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 = 100
INF = float('inf')
M = [[INF for _ in range(N)] for _ in range(N)]
n = 0
WHITE = 0
GRAY = 1
BLACK = 2
color = [WHITE for _ in range(N)]
d = [INF for _ in range(N)]
p = [0 for _ in range(N)]


def main():
    global N
    n = int(input())
    for i in range(n):
        a_s = list(map(int, input().split(' ')[1:]))
        for j in range(n):
            if a_s[j] != -1:
                M[i][j] = M[j][i] = a_s[j]
    print(prim(n))


def prim(n):
    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] < INF:
                if M[u][v] < d[v]:
                    d[v] = M[u][v]
                    p[v] = u
                    color[v] = GRAY
    return sum(d[:n])


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
# https://onlinejudge.u-aizu.ac.jp/courses/lesson/1/ALDS1/12/ALDS1_12_A
# 本よりこっちのほうがぶっちゃけわかりやすい http://www.deqnotes.net/acmicpc/prim/
# 螺旋本ではダイクストラとの違いをあまり解説していないが、違いはダイクストラのところで考えよう
# 記号は本に合わせる。
# 制約条件によりノードはたかだか100なのでオーダーを木にせずにナイーブに実装できる。本ではdを導入することにより計算量を少し削減している

INF = 10**5
# load data
N = int(input())
M = []  # 隣接行列
Color = []  # 訪問状態を記録 0:未訪問, 1:訪問経験あり, 2:訪問済み(用済み) #そうはこいつが2になっているノードはMST
D = []  # 本で言うd #こいつの役割はP299の図を追うとわかりやすい #MSTに隣接しているノードへのコストをノードのところに記録する
P = []  # 本で言うp # MSTにおける親を記録

for _ in range(N):
    Color.append(0)  # ノードはすべて未訪問
    D.append(INF)  # 無限で初期化しておく
    P.append(None)
    M.append([x if x != -1 else INF for x in map(int, input().split())])

# primのアルゴリズムを適応する
# ノード0からMSTを構築していく #まずはノード0をMSTに追加する
D[0] = 0
P[0] = None  # 親が存在しないことをNoneで示す

while True:  # MSTができるまで繰り返す ちなみにループの一周目は0をMSTに追加するところから始まる
    # MSTに隣接するノードへのpathの中で一番小さなコストを見つける、ついでにそのノード番号も
    min_cost = INF
    for i in range(N):
        if Color[i] != 2 and D[i] < min_cost:  # 訪問済みかつ最小値を更新したら
            min_cost = D[i]
            u = i  # uにはコストが一番小さい時のノードが追加される

    if min_cost == INF:
        break  # つながりがもうない

    Color[u] = 2  # つながるのに一番コストの小さい訪問済みに(MSTに追加)する

    for v in range(N):
        if Color[v] != 2 and M[u][v] != INF:  # MSTに追加されていなくてかつ、uとつながっている
            if M[u][v] < D[v]:  # 新たに追加したノードuからvに行くほうがコストが小さいならばそれをメモする
                D[v] = M[u][v]
                P[v] = u  # vの親の候補としてuを代入しておく(だいぶ無駄では？)
                Color[v] = 1  # 一度見たことあるのはgrayにしておくが、ぶっちゃけ意味はない

# これにてPに木構造が入ったのでこれをもとにコストを計算すれば良い
# ぶっちゃけこの操作は上のwhileに組み込み可能なんだけどあえてね
ans = 0
for i, p in enumerate(P[1:], start=1):
    ans += M[i][p]

print(ans)

Submission status: Accepted

Solution code:

INFINITY = 10 ** 10
WHITE = 0
GRAY = 1
BLACK = 2


n = int(input())
M = [[INFINITY] * n for _ in range(n)]

for i in range(n):
    for j, weight in enumerate(map(int, input().split())):
        if weight == -1:
            weight = INFINITY

