Buggy python submission (verdict: Time Limit Exceeded):
def warshall_floyd(d):
    #d[i][j]: iからjへの最短距離
    for k in range(n):
        for i in range(n):
            for j in range(n):
                d[i][j] = min(d[i][j],d[i][k] + d[k][j])
    return d

n,m = map(int,input().split()) #n:頂点数　w:辺の数
l=[list(map(int,input().split())) for i in range(m)]
ans=0

#d[u][v] : 辺uvのコスト(存在しないときはinf)
for j in range(m):
	d = [[float("inf") for i in range(n)] for i in range(n)]
	b=l[:j]+l[j+1:]
	for i in range(m-1):
		x,y = b[i][0],b[i][1]
		x-=1;y-=1
		d[x][y] = 1
		d[y][x] = 1
	for i in range(n):
		d[i][i] = 0 #自身のところに行くコストは０
	#print(warshall_floyd(d))
	for i in range(n):
		for k in range(n):
			if warshall_floyd(d)[i][k]==float("inf"):
				ans+=1
				break
		else:
			continue
		break
	#print(ans)
print(ans)

Fixed submission:
import heapq
def dijkstra_heap(s):
    #始点sから各頂点への最短距離
    d = [float("inf")] * n
    used = [True] * n #True:未確定
    d[s] = 0
    used[s] = False
    edgelist = []
    for e in edge[s]:
        heapq.heappush(edgelist,e)
    while len(edgelist):
        minedge = heapq.heappop(edgelist)
        #まだ使われてない頂点の中から最小の距離のものを探す
        if not used[minedge[1]]:
            continue
        v = minedge[1]
        d[v] = minedge[0]
        used[v] = False
        for e in edge[v]:
            if used[e[1]]:
                heapq.heappush(edgelist,[e[0]+d[v],e[1]])
    return d

n,w = map(int,input().split())
l=[list(map(int,input().split())) for i in range(w)]
ans=0
#edge[i] : iから出る道の[重み,行先]の配列
for j in range(w):
    edge = [[] for i in range(n)]
    b=l[:j]+l[j+1:]
    for i in range(w-1):
        x,y = b[i][0],b[i][1]
        x-=1;y-=1
        z=1
        edge[x].append([z,y]) #有向辺
        edge[y].append([z,x]) #有向辺
    if float("inf") in dijkstra_heap(0):
            ans+=1
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
def warshall_floyd(d):
    #d[i][j]: iからjへの最短距離
    for k in range(n):
        for i in range(n):
            for j in range(n):
                d[i][j] = min(d[i][j],d[i][k] + d[k][j])
    return d

import copy

n,m = map(int,input().split()) #n:頂点数　w:辺の数
l=[list(map(int,input().split())) for i in range(m)]
ans=0

#d[u][v] : 辺uvのコスト(存在しないときはinf)
for j in range(m):
	d = [[float("inf") for i in range(n)] for i in range(n)]
	b=l[:j]+l[j+1:]
	for i in range(m-1):
		x,y = b[i][0],b[i][1]
		x-=1;y-=1
		d[x][y] = 1
		d[y][x] = 1
	for i in range(n):
		d[i][i] = 0 #自身のところに行くコストは０
	for i in range(n):
		for k in range(n):
			if warshall_floyd(d)[i][k]==float("inf"):
				ans+=1
				break
		else:
			continue
		break
	b=copy.deepcopy(l)
print(ans)

Fixed submission:
import heapq
def dijkstra_heap(s):
    #始点sから各頂点への最短距離
    d = [float("inf")] * n
    used = [True] * n #True:未確定
    d[s] = 0
    used[s] = False
    edgelist = []
    for e in edge[s]:
        heapq.heappush(edgelist,e)
    while len(edgelist):
        minedge = heapq.heappop(edgelist)
        #まだ使われてない頂点の中から最小の距離のものを探す
        if not used[minedge[1]]:
            continue
        v = minedge[1]
        d[v] = minedge[0]
        used[v] = False
        for e in edge[v]:
            if used[e[1]]:
                heapq.heappush(edgelist,[e[0]+d[v],e[1]])
    return d

n,w = map(int,input().split())
l=[list(map(int,input().split())) for i in range(w)]
ans=0
#edge[i] : iから出る道の[重み,行先]の配列
for j in range(w):
    edge = [[] for i in range(n)]
    b=l[:j]+l[j+1:]
    for i in range(w-1):
        x,y = b[i][0],b[i][1]
        x-=1;y-=1
        z=1
        edge[x].append([z,y]) #有向辺
        edge[y].append([z,x]) #有向辺
    if float("inf") in dijkstra_heap(0):
            ans+=1
print(ans)