p
    elif self.height[p] < self.height[q]:
      self.parents[p] = parent_q
    else:
      self.parents[parent_q] = parent_p
      self.height[p] += self.height[q]

  def same(self, p, q):
    return self.find(p) == self.find(q)

class Edge:
  def __init__(self, f, to, cost):
    self.f = f
    self.to = to
    self.cost = cost

  def __lt__(self, arg):
    return self.cost < arg.cost

n = int(input())
edges = []
for i in range(n):
  input_array = list(map(int, input().split()))
  for k in range(len(input_array)):
    if input_array[k] != -1:
      edges.append(Edge(i, k, input_array[k]))

union_find = UnionFind(n)
union_find.init()
edges.sort()

min_cost = 0
mst = []
while len(mst) < n-1:
  edge = edges.pop(0)
  if union_find.same(edge.f, edge.to) == False:
    min_cost += edge.cost
    union_find.union(edge.f, edge.to)
    mst.append(edge)

print(min_cost)

Submission status: Accepted

Solution code:
n = int(input())
primINF = 2000000000
matrix = []
numV = n
for i in range(n):
    matrix.append(list(map(int, input().split())))

visited = [False] * numV
cost = [primINF] * numV # cost
parent = [-1] * numV # parent node

cost[0] = 0
parent[0] = -1

while True:
    # 訪問済み隣接の最小コストのノードを探索する
    mincost = primINF
    for i in range(n):
        if visited[i] is False and cost[i] < mincost:
            mincost = cost[i]
            u = i
    # 見つからなければ終了する
    if mincost == primINF:
        break
    # 訪問済みにする
    visited[u] = True
    for v in range(n):
        if visited[v] is False and matrix[u][v] != -1:
            if matrix[u][v] < cost[v]:
                cost[v] = matrix[u][v]
                parent[v] = u
res = 0
for i in range(n):
    if parent[i] != -1:
        res += matrix[i][parent[i]]

print(res)

Submission status: Accepted

Solution code:
# input
n = int(input())
A = []
for _ in range(n):
    A.append(list(map(int, input().split())))
    
# 変数定義
inf = 100 * 2000 + 1
M = A.copy()
M = [[a if a > -1 else inf for a in line] for line in M]
d = [inf] * n
V = set([i for i in range(n)])
T = set()

# 探索
start = 0
target = start
d[target] = 0
T.add(target)
while V != T:
    for i in (V - T):
        if M[target][i] < d[i]:
            d[i] = M[target][i]

    min_wheght = min([d[i] for i in (V - T)])
    min_path = [i for i in (V - T) if d[i] == min_wheght][0]
    target = min_path
    T.add(target)

# 出力
print(sum(d))

Submission status: Accepted

Solution code:
def prim(n):
    inf=float("inf")
    D=[inf for i in range(n)]
    P=[0 for i in range(n)]
    M=[[inf for i in range(n)] for j in range(n)]
    color=["white" for i in range(n)]

    P[0]=-1
    D[0]=0

    for i in range(n):
        for j,num in enumerate(list(map(int,input().split()))):
            if num!=-1:
                M[i][j]=num

    while 1:
        cost,point=inf,0
        for i in range(n):
            if color[i]!="black" and D[i]<cost:
                cost=D[i]
                point=i

        if cost==inf:break

        color[point]="black"

        for i in range(n):
            if color[i]!="black" and M[point][i]!=inf:
                if M[point][i]<D[i]:
                    D[i]=M[point][i]
                    P[i]=point
                    color[i]="gray"

    return D


print(sum(prim(int(input()))))

Submission status: Accepted

Solution code:
inf = float("inf")
class Node():

    def __init__(self, _id):
        self.id = _id
        self.d = inf
        self.pi = None
        self.color = 0
    
    def input_data(self):
        data = [int(i) for i in input().split()]
        self.adj = {G[i]: d
                    for i, d in enumerate(data)
                    if d != -1}
    
    def __hash__(self):
        return hash(self.id)
        
