Buggy python submission (verdict: Runtime Error):
from collections import deque
import sys
input = sys.stdin.readline

n, m = map(int, input().split())
G = [[] for _ in range(n+1)]
for _ in range(m):
    u, v, s = map(int, input().split())
    G[u].append((v, s))
    G[v].append((u, s))
val = [None] * (n+1)
val[1] = (1, 0)
queue = deque([1])
while queue:
    u = queue.popleft()
    for v, s in G[u]:
        if val[v]:
            continue
        val[v] = (-val[u][0], s - val[u][1])
        queue.append(v)
ma = float('inf')
mi = 1
x = -1
for u in range(1, n+1):
    if val[u][0] == -1:
        ma = min(ma, val[u][1] - 1)
    else:
        mi = max(mi, -val[u][1] + 1)
    for v, s in G[u]:
        if u > v:
            continue
        if val[u][0] + val[v][0] == 0:
            if val[u][1] + val[v][1] != s:
                print(0)
                exit()
        else:
            a = val[u][0] + val[v][0]
            b = s - (val[u][1] + val[v][1])
            if a < 0:
                b *= -1
            if b <= 0 or b % 2 == 1:
                print(0)
                exit()
            if x == -1:
                x = b // 2
            elif x != b // 2:
                print(0)
                exit()
assert x == -1
print(max(ma - mi + 1, 0) if x == -1 else 1)

Fixed submission:
from collections import deque
import sys
input = sys.stdin.readline

n, m = map(int, input().split())
G = [[] for _ in range(n+1)]
for _ in range(m):
    u, v, s = map(int, input().split())
    G[u].append((v, s))
    G[v].append((u, s))
val = [None] * (n+1)
val[1] = (1, 0)
queue = deque([1])
while queue:
    u = queue.popleft()
    for v, s in G[u]:
        if val[v]:
            continue
        val[v] = (-val[u][0], s - val[u][1])
        queue.append(v)
ma = float('inf')
mi = 1
x = -1
for u in range(1, n+1):
    if val[u][0] == -1:
        ma = min(ma, val[u][1] - 1)
    else:
        mi = max(mi, -val[u][1] + 1)
    for v, s in G[u]:
        if u > v:
            continue
        if val[u][0] + val[v][0] == 0:
            if val[u][1] + val[v][1] != s:
                print(0)
                exit()
        else:
            a = val[u][0] + val[v][0]
            b = s - (val[u][1] + val[v][1])
            if a < 0:
                b *= -1
            if b <= 0 or b % 2 == 1:
                print(0)
                exit()
            if x == -1:
                x = b // 2
            elif x != b // 2:
                print(0)
                exit()
if x != -1:
    if mi <= x <= ma:
        print(1)
    else:
        print(0)
else:
    print(max(ma - mi + 1, 0))

Buggy python submission (verdict: Runtime Error):
from collections import deque
import sys
input = sys.stdin.readline

n, m = map(int, input().split())
G = [[] for _ in range(n+1)]
for _ in range(m):
    u, v, s = map(int, input().split())
    G[u].append((v, s))
    G[v].append((u, s))
val = [None] * (n+1)
val[1] = (1, 0)
queue = deque([1])
while queue:
    u = queue.popleft()
    for v, s in G[u]:
        if val[v]:
            continue
        val[v] = (-val[u][0], s - val[u][1])
        queue.append(v)
ma = float('inf')
mi = 1
x = -1
for u in range(1, n+1):
    if val[u][0] == -1:
        ma = min(ma, val[u][1] - 1)
    else:
        mi = max(mi, -val[u][1] + 1)
    for v, s in G[u]:
        if u > v:
            continue
        if val[u][0] + val[v][0] == 0:
            if val[u][1] + val[v][1] != s:
                print(0)
                exit()
        else:
            a = val[u][0] + val[v][0]
            b = s - (val[u][1] + val[v][1])
            if a < 0:
                b *= -1
            if b <= 0 or b % 2 == 1:
                print(0)
                exit()
            if x == -1:
                x = b // 2
            elif x != b // 2:
                print(0)
                exit()
assert False
print(max(ma - mi + 1, 0) if x == -1 else 1)

