# The big five algorithm

Here is a list L of 103 numbers. Trace the execution of the Big-5 algorithm for

selection on the call Select(45, L). Assume that the base case is when there are 5 or

less numbers in the list (this modification [5, not 50] is necessary to make a small, yet

nontrivial instance).

Diagram the call sequence as in the Big5 Example handout. Show recursive calls to

find the pivot point m as arrows pointing 45 degrees to the left and recursive calls

after the pivot m has been found as arrows pointing vertically downward. Label the

return arrows with the numbers that are returned back up to the calling program.

Give the intermediate lists Mi and sets Si as they are generated. Since there will be

multiple sets S1, S2, S3, add a superscript S1^i to distinguish them.

IMPORTANT: When forming a list of medians Mi retain the input order. Take

groups of 5 as they occur in the input order, keep the medians in the order they occur

in the input. Do this at every stage. See how it is done in the Big5 Example handout.

100 33 34 36 9 10 11 25 29 28 30 16 17 17 22 23 121 125 127 90 91 92 115 130 101

78 79 82 106 108 109 141 120 128 1 2 14 15 16 16 70 70 71 60 62 64 59 111 113 115

130 133 134 136 85 95 96 97 44 49 49 50 8 9 103 31 32 109 139 140 65 69 52 50 36

36 40 115 102 3 4 5 12 53 53 57 83 85 105 89 93 94 41 43 5 7 9 103 73 74 11 12 24`

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