        M[i][j] = weight


def prim():
    color = [WHITE] * n
    d = [INFINITY] * n
    p = [None] * n

    d[0] = 0
    p[0] = -1

    while True:
        cost_min = INFINITY
        for i in range(n):
            if color[i] != BLACK and d[i] < cost_min:
                cost_min = d[i]
                top_now = i

        if cost_min == INFINITY:
            break
    
        color[top_now] = BLACK

        for v in range(n):
            if color[v] == BLACK or M[top_now][v] == INFINITY:
                continue

            if M[top_now][v] < d[v]:
                d[v] = M[top_now][v]
                p[v] = top_now
                color[v] = GRAY

    return sum(d)

cost_min = prim()
print(cost_min)

Submission status: Accepted

Solution code:
from heapq import heappush, heappop, heapify

n = int(input())
G = [[] for _ in range(n)]

for i in range(n):
    for j,dist in enumerate(map(int,input().split())):
        if dist != -1:
            G[i].append((j,dist))
sum = 0

def prim(n):
    que = [(w,c) for c,w in G[0]]
    heapify(que)
    color = [0]*n
    color[0] = 1
    global sum
    while que:
        w,node = heappop(que)
        if color[node] == 1:
            continue
        color[node] = 1
        sum += w
        for x,y in G[node]:
            if color[x] == 1:
                continue
            heappush(que,(y,x))
    return sum

print(prim(n))

Submission status: Accepted

Solution code:
N = int(input())

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

vis = [False] * N
inf = 1e9
d = [inf] * N
d[0] = 0
cost = 0
for _ in range(N):
    nv, ni = inf, -1
    for i in range(N):
        if not vis[i] and d[i] < nv:
            nv, ni = d[i], i
    vis[ni] = True
    cost += nv
    for i in range(N):
        c = a[ni][i]
        if c > -1:
            d[i] = min(d[i], c)
print(cost)

Submission status: Accepted

Solution code:
INF = 10000

def prim():
	color = ["WHITE" for _ in range(n)]
	d = [INF for _ in range(n)]
	pi = [None for _ in range(n)]
	d[0] = 0

	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]
					pi[v] = u
					color[v] = "GRAY"
	sum = 0
	for u in range(n):
		if pi[u] != None:
			sum += M[u][pi[u]]
	return sum

if __name__ == "__main__":
	n = int(input())
	M = []
	for _ in range(n):
		M.append(list(map(int, input().split())))
	print(prim())

Submission status: Accepted

Solution code:
#ALDS1_12_A Minimum Spanning Tree
import sys


n = int(input())
G = []
for i in range(n):
    input_list = list(map(int, sys.stdin.readline().strip().split()))
    adj = [j if j != -1 else float('inf') for j in input_list]
    adj[i] = 0
    G.append(adj)

p = ['unexplored'] * n  # 親を保存するリスト
d = [float('inf')] * n  # 距離を保存するリスト

p[0] = 0
d[0] = 0
u = 0

for _ in range(n):
    mincost = float('inf')
    for i in range(n):
        if (p[i] == 'unexplored') & (d[i] < mincost):
            mincost = d[i]
            u = i  # u is child

    for i in range(n):
        if (p[i] != 'unexplored') & (G[i][u] == mincost):
            p[u] = i
            break
            
    for i in range(n):
        if G[u][i] < d[i]:
            d[i] = G[u][i]
    # print(p)

ans = 0
for i in range(1, n):
    ans += G[p[i]][i]
print(ans)

Submission status: Accepted

Solution code:
import heapq

def make_adj_list(v):
    adj_list = [[-1 for i in range(v)] for j in range(v)]
    return adj_list

def prim(adj_list, v, s):
    # スタートを0とする
    min_d = 0
    heap = []
    used = []
    for i in range(v):
        used.append(False)
    used[s] = True
    for i in range(v):
        if adj_list[s][i] != -1:
            heapq.heappush(heap, (adj_list[s][i], i))
        #　スタートからつなぐことができる辺をheapに入れる

