Buggy python submission (verdict: Time Limit Exceeded):
import heapq
class Graph:
    def __init__(self,v,edgelist,w_v = None,directed = False):
        super().__init__()
        self.v = v
        self.w_e = [{} for _ in [0]*self.v]
        self.neighbor = [[] for _ in [0]*self.v]
        self.w_v = w_v
        self.directed = directed

        for i,j,w in edgelist:
            self.w_e[i][j] = w
            self.neighbor[i].append(j)

    def dijkstra(self,v_n):
        d = [float('inf')]*self.v
        d[v_n] = 0
        prev = [-1]*self.v

        queue = []
        for i,d_i in enumerate(d): heapq.heappush(queue,(d_i,i))
        
        while len(queue)>0:
            d_u,u = queue.pop()
            if d[u]<d_u :continue
            for v in self.neighbor[u]:
                alt = d[u]+self.w_e[u][v]
                if d[v]>alt:
                    d[v] = alt
                    prev[v] = u
                    heapq.heappush(queue,(alt,v))

        return d,prev

    def warshallFloyd(self):
        d = [[10**18]*self.v for _ in [0]*self.v]
        for i in range(self.v):
            d[i][i] = 0
            
        for i in range(self.v):
            for j in self.neighbor[i]:
                d[i][j] = self.w_e[i][j]
            
        for i in range(self.v):
            for j in self.neighbor[i]:
                d[i][j] = self.w_e[i][j]
        
        for k in range(self.v):
            for i in range(self.v):
                for j in range(self.v):
                    check = d[i][k] + d[k][j]
                    if d[i][j] > check:
                        d[i][j] = check
        return d

    def prim(self):
        gb = GraphBuilder(self.v,self.directed)
        queue = []
        for i,w in self.w_e[0].items(): heapq.heappush(queue,(w,0,i))
        rest = [True]*self.v
        rest[0] = False

        v = 1
        while len(queue)>0:
            w,i,j = heapq.heappop(queue)
            if rest[j]:
                gb.addEdge(i,j,w)
                rest[j] = False
                for k,w in self.w_e[j].items():
                    if rest[k]:heapq.heappush(queue,(w,j,k))

        return gb

class Tree():
    def __init__(self,v,e):
        pass

class GraphBuilder():
    def __init__(self,v,directed = False):
        self.v = v
        self.directed = directed
        self.edge = []

    def addEdge(self,i,j,w=1):
        if not self.directed:
            self.edge.append((j,i,w))
        self.edge.append((i,j,w))

    def addEdges(self,edgelist,weight = True):
        if weight:
            if self.directed:
                for i,j,w in edgelist:
                    self.edge.append((i,j,w))
            else:
                for i,j,w in edgelist:
                    self.edge.append((i,j,w))
                    self.edge.append((j,i,w))
        else:
            if self.directed:
                for i,j,w in edgelist:
                    self.edge.append((i,j,1))
            else:
                for i,j,w in edgelist:
                    self.edge.append((i,j,1))
                    self.edge.append((j,i,1))
            

    def addAdjMat(self, mat):
        for i,mat_i in enumerate(mat):
            for j,w in enumerate(mat_i):
                self.edge.append((i,j,w))

    def buildTree(self):
        pass

    def buildGraph(self):
        return Graph(self.v,self.edge,directed=self.directed)

def main():

    n= int(input())
    edge = []
    for i in range(n):
      x,y = list(map(int,input().split()))
      edge.append((x,y,i))
    
    xs = sorted(edge,key=lambda a:a[0])
    ys = sorted(edge,key=lambda a:a[1])

    edge = []
    
    for i in range(n-1):
      x1,y1,p1 = xs[i]
      x2,y2,p2 = xs[i+1]
      edge.append((p1,p2,min(x2-x1,abs(y2-y1))))
      
      x1,y1,p1 = ys[i]
      x2,y2,p2 = ys[i+1]
      edge.append((p1,p2,min(abs(x2-x1),y2-y1)))
      
      
    gb = GraphBuilder(n)
    gb.addEdges(edge)

    mint = gb.buildGraph().prim()

    ans = 0
    for a in mint.edge:
      ans+=a[2]
    print(ans//2)
      
if __name__ == "__main__":
    main()


Fixed submission:
class UnionFind:
    def __init__(self,n):
        super().__init__()
        self.par = [-1]*n
        self.rank = [0]*n
        self.tsize = [1]*n
    
    def root(self,x):
        if self.par[x] == -1:
            return x 
        else:
            self.par[x] = self.root(self.par[x])
            return self.par[x]

    def unite(self, x, y):
        x_r = self.root(x)
        y_r = self.root(y)
        
        if self.rank[x_r]>self.rank[y_r]:
            self.par[y_r] = x_r

        elif self.rank[x_r]<self.rank[y_r]:
            self.par[x_r] = y_r

        elif x_r != y_r:
            self.par[y_r] = x_r
            self.rank[x_r] += 1

        if x_r != y_r:
            size = self.tsize[x_r]+self.tsize[y_r]
            self.tsize[x_r] = size
            self.tsize[y_r] = size

    def isSame(self,x,y):
        return self.root(x) == self.root(y)

