Acertain string-processing language offers a primitive operation which splits astring into two pieces. since this operation involves copying the original string, ittakes n units of time for a string of length n, regardless of the location of the cut. suppose, now, that you want to break a string into many pieces. the order inwhich the breaks are made can affect the total running time. for example, if youwant to cut a 20-character string at positions 3 and 10, then making the first cutat position 3 incurs a total cost of 20 + 17 = 37, while doing position 10 first hasa better cost of 20 + 10 = 30.give a dynamic programming algorithm that, given the locations of m cuts in astring of length n, finds the minimum cost of breaking the string into m+ 1pieces.

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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?