    while len(heap) != 0:
        cost, to = heapq.heappop(heap)
        if used[to]:
            continue
        min_d += cost
        used[to] = True
        for i in range(v):
            if adj_list[to][i] != -1:
                heapq.heappush(heap, (adj_list[to][i], i)) 
            #集合に入れた頂点からつなぐことができる辺をheapに入れる

    return min_d

def main():
    v = int(input())
    adj_list = make_adj_list(v)
    for i in range(v):
        adj_list[i] = [int(j) for j in input().split()]
    min_d = prim(adj_list, v, 0)
    print(min_d)

if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
N = int(input())
M = [list(map(int, input().split())) for i in range(N)]
INF = 2001
MAX = 100
d = [INF for i in range(N)]
d[0] = 0
p = [MAX for i in range(N)]
p[0] = -1
mst = [False for i in range(N)]

while True:
  min_w = INF
  for i in range(N):
    if not mst[i] and d[i] < min_w:
      min_w = d[i]
      u = i
  if min_w == INF:
    break
  mst[u] = True
  for v in range(N):
    if not mst[v] and M[u][v] != -1:
      if M[u][v] < d[v]:
        d[v] = M[u][v]
        p[v] = u

print(sum(d))

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
INF = 100100

def prim(n: int, M: list):
    ans = 0
    visited = [False] * n
    d = [INF] * n
    p = [-1] * n
    d[0] = 0
    while True:
        mincost = INF
        for i in range(n):
            if not visited[i] and d[i] < mincost:
                mincost = d[i]
                u = i
        if mincost == INF:
            break
        ans += mincost
        visited[u] = True
        for v in range(n):
            if not visited[v] and M[u][v] != -1:
                if M[u][v] < d[v]:
                    d[v] = M[u][v]
                    p[v] = u
    return ans

def main():
    n = int(input())
    M = []
    for _ in range(n):
        Mi = list(map(int, input().split()))
        M.append(Mi)
    ans = prim(n,M)
    print(ans)

if __name__ == '__main__': main()

Submission status: Accepted

Solution code:
from heapq import heappush, heappop

def search(v, u):
    while v != root[v]: v = root[v]
    while u != root[u]: u = root[u]
    
    return v, u

def rebuild(v, u, r):
    while v != root[v]: v, root[v] = root[v], r
    while u != root[u]: u, root[u] = root[u], r
    return v, u

n = int(input())
root = [i for i in range(n)]
depth = [1] * n

q = []

for i in range(n):
    for j, c in enumerate(list(map(int, input().split()))):
        if c == -1: continue
        heappush(q, (c, i, j))
        
ans = 0

while q:
    c, v, u = heappop(q)
    
    v_r, u_r = search(v, u)
    if v_r == u_r: continue
    
    ans += c
    
    v_d, u_d = depth[v_r], depth[u_r]
    if v_d == u_d:
        depth[v_r] += 1
        if depth[v_r] > 10: rebuild(v, u, v_r)
        
    elif v_d < u_d: v_r, u_r = u_r, v_r
    
    root[v_r] = u_r
    
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
a = []
lrg = 2000000
for i in range(n):
    tmp = list(map(int, input().split( )))
    for j in range(n):
        if tmp[j] == -1:
            tmp[j] = lrg
    a.append(tmp)
#for i in range(n):
#    print(*a[i])
V = [0]
T = []
weight = 0

while len(V)<n:
    mn = lrg-1###forの外
    tmp = -1###forの外
    for v in V:
        for i in range(n):
            if i not in V and mn>a[v][i]:
                mn = a[v][i]
                tmp = i
    weight += mn
    #print(v,[v,tmp])
    V.append(tmp)
    #print(*V)

print(weight)