Fixed submission:
from collections import deque
import sys
input = sys.stdin.readline

n, m = map(int, input().split())
G = [[] for _ in range(n+1)]
for _ in range(m):
    u, v, s = map(int, input().split())
    G[u].append((v, s))
    G[v].append((u, s))
val = [None] * (n+1)
val[1] = (1, 0)
queue = deque([1])
while queue:
    u = queue.popleft()
    for v, s in G[u]:
        if val[v]:
            continue
        val[v] = (-val[u][0], s - val[u][1])
        queue.append(v)
ma = float('inf')
mi = 1
x = -1
for u in range(1, n+1):
    if val[u][0] == -1:
        ma = min(ma, val[u][1] - 1)
    else:
        mi = max(mi, -val[u][1] + 1)
    for v, s in G[u]:
        if u > v:
            continue
        if val[u][0] + val[v][0] == 0:
            if val[u][1] + val[v][1] != s:
                print(0)
                exit()
        else:
            a = val[u][0] + val[v][0]
            b = s - (val[u][1] + val[v][1])
            if a < 0:
                b *= -1
            if b <= 0 or b % 2 == 1:
                print(0)
                exit()
            if x == -1:
                x = b // 2
            elif x != b // 2:
                print(0)
                exit()
if x != -1:
    if mi <= x <= ma:
        print(1)
    else:
        print(0)
else:
    print(max(ma - mi + 1, 0))

Buggy python submission (verdict: Runtime Error):
from collections import deque
import sys
input = sys.stdin.readline

n, m = map(int, input().split())
G = [[] for _ in range(n+1)]
for _ in range(m):
    u, v, s = map(int, input().split())
    G[u].append((v, s))
    G[v].append((u, s))
queue = deque([1])
color = [-1] * (n+1)
color[1] = 0
ok = True
while queue:
    u = queue.popleft()
    for v, s in G[u]:
        if color[v] == -1:
            color[v] = 1 - color[u]
            queue.append(v)
        elif color[u] == color[v]:
            ok = False
            break
    assert ok
val = [None] * (n+1)
val[1] = (1, 0)
queue = deque([1])
while queue:
    u = queue.popleft()
    for v, s in G[u]:
        if val[v] is None:
            val[v] = (-val[u][0], s - val[u][1])
            queue.append(v)
ma = float('inf')
mi = 1
x = -1
for u in range(1, n+1):
    if val[u][0] == -1:
        ma = min(ma, val[u][1] - 1)
    else:
        mi = max(mi, -val[u][1] + 1)
    for v, s in G[u]:
        if u > v:
            continue
        if val[u][0] + val[v][0] == 0:
            if val[u][1] + val[v][1] != s:
                print(0)
                exit()
        else:
            a = val[u][0] + val[v][0]
            b = s - (val[u][1] + val[v][1])
            if a < 0:
                b *= -1
            if b <= 0 or b % 2 == 1:
                print(0)
                exit()
            if x == -1:
                x = b // 2
            elif x != b // 2:
                print(0)
                exit()
if x != -1:
    print(1)
else:
    print(max(ma - mi + 1, 0))

Fixed submission:
from collections import deque
import sys
input = sys.stdin.readline

n, m = map(int, input().split())
G = [[] for _ in range(n+1)]
for _ in range(m):
    u, v, s = map(int, input().split())
    G[u].append((v, s))
    G[v].append((u, s))
val = [None] * (n+1)
val[1] = (1, 0)
queue = deque([1])
while queue:
    u = queue.popleft()
    for v, s in G[u]:
        if val[v]:
            continue
        val[v] = (-val[u][0], s - val[u][1])
        queue.append(v)
ma = float('inf')
mi = 1
x = -1
for u in range(1, n+1):
    if val[u][0] == -1:
        ma = min(ma, val[u][1] - 1)
    else:
        mi = max(mi, -val[u][1] + 1)
    for v, s in G[u]:
        if u > v:
            continue
        if val[u][0] + val[v][0] == 0:
            if val[u][1] + val[v][1] != s:
                print(0)
                exit()
        else:
            a = val[u][0] + val[v][0]
            b = s - (val[u][1] + val[v][1])
            if a < 0:
                b *= -1
            if b <= 0 or b % 2 == 1:
                print(0)
                exit()
            if x == -1:
                x = b // 2
            elif x != b // 2:
                print(0)
                exit()
if x != -1:
    if mi <= x <= ma:
        print(1)
    else:
        print(0)
else:
    print(max(ma - mi + 1, 0))