Question

design algorithm and say what the big O is by analying it

When making change, we want to give the least number of coins as possible. Design an O(number of denominations) algorithm that does this for any set of coin denominations. You can assume that the denominations are sorted from low to high, and will always have a penny (and so every amount of change will be possible). You can also assume that the coins are all powers of some denomination (so, for example: 1,5,25 or 1,3,9,81).  

So, for example, if the coin denominations were 1,5, and 25, and the number of cents of change was 66, you should say that you should give two 25-cent coins, three 5-cent coins, and one 1-cent coin.

Answer 1

//PSEUDO Code of minimum coin change problem

//coin_value[] contains value or denomination of coins

//n is toatal kind of coins and amount is total money to be paid

min_coins(coin_value[],n,amount)

{

for( i= 1 to n )

while amount > = to coins[i]

{

//while loop is needed since one coin can be used multiple times

amount = amount - coin_value[i]

print coin_value[i]

}

}

Time complexity: O(n) where n is the number of coins.