Submission status: Accepted

Solution code:
import heapq


def prim(adj):
    INF = 3000
    n = len(adj)
    state, d, p = [False] * n, [INF] * n, [-1] * n
    d[0] = 0
    pq = [(d[0], 0)]
    while pq:
        f, u = heapq.heappop(pq)
        state[u] = True
        if d[u] < f:
            continue
        for v, c in adj[u]:
            if state[v]:
                continue
            if c < d[v]:
                d[v] = c
                p[v] = u
                heapq.heappush(pq, (d[v], v))
    return d


def adj_matrix_to_list(matrix):
    n = len(matrix)
    li = [[] for _ in range(n)]
    for u in range(n):
        for v in range(n):
            if matrix[u][v] != -1:
                li[u].append((v, matrix[u][v]))
    return li


def main():
    n = int(input())
    m = [list(map(int, input().split())) for _ in range(n)]
    adj = adj_matrix_to_list(m)
    print(sum(prim(adj)))


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
from heapq import heappush, heappop, heapify
from typing import List, Tuple


if __name__ == "__main__":
    num_vertices = int(input())
    adj_list: List[List[Tuple[int, int]]] = [[] for _ in range(num_vertices)]

    for vertex in range(num_vertices):
        for adj, cost in enumerate(map(lambda x: int(x), input().split())):
            if -1 != cost:
                # Store values as (cost, adj) to aplly heapify to cost values.
                adj_list[vertex].append((cost, adj))

    visited: List[bool] = [False] * num_vertices
    # Set the root node.
    que = [(cost, adj) for cost, adj in adj_list[0]]
    visited[0] = True
    heapify(que)

    total_cost = 0
    while [] != que:
        cost, adj = heappop(que)
        if visited[adj]:
            continue
        visited[adj] = True
        total_cost += cost
        for n_cost, n_adj in adj_list[adj]:
            if visited[n_adj]:
                continue
            heappush(que, (n_cost, n_adj))

    print(total_cost)

Submission status: Accepted

Solution code:
WHITE = 0
GRAY = 1
BLACK = 2

INF = 1.0e+6

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

    d[0] = 0

    while True:
        minv = INF
        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] != INF:
                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


if __name__ == "__main__":
    n = int(input())

    M = [] * n

    for i in range(n):
        M.append(list(map(int, input().split())))
        M[i] = [INF if j == -1 else j for j in M[i]]

    print(prim(M))

Submission status: Accepted

Solution code:
INFINITY = 10 ** 10
WHITE = 0
GRAY = 1
BLACK = 2


n = int(input())
M = [[INFINITY] * n for _ in range(n)]

for i in range(n):
    for j, weight in enumerate(map(int, input().split())):
        if weight == -1:
            weight = INFINITY

        M[i][j] = weight


def prim():
    color = [WHITE] * n
    d = [INFINITY] * n
    p = [None] * n

    d[0] = 0
    p[0] = -1

    while True:
        cost_min = INFINITY
        for i in range(n):
            if color[i] != BLACK and d[i] < cost_min:
                cost_min = d[i]
                top_now = i

        if cost_min == INFINITY:
            break
    
        color[top_now] = BLACK

        for v in range(n):
            if color[v] == BLACK or M[top_now][v] == INFINITY:
                continue

            if M[top_now][v] < d[v]:
                d[v] = M[top_now][v]
                p[v] = top_now
                color[v] = GRAY

    return sum(d)

cost_min = prim()
print(cost_min)

Submission status: Accepted

Solution code:
def root(x):
    path_to_root = []
    while x != P[x]:
        path_to_root.append(x)
        x = P[x]
    for node in path_to_root:
        P[node]=x
    return x

def unite(x,y):
    P[root(x)] = root(y)

def is_same_set(x,y):
    return root(x) == root(y)

n = int(input())
P = [i for i in range(n)]
length=[]
points=[]
for i in range(n):
    length.append(list(map(int,input().split())))
for i in range(n):
    for j in range(i,n):
        if length[i][j] != -1:
            points.append((i,j,length[i][j]))
	
points.sort(key=lambda x:x[2])

totalweight = 0
for p in points:
    i,j,w = p
    if not is_same_set(i,j):
       totalweight += w
       unite(i,j)

print(totalweight)

