hi guys need help......please

1. each student in a group of n students is scheduled to work one
shift, where each shift is a single congiguous interval of time. there
can be multiple shifts going on at once. devise an effiecient algorithm
to choose a smallest subset of these n students to form a committee so
that for ever student not on the committee, that students's shift
overlaps(at least partially) the shift of some student who is on the
committee.

2.
given a sequence of n distinct numbers a1,a2,.....,an , a pair (ai,aj)
is known as significant inversion if i<j and ai>2aj. give O(n lg n)
algorithm to count the number of significant inversions in the given
sequence.

3. let a machine known as, equivalence tester, can determine whether
two bank card correspond to the same account by taking two cards at a
time as input and outputting whether they are equivalent. give an
algorithm which invokes equivalence tester at most O(nlgn) to determine
whether there is a set of more than n/2 equivalent cards in the given n
bank cards.

i appreciate your time...

thank you
please reply


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