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The Currency of some country has 'k' number of denominations. For each
denominaion , there is a coin .
Whenever a transaction happens with the shopkeeper, then to pay an amount 'X',
you give exactly or some amount greater than 'X' ( let us say 'Y' ) to the
shopkeeper. He then pays back the extra amount ( Y-X ) back to you. Both of
you try to minimize the number of coins exchanged in the process.
For example, if X = 68 and you have the denominations , 1,2,5,10,20,50 , then
the optimal transaction could be you paying the shopkeeper 50+20 units ( 2 coins
) and then the shopkeeper paying you back 2 units ( 1 coin ) . Hence , the total
number of coin exchanged in the process being 3 ( 50 + 20 - 2 ).
The efficiency of a set of denominations is calculated by the minimum number of
coin exchange required for every integer coin value between 1 and N ( some upper
bound, lets assume ) and taking their average as A. Lower the A, better is the
set of denomination.
Write a program that, given a series of coins, calculates the average and
maximum number of coins needed to pay any amount in the range [1,N]. You may
assume that both parties involved have sufficient numbers of any coin at their
The first line contains the number of test cases.
For each test case, there is a single line containing N ( 1<=N<=100 ),Number of
denominations K( K<=10 ) and then the value of each denomination ; all separated
by a single space.
For each test case the output is a single line containing first the average and
then the maximum number of coins involved in paying an amount in range [1,N]. The
average should be accurate upto 2 decimal places.
3 100 6 1 2 5 10 20 50 100 6 1 3 10 15 51 84 100 6 1 4 9 16 25 36
2.96 5 2.56 3 2.85 5
|Time Limit:||0.285714 sec|
|Source Limit:||50000 Bytes|
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