Submission status: Accepted

Solution code:
def main():
     def root(x):
          path=[]
          while x!=P[x]:
               path.append(x)
               x=P[x]
          for i in path:
               P[i]=x
          return x
     
     def is_same_set(x,y):
          return root(x)==root(y)
     
     def unite(x,y):
          P[root(x)]=root(y)
     
     n=int(input())
     P=[i for i in range(n)]
     edge_CostAndVertex=[]
     for i in range(n):
          cost=list(map(int,input().split()))
          for j in range(i):
               if cost[j]!=-1:
                    edge_CostAndVertex.append([cost[j],[i,j]])
                    
     edge_CostAndVertex.sort(key=lambda x:x[0])
     ans=0
     check=[]#連結されている頂点
     main_edge=edge_CostAndVertex[0][1][0]
     for i in edge_CostAndVertex:
          cost_i,a,b=i[0],i[1][0],i[1][1]
          if is_same_set(a,b):
               continue
          else:

               unite(a,b)
               ans+=cost_i
               if a not in check:
                    check.append(a)
               if b not in check:
                    check.append(b)
               if len(check)==n:
                    flag=1
                    for i in range(n):
                         for j in range(i):
                              if is_same_set(i,j):
                                   continue
                              else:
                                   flag=0
                                   break
                    if flag==1:
                         break
                    
     print(ans)
                    
if __name__=='__main__':
     main()

Submission status: Accepted

Solution code:
import itertools

n = int(input())
A = [list(map(int, input().strip().split(' '))) for _ in range(n)]
uvc = [] # A list of tuples of start, end, and cost
for i in range(n-1):
    for j in range(i+1, n):
        if A[i][j] >= 0:
            uvc.append((i, j, A[i][j]))

# コストでソート
uvc.sort(key=lambda x: x[2])

uf = list(range(n))

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

def union(x, y):
    global uf
    uf[find_root(x)] = find_root(y)

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

def costs():
    global uvc
    for u, v, c in uvc:
        if not is_same_set(u, v):
            union(u, v)
            yield c
print(sum(itertools.islice(costs(), n - 1)))

Submission status: Accepted

Solution code:
N = int(input())
color = ["w" for _ in range(N)]
d = [float("inf") for _ in range(N)]
p = [-1 for _ in range(N)]

# Make M
M = [list(map(int, input().split())) for _ in range(N)]

d[0] = 0
while True:
    mincost = float("inf")
    for i in range(N):
        if color[i] != "b" and d[i] < mincost:
            mincost = d[i]
            u = i
    
    if mincost == float("inf"):
        break
    color[u] = "b"

    for v in range(N):
        if color[v] != "b" and M[u][v] != -1:
            if d[v] > M[u][v]:
                d[v] = M[u][v]
                p[v] = u

s = 0 
for i in range(1, N):
    s += M[i][p[i]]
print(s)

Submission status: Accepted

Solution code:
n=int(input())
matrix=[list(map(int,input().split())) for _ in range(n)]
weight=[]
for x in range(n):
    for y in range(x,n):
        if matrix[x][y]>=0: weight.append((x,y,matrix[x][y]))
weight.sort(key=lambda x:x[2])
ans=0
p=[i for i in range(n)]

def root(x):
    path_to_root=[]
    while p[x]!=x:
        path_to_root.append(x)
        x=p[x]
    for node in path_to_root:
        p[node]=x
    return x
    
def is_same_set(x,y):
    return root(x)==root(y)
    
def unite(x,y):
    p[root(x)]=root(y)
        
for x,y,w in weight:
    if not is_same_set(x,y):
        unite(x,y)
        ans+=w
print(ans)

Submission status: Accepted

Solution code:
def root(x):
    path = []
    while P[x] != x:
        path.append(x)
        x = P[x]
    for node in path:
        P[node] = x
    return x
def check(x,y):
    if root(x) == root(y):
        return 1
    else:
        return 0
def unite(x,y):
    P[root(x)] = root(y)        

n = int(input())
P = [i for i in range(n)]
omomi = []
for k in range(n):
    s = list(map(int,input().split()))
    for l in range(n):
        if s[l] != -1:
            omomi.append([s[l],k,l])
omomi.sort()
ans = 0
for yee in range(len(omomi)):
    if check(omomi[yee][1],omomi[yee][2]) == False:
            unite(omomi[yee][1],omomi[yee][2])
            ans+=omomi[yee][0]
print(ans)

