def can_traverse_all_bridges(n, m, bridges):
    from collections import defaultdict, deque

    # 构建图
    graph = defaultdict(list)
    degree = defaultdict(int)
    
    for a, b in bridges:
        graph[a].append(b)
        graph[b].append(a)
        degree[a] += 1
        degree[b] += 1
    
    # 计算奇数度顶点的数量
    odd_count = sum(1 for d in degree.values() if d % 2 != 0)
    
    # 如果奇数度顶点的数量不是0或2，则返回NO
    if odd_count != 0 and odd_count != 2:
        return "NO"
    
    # 检查图的连通性
    def is_connected():
        visited = set()
        nodes = list(graph.keys())
        if not nodes:
            return True
        start_node = nodes[0]
        queue = deque([start_node])
        
        while queue:
            node = queue.popleft()
            if node not in visited:
                visited.add(node)
                queue.extend(graph[node])
        
        # 检查是否所有有边的节点都被访问过
        return len(visited) == len(nodes)
    
    if not is_connected():
        return "NO"
    
    return "YES"

# 读取输入
import sys
input = sys.stdin.read
data = input().split()
n = int(data[0])
m = int(data[1])
bridges = [(int(data[i]), int(data[i + 1])) for i in range(2, 2 * m + 2, 2)]

# 输出结果
print(can_traverse_all_bridges(n, m, bridges))

def can_traverse_all_bridges(n, m, bridges):
    from collections import defaultdict, deque

    # 构建图
    graph = defaultdict(list)
    degree = defaultdict(int)
    
    for a, b in bridges:
        graph[a].append(b)
        graph[b].append(a)
        degree[a] += 1
        degree[b] += 1
    
    # 计算奇数度顶点的数量
    odd_count = sum(1 for d in degree.values() if d % 2 != 0)
    
    # 如果奇数度顶点的数量不是0或2，则返回NO
    if odd_count != 0 and odd_count != 2:
        return "NO"
    
    # 检查图的连通性
    def is_connected():
        visited = set()
        nodes = list(graph.keys())
        if not nodes:
            return True
        start_node = nodes[0]
        queue = deque([start_node])
        
        while queue:
            node = queue.popleft()
            if node not in visited:
                visited.add(node)
                queue.extend(graph[node])
        
        # 检查是否所有有边的节点都被访问过
        return len(visited) == len(nodes)
    
    if not is_connected():
        return "NO"
    
    return "YES"

# 读取输入
import sys
input = sys.stdin.read
data = input().split()
n = int(data[0])
m = int(data[1])
bridges = [(int(data[i]), int(data[i + 1])) for i in range(2, 2 * m + 2, 2)]

# 输出结果
print(can_traverse_all_bridges(n, m, bridges))

优化与修正说明

1. 度数计算：直接在构建图的过程中计算每个顶点的度数，简化了代码结构。
2. 奇顶点数量计算：使用列表生成式计算奇数度顶点的数量，使代码更紧凑。
3. 输入读取：修正了输入读取部分的错误，确保正确读取桥梁数据。
4. 图的连通性检查：使用广度优先搜索（BFS）检查图的连通性，确保所有有边的节点都被访问过。