> In a case where a passenger who changed from some company A's line to another company's line changes to company A's line again, the additional fare is incurred again.

Does that mean that the fare will be 2 yen for changing (1 for changing itself and one extra for change line A to line B to line A?) What will happen in case when A changed to B, then to A, then to B and then to A again? Will the cost for final change be 3 yen or 2 yen?

The cost for changing company is always 1 yen.

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別の会社に乗り換えるときは常に 1 かかります。

On the first line:

"consisting of N stations and M railway lines. The stations are numbered 1 through M. "

M -> N, right?
Please fix this.

:)

"The stations are numbered 1 through N" is correct. Sorry for inconvenience.

The issue is fixed.

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この質問は英語問題文に関する質問なので、日本語問題文の読んでいる方は気にしないでもらって結構です。