The kth quantiles of an n-element set are the − 1 order statistics that divide the sorted set into k equal-sized sets (to within 1). Give an ( log ) time algorithm to list the kth quantiles of a set.
1. If k=1 we return an empty list.
2. If k is even, we find the median, partition around it, solve two similar subproblems of size ⌊n/2⌋ and return their solutions plus the median.
3. If k is odd, we find the ⌊k/2⌋ and ⌈k/2⌉ boundaries and then we reduce to two subproblems, each with size less than n/2. The worst-case recurrence is:
T(n, k) = 2T(⌊n/2⌋,k/2)+O(n)
Which is the desired bound ­ O(nlgk).
This works easily when the number of elements is ak+k−1 for a positive integer a. When they are a different number, some care with rounding needs to be taken in order to avoid creating two segments that differ by more than 1.

Type the correct answer in the box. spell all words correctly.what kind of graph or chart does this image represent? the given image represents a (blank).

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?

The managing director of a company sends a christmas greeting to all his employees through the company email. which type of network does he use? he uses an .