Buggy python submission (verdict: Time Limit Exceeded):
import math,heapq,sys
input = sys.stdin.readline
xs,ys,xe,ye = map(int,input().split())
cs = [(xs,ys,0), (xe,ye,0)]
N = int(input())
for i in range(N):
    cs.append(tuple(map(int,input().split())))

def calc_cost(i,j):
    if i == j: return float('inf')
    x1,y1,r1 = cs[i]
    x2,y2,r2 = cs[j]
    cost = max(0, math.hypot(x1-x2,y1-y2) - r1 - r2)
    return cost

INF = float('inf')
direct = calc_cost(0,1)
hq = []
for i in range(1,N+2):
    c = calc_cost(0,i)
    if c > direct: continue
    hq.append((c,i))
heapq.heapify(hq)
visited = [1] + [0] * (N+1)
cost = [0] + [INF] * (N+1)
while hq:
    c,v = heapq.heappop(hq)
    if v == 1:
        print(c)
        exit()
    cost[v] = c
    visited[v] = 1
    for to in range(1,N+2):
        if to == v or visited[to]: continue
        newcost = calc_cost(v, to)
        if cost[to] <= cost[v] + newcost: continue
        if direct < cost[v] + newcost: continue
        heapq.heappush(hq, (cost[v] + newcost, to))

Fixed submission:
import math,heapq,sys
input = sys.stdin.readline
xs,ys,xe,ye = map(int,input().split())
cs = [(xs,ys,0), (xe,ye,0)]
N = int(input())
for i in range(N):
    cs.append(tuple(map(int,input().split())))

def calc_cost(i,j):
    if i == j: return float('inf')
    x1,y1,r1 = cs[i]
    x2,y2,r2 = cs[j]
    cost = max(0, math.hypot(x1-x2,y1-y2) - r1 - r2)
    return cost

INF = float('inf')
direct = calc_cost(0,1)
hq = []
for i in range(1,N+2):
    c = calc_cost(0,i)
    if c > direct: continue
    hq.append((c,i))
heapq.heapify(hq)
not_visited = set(range(1,N+2))
cost = [0] + [INF] * (N+1)
while hq:
    c,v = heapq.heappop(hq)
    if v not in not_visited: continue
    if v == 1:
        print(c)
        exit()
    cost[v] = c
    not_visited.remove(v)
    for to in not_visited:
        newcost = calc_cost(v, to)
        if cost[to] <= cost[v] + newcost: continue
        if direct < cost[v] + newcost: continue
        heapq.heappush(hq, (cost[v] + newcost, to))

Buggy python submission (verdict: Time Limit Exceeded):
import math
import heapq
xs,ys,xe,ye = map(int,input().split())
cs = [(xs,ys,0), (xe,ye,0)]
N = int(input())
for i in range(N):
    cs.append(tuple(map(int,input().split())))

def dist(x1,y1,x2,y2):
    dx,dy = x2-x1,y2-y1
    return math.sqrt(dx**2 + dy**2)

def calc_cost(i,j):
    if i == j: return float('inf')
    x1,y1,r1 = cs[i]
    x2,y2,r2 = cs[j]
    cost = max(0, dist(x1,y1,x2,y2) - r1 - r2)
    return cost

INF = float('inf')
direct = calc_cost(0,1)
hq = []
for i in range(1,N+2):
    c = calc_cost(0,i)
    if c > direct: continue
    hq.append((c,i))
heapq.heapify(hq)
visited = [1] + [0] * (N+1)
cost = [0] + [INF] * (N+1)
while hq:
    c,v = heapq.heappop(hq)
    if v == 1:
        print(c)
        exit()
    cost[v] = c
    visited[v] = 1
    for to in range(1,N+2):
        if to == v or visited[to]: continue
        newcost = calc_cost(v, to)
        if cost[to] <= cost[v] + newcost: continue
        if direct < cost[v] + newcost: continue
        heapq.heappush(hq, (cost[v] + newcost, to))

Fixed submission:
import math,heapq,sys
input = sys.stdin.readline
xs,ys,xe,ye = map(int,input().split())
cs = [(xs,ys,0), (xe,ye,0)]
N = int(input())
for i in range(N):
    cs.append(tuple(map(int,input().split())))

def calc_cost(i,j):
    if i == j: return float('inf')
    x1,y1,r1 = cs[i]
    x2,y2,r2 = cs[j]
    cost = max(0, math.hypot(x1-x2,y1-y2) - r1 - r2)
    return cost

INF = float('inf')
direct = calc_cost(0,1)
hq = []
for i in range(1,N+2):
    c = calc_cost(0,i)
    if c > direct: continue
    hq.append((c,i))
heapq.heapify(hq)
not_visited = set(range(1,N+2))
cost = [0] + [INF] * (N+1)
while hq:
    c,v = heapq.heappop(hq)
    if v not in not_visited: continue
    if v == 1:
        print(c)
        exit()
    cost[v] = c
    not_visited.remove(v)
    for to in not_visited:
        newcost = calc_cost(v, to)
        if cost[to] <= cost[v] + newcost: continue
        if direct < cost[v] + newcost: continue
        heapq.heappush(hq, (cost[v] + newcost, to))