Submission status: Accepted

Solution code:
n = int(input())

A = []
# A = [[] for _ in range(n)]

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

max_d = 2001

flag = [0] * n
d = [max_d] * n
d[0] = 0
p = [-1] * n

while True:
    min_d = max_d
    for i in range(n):
        if flag[i] == 0 and d[i] < min_d:
            min_d = d[i]
            u = i
    
    if min_d == max_d:
        break
    
    flag[u] = 1
    
    for i in range(n):
        if flag[i] == 0 and A[u][i] >= 0:
            if d[i] > A[u][i]:
                d[i] = A[u][i]
                p[i] = u

print(sum(d))

Submission status: Accepted

Solution code:
n = int(input())
A = []
for ni in range(n):
    tmp = [int(i) for i in input().split()]
    A.append([[i, t] for i, t in enumerate(tmp) if t != -1])

INF = 2001
V = [i for i in range(n)]
T = [0]
ans = 0
while len(T) != n:
    w = [-1, INF]
    for t in T:
        for a in A[t]:
            if a[1] < w[1]:
                w = a
                p = t
    ans += w[1]
    T.append(w[0])
    for ni in range(n):
        for i in range(len(A[ni])):
            if w[0] == A[ni][i][0]:
                del A[ni][i]
                break
    for ni in range(n):
        for i in range(len(A[ni])):
            if A[ni][i][0] == p:
                del A[ni][i]
                break

print(ans)

Submission status: Accepted

Solution code:
import sys
from collections import deque

sys.setrecursionlimit(1000000)
n = int(input())
graph = [[] for _ in range(n)]

global visited 
visited = [0 for _ in range(n)]
global Q, S, T

S = [0] #訪れた順
T = []
visited[0] = 1 #開始位置はすでに訪れたことにする

def input_graph(n):
  for i in range(n):
    vs = list(map(int, input().split()))
    graph[i] = vs
    """for j in range(n):
      if vs[j] != -1:
        tree[i].append([j, vs[j]])"""

def prim():
  global S
  cost = 0
  while len(S) < n:
    max_e = 3000
    ad_v = 0
    ad_list = []
    for s in S:
      for j in range(n):
        if graph[s][j] != -1 and j not in S:
          ad_list.append(graph[s][j])
          #print("s: ",s, " j: ",j, graph[s][j])
          if max_e > graph[s][j]:
            max_e = graph[s][j]
            ad_v = j
    S.append(ad_v)
    cost += max_e
  print(cost)
  

if __name__ == "__main__":
  input_graph(n)
  prim()

Submission status: Accepted

Solution code:
def prim(n):
    d[0] = 0
    while True:
        cost_min = 10**9
        u = -1
        for i in range(n):
            weight = d[i]
            if flag_list[i] < 2 and weight < cost_min:
                u = i
                cost_min = weight
        if u == -1:
            break
        flag_list[u] = 2
        for v in range(n):
            edge = m[u][v]
            if flag_list[v] < 2 and edge > -1:
                if d[v] > edge:
                    d[v] = edge
                    p[v] = u
                    flag_list[v] = 1
    cnt = 0
    for i in range(n):
        if p[i] != -1:
            cnt += m[i][p[i]]
    return cnt


if __name__ == "__main__":
    n = int(input())
    m = []
    for _ in range(n):
        in_list = list(map(int, input().split()))
        m.append(in_list)

    flag_list = [0]*n # 0: 未到達, 1: 処理中, 2: 完了
    d = [10**9]*n
    p = [-1]*n
    print(prim(n))