    

def prim():
    G[0].d = 0
    while True:
        mincost = inf
        for i in G:
            if i.color != 1 and i.d < mincost:
                mincost = i.d
                u = i
        
        if mincost == inf:
            break

        u.color = 1
        for v in u.adj.keys():
            if v.color != 1 and u.adj[v] < v.d:
                v.pi = u.id
                v.d = u.adj[v]

if __name__ == "__main__":
    n = int(input())
    G = [Node(i) for i in range(n)]
    [i.input_data() for i in G]
    prim()
    print(sum(g.d for g in G))

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
'''
所要時間は、分位であった。
'''
# ライブラリのインポート
#import re #正規表現
import sys
#import heapq
import bisect
#import collections
#import math

def main():
    n = int(input())
    X = [[] for i in range(n)]
    l = []
    for i, line in enumerate(sys.stdin):
        X[i] = list(line.strip("\n").split())
        for j in range(i,n):
            c = int(X[i][j])
            if c == -1:
                continue
            else:
                r = (c,i,j)
                bisect.insort(l, r)
    
    uf = UnionFind(n)
    k = 0
    ans = 0
    count = 0
    while(count < n):
        try: tmp = l[k]
        except: break
        x = tmp[1]
        y = tmp[2]
        if not uf.same(x,y):
            uf.unite(x, y)
            ans += tmp[0] 
            count += 0
        k += 1
    print(ans)

class UnionFind:
    def __init__(self,n):
        self.p = [i for i in range(n)]
        return
    
    def root(self,x):
        while(1):
            if (self.p[x] == x): break
            y = x
            x = self.p[x]
            self.p[y] = self.p[x]
        return x

    def unite(self ,x, y):
        rx = self.root(x)
        ry = self.root(y)
        if rx == ry: return
        else:
            self.p[rx] = ry
            return 
    
    def same(self, x, y):
        rx = self.root(x)
        ry = self.root(y)
        return rx == ry


    
if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
from collections import deque

class Node:
    def __init__(self, val):
        self.val = val
        self.child = []

n = int(input())
g = []
# mst = [[] for _ in range(n)]
# mst = [None for _ in range(n)]

for i in range(n):
    g.append(list(map(int, input().split())))

# print(g)

for i in range(n):
    for j in range(n):
        if g[i][j] == -1:
            g[i][j] = 10**5

mst = Node(0)
# done = set()

def getClosestVertex(done):
    w = 10**10
    closest = None
    for i in done:
        for j in range(len(g[i])):
            if j in done:
                continue
            if g[i][j] < w:
                w = g[i][j]
                closest = j
    return closest, w

done = set()
done.add(0)
ans = 0

while True:
    closest, w = getClosestVertex(done)
    if closest is None:
        break
    else:
        done.add(closest)
        ans += w

print(ans)

Submission status: Accepted

Solution code:
# minimum_spanning_tree
def prim(adj_matrix, n):
    dist = [float("inf") for _ in range(n)]  # 訪問確定したノードからの最短距離
    visited = [False for _ in range(n)]  # ノードの訪問が確定したか
    parent = [-1 for _ in range(n)]  # start -> endを保存するためのstart？
    cost = 0
    inf = float("inf")

    start = 0
    visited[start] = True
    dist[start] = 0
    while True:
        # startから直接つながっている未訪問ノードをもとに、距離の最小値を更新する
        for end in range(n):
            if not visited[end] and adj_matrix[start][end] > -1 and adj_matrix[start][end] < dist[end]:
                dist[end] = adj_matrix[start][end]
                parent[end] = start

        min_cost = inf
        for nextnode in range(n):
            # dist_nodeの中から最もコストの短いノードを探す。そのノードは訪問確定。それを次回のstartとする。
            if not visited[nextnode] and dist[nextnode] < min_cost:
                min_cost = dist[nextnode]
                start = nextnode
        if min_cost == inf:
            break