Buggy python submission (verdict: Time Limit Exceeded):
import math
import heapq
xs,ys,xe,ye = map(int,input().split())
cs = [(xs,ys,0), (xe,ye,0)]
N = int(input())
for i in range(N):
    cs.append(tuple(map(int,input().split())))

def dist(x1,y1,x2,y2):
    dx,dy = x2-x1,y2-y1
    return math.sqrt(dx**2 + dy**2)

def calc_cost(i,j):
    if i == j: return float('inf')
    x1,y1,r1 = cs[i]
    x2,y2,r2 = cs[j]
    cost = max(0, dist(x1,y1,x2,y2) - r1 - r2)
    return cost

INF = float('inf')
direct = calc_cost(0,1)
hq = []
for i in range(1,N+2):
    c = calc_cost(0,i)
    if c > direct: continue
    hq.append((c,i))
heapq.heapify(hq)
visited = [1] + [0] * (N+1)
cost = [0] + [INF] * (N+1)
while hq:
    c,v = heapq.heappop(hq)
    if v == 1:
        print(c)
        exit()
    cost[v] = c
    visited[v] = 1
    for to in range(1,N+2):
        if to == v or visited[to]: continue
        newcost = calc_cost(v, to)
        if cost[to] <= cost[v] + newcost: continue
        if direct < cost[v] + newcost: continue
        heapq.heappush(hq, (cost[v] + newcost, to))


Fixed submission:
import math,heapq,sys
input = sys.stdin.readline
xs,ys,xe,ye = map(int,input().split())
cs = [(xs,ys,0), (xe,ye,0)]
N = int(input())
for i in range(N):
    cs.append(tuple(map(int,input().split())))

def calc_cost(i,j):
    if i == j: return float('inf')
    x1,y1,r1 = cs[i]
    x2,y2,r2 = cs[j]
    cost = max(0, math.hypot(x1-x2,y1-y2) - r1 - r2)
    return cost

INF = float('inf')
direct = calc_cost(0,1)
hq = []
for i in range(1,N+2):
    c = calc_cost(0,i)
    if c > direct: continue
    hq.append((c,i))
heapq.heapify(hq)
not_visited = set(range(1,N+2))
cost = [0] + [INF] * (N+1)
while hq:
    c,v = heapq.heappop(hq)
    if v not in not_visited: continue
    if v == 1:
        print(c)
        exit()
    cost[v] = c
    not_visited.remove(v)
    for to in not_visited:
        newcost = calc_cost(v, to)
        if cost[to] <= cost[v] + newcost: continue
        if direct < cost[v] + newcost: continue
        heapq.heappush(hq, (cost[v] + newcost, to))

Buggy python submission (verdict: Time Limit Exceeded):
import math
import heapq
xs,ys,xe,ye = map(int,input().split())
cs = [(xs,ys,0), (xe,ye,0)]
N = int(input())
for i in range(N):
    cs.append(tuple(map(int,input().split())))

def dist(x1,y1,x2,y2):
    dx,dy = x2-x1,y2-y1
    return math.sqrt(dx**2 + dy**2)

def calc_cost(i,j):
    if i == j: return float('inf')
    x1,y1,r1 = cs[i]
    x2,y2,r2 = cs[j]
    cost = max(0, dist(x1,y1,x2,y2) - r1 - r2)
    return cost

INF = float('inf')
hq = [(calc_cost(0,i),i) for i in range(1,N+2)]
heapq.heapify(hq)
visited = [1] + [0] * (N+1)
cost = [0] + [INF] * (N+1)
while hq:
    c,v = heapq.heappop(hq)
    if v == 1:
        print(c)
        exit()
    cost[v] = c
    visited[v] = 1
    for to in range(1,N+2):
        if to == v or visited[to]: continue
        newcost = calc_cost(v, to)
        if cost[to] <= cost[v] + newcost: continue
        heapq.heappush(hq, (cost[v] + newcost, to))


Fixed submission:
import math,heapq,sys
input = sys.stdin.readline
xs,ys,xe,ye = map(int,input().split())
cs = [(xs,ys,0), (xe,ye,0)]
N = int(input())
for i in range(N):
    cs.append(tuple(map(int,input().split())))

def calc_cost(i,j):
    if i == j: return float('inf')
    x1,y1,r1 = cs[i]
    x2,y2,r2 = cs[j]
    cost = max(0, math.hypot(x1-x2,y1-y2) - r1 - r2)
    return cost

INF = float('inf')
direct = calc_cost(0,1)
hq = []
for i in range(1,N+2):
    c = calc_cost(0,i)
    if c > direct: continue
    hq.append((c,i))
heapq.heapify(hq)
not_visited = set(range(1,N+2))
cost = [0] + [INF] * (N+1)
while hq:
    c,v = heapq.heappop(hq)
    if v not in not_visited: continue
    if v == 1:
        print(c)
        exit()
    cost[v] = c
    not_visited.remove(v)
    for to in not_visited:
        newcost = calc_cost(v, to)
        if cost[to] <= cost[v] + newcost: continue
        if direct < cost[v] + newcost: continue
        heapq.heappush(hq, (cost[v] + newcost, to))

