Write a program in which the programmer would like to modify the Puzzle class to keep track of how many times a call to changeKey results in a change to a key. Any time a call to changeKey results in a change to the key, the count of key modifications should be increased by one. The programmer would like to implement this change without making any changes to the signature of the changeKey method or overloading changeKey.

Consider a slotted aloha system, where the time slot equals the fixed duration of each packet. assume that there are 4 stations a, b,c, d sharing the medium. (a) stations a, b,c, d receive one packet each from higher layers at times 1.3, 1.5, 2.6,5.7 respectively. show which transmissions take place when, according to the slottedaloha protocol; describe all transmissions until all four packets have been successful. when needed, each station has access to the following sequence of random number, provided by a random number generator and drawn uniformly between 0 and 1: (1) station a draws numbers: 0.31, 0.27, 0.78, 0.9, 0.9, 0.11, 0. (2) station b draws numbers: 0.45, 0.28, 0.11, 0.83, 0.37, 0.22, 0. (3)station c draws numbers: 0.1, 0.2, 0.3, 0.4, 0. (4) station d draws numbers: 0.36, 0.77, 0.9, 0.1, 0.1, 0.1, 0.1, 0. (b) in slotted aloha, a station transmits in each time slot with a given probability. what probabilities would you assign to each of the four stations so as to: (i) maximize the efficiency of the protocol? (ii) maximize fairness among the four stations? (c) will the efficiency increase or decrease if we modify slotted aloha as follows: (i) get rid of slots and allow stations to transmit immediately? (ii) implement carrier sensing? (iii) implement collision detection? (iv) implement collision avoidance?

Write a method named addall that could be placed inside the hashintset class. this method accepts another hashintset as a parameter and adds all elements from that set into the current set, if they are not already present. for example, if a set s1 contains [1, 2, 3] and another set s2 contains [1, 7, 3, 9], the call of s1.addall(s2); would change s1 to store [1, 2, 3, 7, 9] in some order. you are allowed to call methods on your set and/or the other set. do not modify the set passed in. this method should run in o(n) time where n is the number of elements in the parameter set passed in.

Problem 1 - hashing we would like to use initials to locate an individual. for instance, mel should locate the person mark e. lehr. note: this is all upper case. generate a hash function for the above using the numbers on your telephone. you know, each letter has a number associated with it, so examine your telephone keypad. generate 512 random 3 letter initials and take statistics on a linked list array size 512 to hold this information report how many have no elements, 1 element, 2 elements, does this agree with the hashing statistics distribution?