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

def main():

    n= int(input())
    edge = []
    for i in range(n):
      x,y = list(map(int,input().split()))
      edge.append((x,y,i))
    
    xs = sorted(edge,key=lambda a:a[0])
    ys = sorted(edge,key=lambda a:a[1])

    edge = []
    
    for i in range(n-1):
      x1,y1,p1 = xs[i]
      x2,y2,p2 = xs[i+1]
      edge.append((p1,p2,min(x2-x1,abs(y2-y1))))
      
      x1,y1,p1 = ys[i]
      x2,y2,p2 = ys[i+1]
      edge.append((p1,p2,min(abs(x2-x1),y2-y1)))
    edge.sort(key = lambda a:a[2])  
    uf = UnionFind(n)
    
    ans = 0
    for x,y,w in edge:
      if uf.isSame(x,y):continue
      uf.unite(x,y)
      ans+=w
    print(ans)
      
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Runtime Error):
    def prim(self):
        gb = GraphBuilder(self.v,self.directed)

        queue = []
        for i,w in self.w_e[0].items(): heapq.heappush(queue,(w,0,i))
        rest = [True]*self.v
        rest[0] = False

        v = 1
        while len(queue)>0:
            w,i,j = heapq.heappop(queue)
            if rest[j]:
                gb.addEdge(i,j,w)
                rest[j] = False
                for k,w in self.w_e[j].items():
                    if rest[k]:heapq.heappush(queue,(w,j,k))

        return gb

Fixed submission:
class UnionFind:
    def __init__(self,n):
        super().__init__()
        self.par = [-1]*n
        self.rank = [0]*n
        self.tsize = [1]*n
    
    def root(self,x):
        if self.par[x] == -1:
            return x 
        else:
            self.par[x] = self.root(self.par[x])
            return self.par[x]

    def unite(self, x, y):
        x_r = self.root(x)
        y_r = self.root(y)
        
        if self.rank[x_r]>self.rank[y_r]:
            self.par[y_r] = x_r

        elif self.rank[x_r]<self.rank[y_r]:
            self.par[x_r] = y_r

        elif x_r != y_r:
            self.par[y_r] = x_r
            self.rank[x_r] += 1

        if x_r != y_r:
            size = self.tsize[x_r]+self.tsize[y_r]
            self.tsize[x_r] = size
            self.tsize[y_r] = size

    def isSame(self,x,y):
        return self.root(x) == self.root(y)

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

def main():

    n= int(input())
    edge = []
    for i in range(n):
      x,y = list(map(int,input().split()))
      edge.append((x,y,i))
    
    xs = sorted(edge,key=lambda a:a[0])
    ys = sorted(edge,key=lambda a:a[1])

    edge = []
    
    for i in range(n-1):
      x1,y1,p1 = xs[i]
      x2,y2,p2 = xs[i+1]
      edge.append((p1,p2,min(x2-x1,abs(y2-y1))))
      
      x1,y1,p1 = ys[i]
      x2,y2,p2 = ys[i+1]
      edge.append((p1,p2,min(abs(x2-x1),y2-y1)))
    edge.sort(key = lambda a:a[2])  
    uf = UnionFind(n)
    
    ans = 0
    for x,y,w in edge:
      if uf.isSame(x,y):continue
      uf.unite(x,y)
      ans+=w
    print(ans)
      
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import heapq
class Graph:
    def __init__(self,v,edgelist,w_v = None,directed = False):
        super().__init__()
        self.v = v
        self.w_e = [{} for _ in [0]*self.v]
        self.neighbor = [[] for _ in [0]*self.v]
        self.w_v = w_v
        self.directed = directed

        for i,j,w in edgelist:
            self.w_e[i][j] = w
            self.neighbor[i].append(j)

    def dijkstra(self,v_n):
        d = [float('inf')]*self.v
        d[v_n] = 0
        prev = [-1]*self.v

        queue = []
        for i,d_i in enumerate(d): heapq.heappush(queue,(d_i,i))
        
        while len(queue)>0:
            d_u,u = queue.pop()
            if d[u]<d_u :continue
            for v in self.neighbor[u]:
                alt = d[u]+self.w_e[u][v]
                if d[v]>alt:
                    d[v] = alt
                    prev[v] = u
                    heapq.heappush(queue,(alt,v))

        return d,prev

    def warshallFloyd(self):
        d = [[10**18]*self.v for _ in [0]*self.v]
        for i in range(self.v):
            d[i][i] = 0
            