Submission status: Accepted

Solution code:
n = int(input())
#簡単のため、プリム法で回答する
data = []
for _ in range(n):
    line = list(map(int,input()[1:].split(' ')))
    for i in range(len(line)):
        if line[i] == -1:
            line[i] = 2001
    data.append(line)

been = [0]
unBeen = []
count = 0
while True:
    minIndex = [0,0]
    min = 2001
    for ele in been:
        for i in range(len(data[ele])):
            if min > data[ele][i] and not i in been:
                min = data[ele][i]
                minIndex = [ele,i]

    count += data[minIndex[0]][minIndex[1]]
    data[minIndex[0]][minIndex[1]] = 2001
    data[minIndex[1]][minIndex[0]] = 2001
    been.append(minIndex[1])
    if len(been) == n:
        break

print(count)

Submission status: Accepted

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

WHITE = 0
GREY = 1
BLACK = 2
INFTY = 10**10

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


def prim():
    # すべての頂点u について color[u] をwhiteとして、d[u]をINFINITYへ
    d[0] = 0
    p[0] = -1  # 親なし

    while True:
        mincost = INFTY
        for i in range(0, n):
            if color[i] != BLACK and d[i] < mincost:
                # まだ未訪問でコストが最小になるところを探す。
                # WHITEなところはd[i]=INFTYなので来ない
                mincost = d[i]
                # 最小コストになる場所を見つける
                u = i
                # 訪れる場所を決定
        if mincost == INFTY:
            break

        color[u] = BLACK
        # 起点座標の決定

        for v in range(0, n):
            if color[v] != BLACK and M[u][v] != -1:
                if M[u][v] < d[v]:
                    # 最初コストになるノードを探索
                    d[v] = M[u][v]
                    p[v] = u
                    color[v] = GREY


prim()
print(sum(d))

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
"""
Created on Sat Apr  6 18:01:32 2019

@author: Yamazaki Kenichi
"""

n = int(input())
A = [list(map(int,input().split())) for i in range(n)]
INFTY = 10**6
T = [-1 for i in range(n)]
d = [INFTY for i in range(n)]
p = [0 for i in range(n)]
d[0], p[0] = 0, -1
for j in range(n):
    mincost = 10**6
    for i in range(n):
        if T[i] != 1 and d[i] < mincost:
            mincost = d[i]
            u = i
    T[u] = 1
    for v in range(n):
        if T[v] != 1 and A[u][v] != -1:
            if A[u][v] < d[v]:
                d[v] = A[u][v]
                p[v] = u
                T[v] = 0
print(sum(d))

Submission status: Accepted

Solution code:
n = int(input())
g = [[] for i in range(n)]
for i in range(n):
    *v, = map(int, input().split())
    for j in range(n):
        if v[j] < 0:
            v[j] = 10000
    g[i] = v

ans = 0
t = [0]
v = [i for i in range(1, n)]
while len(t) < n:
    u = [2000, 0, 0]
    for tv in t:
        for vv in v:
            if g[tv][vv] < u[0]:
                u = [g[tv][vv], tv, vv]
    ans += u[0]
    t.append(u[2])
    v.remove(u[2])
print(ans)

Submission status: Accepted

Solution code:
#minimum spaning tree

n = int(input())
a = [list(map(int, input().split())) for _ in range(n)]
d = [0] + [1e4]*(n-1)
color = [0]*n

# break = 1 ; glay = 2
while 1:
    mincost = pow(10, 4)
    for i in range(n):
        if color[i] != 1 and d[i] < mincost:mincost = d[i];min_key = i
    if mincost == pow(10,4):
        break
    
    color[min_key] = 1
    
    for i in range(n):
        if color[i] != 1 and a[min_key][i] != -1 and d[i] > a[min_key][i]:
            d[i] = a[min_key][i]
            color[i] = 2
#             parent[i] = min_key
print(f"{sum(d)}")