Buggy python submission (verdict: Time Limit Exceeded):
import math
import heapq
xs,ys,xe,ye = map(int,input().split())
cs = [(xs,ys,0), (xe,ye,0)]
N = int(input())
for i in range(N):
    cs.append(tuple(map(int,input().split())))

def dist(x1,y1,x2,y2):
    dx,dy = x2-x1,y2-y1
    return math.sqrt(dx**2 + dy**2)

def calc_cost(i,j):
    if i == j: return float('inf')
    x1,y1,r1 = cs[i]
    x2,y2,r2 = cs[j]
    cost = max(0, dist(x1,y1,x2,y2) - r1 - r2)
    return cost

hq = [(calc_cost(0,i),i) for i in range(1,N+2)]
heapq.heapify(hq)
visited = [1] + [0] * (N+1)
while hq:
    cost,v = heapq.heappop(hq)
    if v == 1:
        print(cost)
        exit()
    visited[v] = 1
    for to in range(N+2):
        if to == v or visited[to]: continue
        newcost = calc_cost(v, to)
        heapq.heappush(hq, (cost + newcost, to))


Fixed submission:
import math,heapq,sys
input = sys.stdin.readline
xs,ys,xe,ye = map(int,input().split())
cs = [(xs,ys,0), (xe,ye,0)]
N = int(input())
for i in range(N):
    cs.append(tuple(map(int,input().split())))

def calc_cost(i,j):
    if i == j: return float('inf')
    x1,y1,r1 = cs[i]
    x2,y2,r2 = cs[j]
    cost = max(0, math.hypot(x1-x2,y1-y2) - r1 - r2)
    return cost

INF = float('inf')
direct = calc_cost(0,1)
hq = []
for i in range(1,N+2):
    c = calc_cost(0,i)
    if c > direct: continue
    hq.append((c,i))
heapq.heapify(hq)
not_visited = set(range(1,N+2))
cost = [0] + [INF] * (N+1)
while hq:
    c,v = heapq.heappop(hq)
    if v not in not_visited: continue
    if v == 1:
        print(c)
        exit()
    cost[v] = c
    not_visited.remove(v)
    for to in not_visited:
        newcost = calc_cost(v, to)
        if cost[to] <= cost[v] + newcost: continue
        if direct < cost[v] + newcost: continue
        heapq.heappush(hq, (cost[v] + newcost, to))

Buggy python submission (verdict: Time Limit Exceeded):
import math
import heapq
xs,ys,xe,ye = map(int,input().split())
cs = [(xs,ys,0), (xe,ye,0)]
N = int(input())
for i in range(N):
    cs.append(tuple(map(int,input().split())))

def dist(x1,y1,x2,y2):
    dx,dy = x2-x1,y2-y1
    return math.sqrt(dx**2 + dy**2)

es = [[None for j in range(N+2)] for i in range(N+2)]
for i,(x1,y1,r1) in enumerate(cs[:-1]):
    for j,(x2,y2,r2) in enumerate(cs[i+1:]):
        j += i+1
        cost = max(0, dist(x1,y1,x2,y2) - r1 - r2)
        es[i][j] = es[j][i] = cost

hq = [(cost,i+1) for i,cost in enumerate(es[0][1:])]
heapq.heapify(hq)
visited = [1] + [0] * (N+1)
while hq:
    cost,v = heapq.heappop(hq)
    if v == 1:
        print(cost)
        exit()
    visited[v] = 1
    for to,newcost in enumerate(es[v]):
        if to == v or visited[to]: continue
        heapq.heappush(hq, (cost + newcost, to))


Fixed submission:
import math,heapq,sys
input = sys.stdin.readline
xs,ys,xe,ye = map(int,input().split())
cs = [(xs,ys,0), (xe,ye,0)]
N = int(input())
for i in range(N):
    cs.append(tuple(map(int,input().split())))

def calc_cost(i,j):
    if i == j: return float('inf')
    x1,y1,r1 = cs[i]
    x2,y2,r2 = cs[j]
    cost = max(0, math.hypot(x1-x2,y1-y2) - r1 - r2)
    return cost

INF = float('inf')
direct = calc_cost(0,1)
hq = []
for i in range(1,N+2):
    c = calc_cost(0,i)
    if c > direct: continue
    hq.append((c,i))
heapq.heapify(hq)
not_visited = set(range(1,N+2))
cost = [0] + [INF] * (N+1)
while hq:
    c,v = heapq.heappop(hq)
    if v not in not_visited: continue
    if v == 1:
        print(c)
        exit()
    cost[v] = c
    not_visited.remove(v)
    for to in not_visited:
        newcost = calc_cost(v, to)
        if cost[to] <= cost[v] + newcost: continue
        if direct < cost[v] + newcost: continue
        heapq.heappush(hq, (cost[v] + newcost, to))