        visited[start] = True
        cost += min_cost

    return parent, cost


def main():
    n = int(input())
    adj_matrix = []
    for _ in range(n):
        row = input().split()
        adj_matrix.append(list(map(int, row)))
    parent, cost = prim(adj_matrix, n)
    print(cost)


if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
M=[]
n=int(input())
for i in range(n):
	b=list(map(int,input().split()))
	M.append(b)
ans=0
from copy import copy
t=[0]
dis=copy(M[0])
dis[0]=10**12
for i in range(n):
	if dis[i]==-1:
		dis[i]=10**10
for i in range(n-1):
	p=10**10
	for j in range(n):
		if dis[j]<p:
			p=dis[j]
			q=j
	ans+=p
	t.append(q)
	dis[q]=10**12
	for j in range(n):
		if dis[j]>M[j][q] and M[j][q]!=-1 and dis[j]!=10**12:
			dis[j]=M[j][q]
print(ans)

Submission status: Accepted

Solution code:


WHITE = 0
GRAY = 1
BLACK = 2

INF = 2000000000

def prim():
    d[0] = 0
    p[0] = -1
    
    while True:
        mincost = INF
        for i in range(n):
            if color[i] != BLACK and d[i] < mincost:
                mincost = d[i]
                u = i
        if mincost == INF:
            break
        color[u] = BLACK
        
        for v in range(n):
            if color[v] != BLACK and m[u][v] != -1:
                if m[u][v] < d[v]:
                    d[v] = m[u][v]
                    p[v] = u
                    color[v] = GRAY
            

n = int(input())

m = [[0 for i in range(n)] for j in range(n)]
for i in range(n):
    nums=list(map(int,input().split()))
    for j in range(n):
        m[i][j] = nums[j]

color = [WHITE] * n
d = [INF] * n
p = [-1] * n


prim()

sum = 0
for i in range(n):
    sum += d[i]

print(sum)

Submission status: Accepted

Solution code:
n = int(input())
edges = [[-1 for i in range(n)] for j in range(n)]

for i in range(n):
  for index, j in enumerate(list(map(int, input().split()))):
    edges[i][index] = j

inf = 9999999999999999
distances = [inf] * n
colors = ["white"] * n

def mst(u):
  distances[u] = 0
  colors[u] = "gray"

  while True:
    mincost = inf
    for i in range(n):
      if colors[i] != "black" and distances[i] < mincost:
        mincost = distances[i]
        u = i

    if mincost == inf:
      break

    colors[u] = "black"

    for index, weight in enumerate(edges[u]):
      if weight != -1 and colors[index] != "black" and distances[index] > weight:
        distances[index] = weight
        colors[index] = "gray"

mst(0)
print(sum(distances))

Submission status: Accepted

Solution code:
import heapq
n = int(input())
ans = 0
cost = []
for i in range(n):
    L = list(map(int,input().split()))
    cost.append(L)
used = [False]*n
used[0] = True #島0から探索を始める。
edge = []
for i in range(n):
    T = []
    edge.append(T)
for i in range(n):
    for j in range(n):
        if cost[i][j] != -1:
            edge[i].append([cost[i][j],j])
P = edge[0]
P.sort()
while len(P) != 0:
    cur = heapq.heappop(P)
    d = cur[0]
    next = cur[1]
    if used[next] == True:
        continue
    used[next] = True
    ans += d
    for e in edge[next]:
        heapq.heappush(P,[e[0],e[1]])
print(ans)