        for i in range(self.v):
            for j in self.neighbor[i]:
                d[i][j] = self.w_e[i][j]
            
        for i in range(self.v):
            for j in self.neighbor[i]:
                d[i][j] = self.w_e[i][j]
        
        for k in range(self.v):
            for i in range(self.v):
                for j in range(self.v):
                    check = d[i][k] + d[k][j]
                    if d[i][j] > check:
                        d[i][j] = check
        return d

    def prim(self):
        gb = GraphBuilder(self.v,self.directed)

        queue = []
        for i,w in self.w_e[0].items(): heapq.heappush(queue,(w,0,i))
        rest = [True]*self.v
        rest[0] = False

        while len(queue)>0:
            w,i,j = heapq.heappop(queue)
            if rest[j]:
                gb.addEdge(i,j,w)
                rest[j] = False
                for k,w in self.w_e[j].items():
                    heapq.heappush(queue,(w,j,k))

        return gb

class Tree():
    def __init__(self,v,e):
        pass

class GraphBuilder():
    def __init__(self,v,directed = False):
        self.v = v
        self.directed = directed
        self.edge = []

    def addEdge(self,i,j,w=1):
        if not self.directed:
            self.edge.append((j,i,w))
        self.edge.append((i,j,w))

    def addEdges(self,edgelist,weight = True):
        if weight:
            if self.directed:
                for i,j,w in edgelist:
                    self.edge.append((i,j,w))
            else:
                for i,j,w in edgelist:
                    self.edge.append((i,j,w))
                    self.edge.append((j,i,w))
        else:
            if self.directed:
                for i,j,w in edgelist:
                    self.edge.append((i,j,1))
            else:
                for i,j,w in edgelist:
                    self.edge.append((i,j,1))
                    self.edge.append((j,i,1))
            

    def addAdjMat(self, mat):
        for i,mat_i in enumerate(mat):
            for j,w in enumerate(mat_i):
                self.edge.append((i,j,w))

    def buildTree(self):
        pass

    def buildGraph(self):
        return Graph(self.v,self.edge,directed=self.directed)

def main():

    n= int(input())
    edge = []
    for i in range(n):
      x,y = list(map(int,input().split()))
      edge.append((x,y,i))
    
    xs = sorted(edge,key=lambda a:a[0])
    ys = sorted(edge,key=lambda a:a[1])

    edge = []
    
    for i in range(n-1):
      x1,y1,p1 = xs[i]
      x2,y2,p2 = xs[i+1]
      edge.append((p1,p2,min(x2-x1,abs(y2-y1))))
      
      x1,y1,p1 = ys[i]
      x2,y2,p2 = ys[i+1]
      edge.append((p1,p2,min(abs(x2-x1),y2-y1)))
      
      
    gb = GraphBuilder(n)
    gb.addEdges(edge)

    mint = gb.buildGraph().prim()

    ans = 0
    for a in mint.edge:
      ans+=a[2]
    print(ans//2)
      
if __name__ == "__main__":
    main()

Fixed submission:
class UnionFind:
    def __init__(self,n):
        super().__init__()
        self.par = [-1]*n
        self.rank = [0]*n
        self.tsize = [1]*n
    
    def root(self,x):
        if self.par[x] == -1:
            return x 
        else:
            self.par[x] = self.root(self.par[x])
            return self.par[x]

    def unite(self, x, y):
        x_r = self.root(x)
        y_r = self.root(y)
        
        if self.rank[x_r]>self.rank[y_r]:
            self.par[y_r] = x_r

        elif self.rank[x_r]<self.rank[y_r]:
            self.par[x_r] = y_r

        elif x_r != y_r:
            self.par[y_r] = x_r
            self.rank[x_r] += 1

        if x_r != y_r:
            size = self.tsize[x_r]+self.tsize[y_r]
            self.tsize[x_r] = size
            self.tsize[y_r] = size

    def isSame(self,x,y):
        return self.root(x) == self.root(y)

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

def main():

    n= int(input())
    edge = []
    for i in range(n):
      x,y = list(map(int,input().split()))
      edge.append((x,y,i))
    
    xs = sorted(edge,key=lambda a:a[0])
    ys = sorted(edge,key=lambda a:a[1])

    edge = []
    
    for i in range(n-1):
      x1,y1,p1 = xs[i]
      x2,y2,p2 = xs[i+1]
      edge.append((p1,p2,min(x2-x1,abs(y2-y1))))
      
      x1,y1,p1 = ys[i]
      x2,y2,p2 = ys[i+1]
      edge.append((p1,p2,min(abs(x2-x1),y2-y1)))
    edge.sort(key = lambda a:a[2])  
    uf = UnionFind(n)
    
    ans = 0
    for x,y,w in edge:
      if uf.isSame(x,y):continue
      uf.unite(x,y)
      ans+=w
    print(ans)
      
if __name__ == "__main__":
    main()