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1. For each of the following, write a regular expression using only the constructs shown in class. Do not use non-regular features such as forward reference and back reference. If you want to use a regex shortcut, such as "\d," you should specify the intended meaning of that shortcut to be absolutely clear about your intent. Assume that all expressions will be interpreted using "lazy" semantics. (a) Write a regular expression recognizing strings over the alphabet {(1, b, c} which contain exactly one 'a' along With any number of b's and c's. (b) Write a regular expression recognizing strings over the alphabet {(1, b, c} where all occurrences of 'a' appear in groups of three. (Please keep in mind that zero is a multiple of three).
(c) Write a regular expression recognizing strings over the alphabet {(1, b, C} whose length is a multiple of 5 (Please keep in mind that zero is a multiple of 5). (d) Write a regular expression recognizing even integers.
(e) Write a regular expression recognizing all strings of 0's and 1's not containing the substring 101.
Binary search tree, and postorder and preorder traversal Determine the shortest path in Graph
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