Submission status: Accepted

Solution code:
N = int(input())
L = []  # input


def prim():
    # 頂点を適当に選ぶ
    s = None
    for i in range(N):
        for j in range(N):
            if L[i][j] != -1:
                s = i
                break
        if s is not None:
            break
    p = {s}
    T = []
    k = 0
    while k < N - 1:
        # 最終のP内で一番短いやつを加える
        len = float("inf")
        lenside = []
        for sg in p:
            for i in range(N):
                isT = False
                for t in T:
                    if (t[0] == sg and t[1] == i) or (t[0] == i and t[1] == sg):
                        # print("ignore")
                        isT = True
                        continue
                if isT is False and i not in p and L[sg][i] != -1 and L[sg][i] < len:
                    len = L[sg][i]
                    lenside = [sg, i]

        p.add(lenside[0])
        p.add(lenside[1])
        T.append(lenside)
        k = k + 1
        #print(p,T,k)
    cnt = 0
    for t in T:
        cnt += L[t[0]][t[1]]
    print(cnt)


for i in range(N):
    L.append(list(map(int, input().split())))
prim()

Submission status: Accepted

Solution code:
n = int(input())
M = [list(map(int, input().split())) for _ in range(n)]
INF = 100000000000
color = ['White']*n
d = [INF]*n
p = [-1]*n
d[0] = 0
sum = 0

while True:
    minct = INF
    u = -1
    for i in range(n):
        if color[i] != 'Black' and d[i] < minct:
            minct = d[i]
            u = i
    if minct == INF:
        break
    color[u] = 'Black'
    for j in range(n):
        if color[j] != 'Black' and M[u][j] != -1:
            if M[u][j] < d[j]:
                d[j] = M[u][j]
                p[j] = u
                color[j] = 'Gray'
for k in range(n):
    if p[k] != -1:
        sum += M[k][p[k]]
print(sum)

Submission status: Accepted

Solution code:
import sys

n = int(sys.stdin.readline())
g = [list(map(int, sys.stdin.readline().split())) for _ in range(n)]

V = set(range(n))
U = set()
E = []

U.add(V.pop())

while len(U)<n:
    minw = 1e10
    mine = []
    for u in U:
        for v in V:
            if g[u][v]>=0 and minw>g[u][v]:
                minw = g[u][v]
                mine = [u, v]
    E.append(mine)
    U.add(mine[1])
    V.remove(mine[1])

vv=0
for u, v in E:
    vv += g[u][v]
print(vv)

Submission status: Accepted

Solution code:
import heapq
from collections import deque
from enum import Enum
import sys
import math
from _heapq import heappush, heappop

BIG_NUM = 2000000000
MOD = 1000000007
EPS = 0.000000001


class UnionFind:
    def __init__(self,arg_V):
        self.V = arg_V
        self.boss = [None]*arg_V
        self.height = [None]*arg_V

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

    def get_boss(self,index):
        if index == self.boss[index]:
            return index
        else:
            self.boss[index] = self.get_boss(self.boss[index])
            return self.boss[index]


    def is_same_group(self,a,b):
        return self.get_boss(a) == self.get_boss(b)

    def unite(self,x,y):
        boss_x = self.get_boss(x)
        boss_y = self.get_boss(y)

        if boss_x == boss_y:
            return

        if self.height[x] > self.height[y]:

            self.boss[boss_y] = boss_x

        elif self.height[x] < self.height[y]:

            self.boss[boss_x] = boss_y

        else:
            self.boss[boss_y] = boss_x
            self.height[x] += 1

class Edge:
    def __init__(self,arg_FROM,arg_TO,arg_WEIGHT):
        self.FROM = arg_FROM
        self.TO = arg_TO
        self.WEIGHT = arg_WEIGHT

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


V = int(input())

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

UF = UnionFind(V)
UF.init()

TABLE.sort()

ans = 0

for i in range(len(TABLE)):
    if UF.is_same_group(TABLE[i].FROM, TABLE[i].TO) == False:
        UF.unite(TABLE[i].FROM, TABLE[i].TO)
        ans += TABLE[i].WEIGHT

print("%d"%(ans))