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CSE |\ 310 |\Exam |\ 1 |\questions |\with |\answers
Big |\O |\notation |- |\CORRECT |\ANSWERS |\✔✔O(g(n) |= |\f(n) |\if |\f(n) |<= |
ag(n) |\while |\n |>= |\b Big |\Ω |\notation |- |\CORRECT |\ANSWERS |\✔✔Ω(g(n)) |= |\f(n) |\if |\f(n) |>= |
ag(n) |\while |\n |>= |\b Big |\Θ |\notation |- |\CORRECT |\ANSWERS |\✔✔Θ(g(n)) |= |\f(n) |\if |\f(n) |<= |
ag(n) |\and |\f(n) |>= |\bg(n) |\for |\all |\n |>= |\c To |\prove |\correctness |\of |\algorithm, |\show |______, |_____ |\and |_____ |\hold |- |\CORRECT |\ANSWERS |\✔✔initialization, |\maintenance, |\and |
termination Index |\of |\left |\child |\of |\node |- |\CORRECT |\ANSWERS |\✔✔i |= |\index |\of |
node 2*i |= |\index |\of |\node's |\left |\child parent |\index |\in |\heap |- |\CORRECT |\ANSWERS |\✔✔i |= |\index |\of |\node floor(i/2) |= |\index |\of |\node's |\parent
What |\does |\heap-extract |\max |\do? |- |\CORRECT |\ANSWERS |\✔✔1) |\takes |
out |\the |\head |\of |\heap |\and |\replaces |\it |\with |\last |\node
- |\performs |\max-heapify |\on |\head Find |\the |\expression |\associated |\with |\the |\runtime |\of |\this |\pseudocode |(i.e. |\C1 |\x |\n |+ |\C2 |\x |\n |... |\etc) |\and |\find |\the |\big |\O |\approximation k=1 |// |\C do |// |\C { |\j |= |\ 1 |// |\C |\do |// |\C |{ |\j |= |\j*2 |// |\C |}while(j |< |\n) |// |\C |\k++ |// |\C }while |(k |< |\n) |// |\C8 |- |\CORRECT |\ANSWERS |\✔✔C1 |\x |\ 1 |+ |\C2 |\x |\n |+ |\C3 |\x |\n |+ |\C4 |\x |\n(log_2(n)) |+ |\C5 |\x |\n(log_2(n)) |+ |\C6 |\x |\n(log_2(n)) |+ |\C7 |\x |\n |+ |\C8 |\x |\n |= |\O(nlogn) Time |\of |\max-heapify |- |\CORRECT |\ANSWERS |\✔✔O(logn)
Min |\heap |- |\CORRECT |\ANSWERS |\✔✔The |\parent |\of |\any |\node |\is |\less |
than |\or |\equal |\to |\the |\node |\itself Which |\tree |\is |\wrong |(there |\are |\two)
|\ 30 |\ 2 |\ 8 10
|\ 20 |\ 10 |\ 11 2 |\ 3 |\ 6
|\ 10 |\ 2 |\ 3 |\ 1 |\ 2 ----------------------------------------------------------------------------- |- |\CORRECT |
ANSWERS |\✔✔ 1 |\and |\ 3
Explicit |\formula |\for |\height |\of |\heap |\and |\O |\approximation |- |\CORRECT |\ANSWERS |\✔✔ceil(log_2(n+1)-1) O(logn) What |\does |\heap-increase-key |\do? |- |\CORRECT |\ANSWERS |\✔✔1) |\makes |\specific |\node's |\value |\large
- |\moves |\it |\up |\until |\it's |\smaller |\than |\its |\parent |\and |\larger |\than |\its |
children O |\notation |\of |\f(n) |= |\100,000(nlog_100(n+30)) |- |\CORRECT |\ANSWERS |
✔✔O(nlogn) O |\notation |\of |\f(n) |= |\x^10 |+ |\1,000,000,000log_2(x) |- |\CORRECT |
ANSWERS |\✔✔O(x^10) index |\of |\right |\child |\of |\node |- |\CORRECT |\ANSWERS |\✔✔i |= |\index |\of |
node 2*i+1 |= |\index |\of |\node's |\right |\child Merge |\sort |\best |\case/worst |\case |- |\CORRECT |\ANSWERS |\✔✔O(nlogn) |
for |\both
does |\indexing |\of |\arrays |\start |\at |\ 1 |\or |\0? |(in |\this |\class) |- |\CORRECT |
ANSWERS |\✔✔ 1 does |\indexing |\of |\hashtables |\start |\at |\ 1 |\or |\0? |(in |\this |\class) |- |
CORRECT |\ANSWERS |\✔✔ 0 What |\does |\heap-insert |\do? |- |\CORRECT |\ANSWERS |\✔✔adds |\node |\to |
bottom, |\then |\rearranges |\heap |\to |\make |\sure |\properties |\are |\not |
broken Runtime |\of |\heap-insert |- |\CORRECT |\ANSWERS |\✔✔O(logn) What |\is |\a |\decision |\tree |- |\CORRECT |\ANSWERS |\✔✔Diagram |\of |\all |
possible |\decisions T/F: |\you |\need |\to |\specify |\a |\number |\of |\elements |\when |\creating |\a |
decision |\tree |(i.e. |\for |\a |\sorting |\algorithm) |- |\CORRECT |\ANSWERS |
✔✔True Worst |\case |\number |\of |\comparisons |\in |\decision |\tree |\is |= |\to |\the |_____ |\of |\the |\decision |\tree |- |\CORRECT |\ANSWERS |\✔✔height Worst |\case |\lower |\bound |\for |\runtime |\of |\sort |\algorithms |- |\CORRECT |
ANSWERS |\✔✔Ω(nlogn)
Number |\of |\comparisons |\to |\find |\min |\and |\max |\in |\any |\array |- |
CORRECT |\ANSWERS |\✔✔3*floor(n/2) |\where |\n |\is |\the |\number |\of |
elements |\in |\the |\array T/F: |\quicksort |\w/out |\randomized |\partition |\is |\equally |\efficient |\in |
worst |\case |\than |\quicksort |\w/ |\randomized |\partition |- |\CORRECT |
ANSWERS |\✔✔True, |\but |\the |\worst |\case |\is |\less |\likely |\with |\randomized |\partition Runtime |\to |\find |\ith |\smallest |\element |\in |\an |\array |- |\CORRECT |
ANSWERS |\✔✔O(n) Direct |\address |\table |\runtime |\of |\search, |\insert, |\and |\delete |\functions |- |\CORRECT |\ANSWERS |\✔✔O(1) What |\does |\chaining |\mean |\in |\the |\context |\of |\hash |\tables? |- |\CORRECT |\ANSWERS |\✔✔When |\collisions |\occur, |\create/add |\to |\linked |\list Runtime |\of |\hash |\table |\search |\and |\delete? |- |\CORRECT |\ANSWERS |
✔✔O(n) simple |\uniform |\hashing |- |\CORRECT |\ANSWERS |\✔✔any |\element |\is |
equally |\likely |\to |\hash |\to |\any |\slot