Submission status: Accepted

Solution code:

def prim():
    global n, color, M, d, p
    d[0] = 0

    while True:
        min_cost = 10000000000
        u = -1

        # まず始点を決める。
        for i in range(n):
            if color[i] != 'BLACK' and d[i] < min_cost:
                min_cost = d[i]
                u = i  # エッジが繋がる中で、最小のもの？？

        if u == -1:
            break

        color[u] = 'BLACK'

        for v in range(n):
            if color[v] != 'BLACK' and M[u][v] != -1:
                if d[v] > M[u][v]:
                    d[v] = M[u][v]
                    p[v] = u
                    color[v] = 'GRAY'

    sum = 0
    for i in range(n):
        if p[i] != -1:
            sum += M[i][p[i]]

    return sum


n = int(input())

color = ['WHITE'] * n
M = []
d = [10000000000] * n  # 重みが最小の辺の重み
p = [-1] * n  # MSTにおけるp[v]の親（どこから来たか？？）

for i in range(n):
    _ = list(map(int, input().split()))
    M.append(_)
# print(A)

print(prim())

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
from operator import itemgetter
sys.setrecursionlimit(10000000)
INF = 10**30
M = []

def prim(G, root, n):
    BLACK = 1<<10
    WHITE = 1<<20
    nodes = [WHITE] * n
    d = [INF] * n
    d[root] = 0
    p = [0] * n
    p[root] = -1
    while True:
        mincost = INF

        # 探索
        for i in range(n):
            if d[i] < mincost and nodes[i] == WHITE:
                mincost = d[i]
                next = i
        if mincost == INF:
            break
        # 移動
        nodes[next] = BLACK

        # 伝播
        for i in range(n):
            if nodes[i] == WHITE and G[next][i] != INF:
                if G[next][i] < d[i]:
                    d[i] = G[next][i]
                    p[i] = next
    return d

def main():
    global M
    n = int(input().strip())
    M = [[0] * n for _ in range(n)]
    for i in range(n):
        M[i] = list(map(lambda x: INF if x == -1 else x, map(int, input().strip().split())))
    d = prim(M, 0, n)
    print(sum(d))

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
def main():
    N = int(input())
    c = [[int(i) for i in input().split()] for j in range(N)]
    edges = []
    for i in range(N):
        for j in range(i+1, N):
            if c[i][j] != -1:
                edges.append((c[i][j], (i, j)))
    edges.sort()

    par = [i for i in range(N)]
    rank = [0 for i in range(N)]

    def find_root(x):
        if par[x] == x:
            return x
        else:
            par[x] = find_root(par[x])
            return par[x]

    def is_same_group(x, y):
        return find_root(x) == find_root(y)

    def unite(x, y):
        x = find_root(x)
        y = find_root(y)
        if x == y:
            return
        if rank[x] < rank[y]:
            par[x] = y
        else:
            par[y] = x
            if rank[x] == rank[y]:
                rank[x] += 1

    ans = 0
    for c, e in edges:
        if find_root(e[0]) != find_root(e[1]):
            unite(e[0], e[1])
            ans += c
    print(ans)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
def kruskal(edges):
    edges.sort(key=lambda pair:pair[2])
    uf_tree = UnionFindTree(n_node)
    total_cost = 0
    for i, j, cost in edges:
        if cost < 0:
            continue

        if not uf_tree.have_same_root(i, j):
            uf_tree.unite(i, j)
            total_cost += cost
    return total_cost


class UnionFindTree:
    def __init__(self, n_node):
        self.parent = [i for i in range(n_node)]
        self.rank = [0] * n_node

    def find(self, x):
        if self.parent[x] != x:
            self.parent[x] = self.find(self.parent[x])
        return self.parent[x]

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

        if x != y:
            if self.rank[x] < self.rank[y]:
                self.parent[x] = y
            else:
                self.parent[y] = x
                if self.rank[x] == self.rank[y]:
                    self.rank[x] += 1

    def have_same_root(self, x, y):
        return self.find(x) == self.find(y)

if __name__ == "__main__":
    n_node = int((input()))
    edges = []
    for i in range(n_node):
        for j, cost in enumerate(map(int, input().split())):
            edges.append((i, j, cost))

    print(kruskal(edges))