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æ¬¡ã®æ®µèœã«é¢é£ãã質åããã | Lemma 1. G has a cycle.
Proof. Suppose G has no cycles. Then every connected component of G is a tree, and hence has at least two leaves (vertices of degree 1). Let v be a leaf of one of the components of G. Removing v and its incident edge from G results in a graph G' with m - 1 edges and n - 1 vertices, and the degree sum of all vertices of G' is even. By our induction hypothesis, G' has an Euler circuit C'. Reattaching v to G' along its unique neighbor on C' results in a cycle C in G, a contradiction. | 1. What is the lemma being discussed in this paragraph?
2. What is the assumption made in the proof?
3. What is the result when v is removed from G?
4. What is G'?
5. Does G have an Euler circuit C? |
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# Python
data_list = [1, 4.3, 'building', True, False]
dtypes = []
for i in data_list:
if type(i) == int:
dtypes.append('int')
elif type(i) == float:
dtypes.append('float')
elif type(i) == str:
dtypes.append('str')
elif type(i) == bool:
dtypes.append('bool')
print(dtypes) |
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