Use a modified Lempel-Ziv algorithm in which, as discussed on p.120, the dictionary of prefixes is pruned by writing new prefixes into the space occupied by prefixes that will not be needed again. Such prefixes can be identified when both their children have been added to the dictionary of prefixes. (You may neglect the issue of termination of encoding.) Use this algorithm to encode the string 0100001000100010101000001. Highlight the bits that follow a prefix on the second occasion that that prefix is used. (As discussed earlier, these bits could be omitted.)