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Problem -7. [15 points) Ubhash Sallabh leads a team of social Yreis. Each Yrei has a unique name: a string of at most k lowercase English letters. Each pair of Yreis has at most two buddyghost names, formed by the concatenations of their names in either order (note it is possible for a pair of Yreis to have only one buddyghost name if both concatenations are the same). Four Yreis are buddyghost buddies if a buddyghost name of two of them is identical to a buddyghost name of the other two. For example, Yreis 'alex', 'isabel', 'alexis', and 'abel' are buddyghost buddies. Given a list A (a...., an) containing the names of Ubhash's n. Yreis, describe an O(kna)-time algorithm to determine whether any four of them are buddyghost buddies. (hint: make use of (a) data structure[s] you learnt in class; assume that string operations such as concatenation etc, take you only an expected O(k) time.)

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