How do you find the optimal denomination?
Table of Contents
- 1 How do you find the optimal denomination?
- 2 What is the largest amount of money in coins you can have and still not be able to make a dollar exactly?
- 3 What is a canonical coin system?
- 4 What is the greatest dollar value in coins you can have in your hand without being able to make change for a dollar?
- 5 What is the minimum number?
- 6 What are the different denominations of currency?
- 7 What is the place value of $100?
How do you find the optimal denomination?
For instance, take the standard USD and its coin denominations of {1,5,10,25,50}. Here, the smallest paper bill is worth 100 of the smallest coin. It takes 4 coins to make 46 cents using this currency; we have c1(46)=1,c2(46)=0,c3(46)=2,c4(46)=1,c5(46)=0.
How many ways can you make the change for a dollar?
293 ways
Larry King said in his USA Today column that there are 293 ways to make change for a dollar….Answer.
| Unit of Currency | Number of Ways to Make Change |
|---|---|
| 10¢ | 3 |
| 25¢ | 12 |
| 50¢ | 49 |
| $1 | 292 |
What is the largest amount of money in coins you can have and still not be able to make a dollar exactly?
Suppose there is a pile of quarters, dimes and pennies with a total value of $1.18. How much of each coin can be present without being able to make change for $1. Explain why $1.19 is the greatest amount of money it is possible to have without being able to make change for a dollar.
What is the formula of calculating the minimum number of coins?
Algorithm Visualization
| 1 | public class MinCoins { |
|---|---|
| 20 | for(int i = 1; i <= sum; i++) { |
| 21 | min = Integer.MAX_VALUE; |
| 22 | for(int j = 0; j < values.length; j++) { |
| 23 | if(i >= values[j]) |
What is a canonical coin system?
The greedy algorithm involves repeatedly choosing a coin of the largest denomination that is less than or equal to the amount still owed, until the amount owed reaches zero. A coin system for which the greedy algorithm is always optimal is called canonical.
How many ways can you make change for a dollar using quarters dimes and nickels?
242 ways
With the four coins (quarters, dimes, nickels, and pennies), there are 242 ways to make change for a dollar.
What is the greatest dollar value in coins you can have in your hand without being able to make change for a dollar?
What is the greatest dollar value in coins you can have in your hands without being able to make change for a dollar? $1.19. There are a few ways to think about this, but the easiest is to start with the largest coin – quarters – first and then work your way down.
How will you find the minimum number of coins in change making problem?
Assume that we are given a set of coins having the values {1, 3, 6}. To make a sum of 7 using these coins, all possible solutions are: {1,1,1,1,1,1,1}, {1,3,3}, and {1,6}. So the minimum number of coins required are 2, i.e. {1,6}.
What is the minimum number?
The minimum is the first number listed as it is the lowest, and the maximum is the last number listed because it is the highest.
How many dollar bill denominations are there?
There are 7 note denominations in US, $1, $2, $5, $10, $20, $50 and $100. One hundred dollars is the highest currency note denomination among them in the US. How Much is $50 in Cents?
What are the different denominations of currency?
Every country has its own currency as well as denominations. For example, the USA has currency Dollars and it can further be divided into different smaller currencies like $1, $2, $5, $10, $20, $50, and $100. In this lesson, we will learn to identify denominations using charts and examples.
How do you find the value of a found denomination?
Find the largest denomination that is smaller than current amount. Add found denomination to result. Subtract value of found denomination from amount. If amount becomes 0, then print result.
What is the place value of $100?
The place values are ones, tens, hundreds, thousands, and so on. $1, $10, $100 are similar to place values of units, tens, and hundreds. There can be any number of one dollar, ten dollars, hundred dollars in a given amount. For example, we can say a hundred dollars comprise a hundred $1 or ten $10 or one $100.