# What is the minimum number of coins that must be

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Code Review Stack Exchange is a question and answer site for peer programmer code reviews. It only takes a minute to sign up. I'm trying to learn dynamic programming and the most popular one is to find the minimum number of coins for the change.

I come up with this but I just want to improve this code which I think it could be shorter in Python but I'm new to Python too. This is already pretty short. Making it shorter doesn't seem a good objective, and risks hurting readability. That being said, there are a few things you could do. While at it, why are there 20 elements? Your program will find the minimum number of coins up to 19, and I have a feeling that you actually want it for In which case you would need:.

And then use range 21 in the loop. One more optimization is possible by flipping the order of the nested loops.

In the current code you need an if statement to skip the amounts that are too small for the coin. If you make the loop over coins to be the outer loop, then you can set a starting value for the inner value to make the if statement unnecessary. To be honest, I don't understand what your program does, even the hints that it has something to do with coins and change don't help me.

Here is the same program with some variables renamed. However, it is inelegant to have to use sys. You can solve both problems by using min with a generator expression. First of all, that's not dynamic programming as I understand the term. You haven't broken the problem down into simpler sub-problems, and in fact you have used an algorithm so convoluted in its logic that it's inordinately difficult to understand. Divide the problem into two parts: 1 a function to compute the number of coins needed to achieve a given total.

Here it is:.So we can find out the solution with both the options and then choose the optimal one, here in this case, select the minimum among all the solutions. Say MC j represents the minimum number of coins required to make change of amount j. We need to find the minimum number of coins required to make change for j amount. So we will select the minimum of all the smaller problems and add 1 to it because we have select one coin. Now smaller problems will be solved recursively.

### Find minimum number of coins that make a given value First we will break the problem into smaller problems. So what are our smaller problems. Amount is A and coins are v1, v2, …….

We can reduce the Time Complexity significantly by using Dynamic programming. Using Bottom-Up Dynamic Programming. We will maintain an array to store the optimal solutions for the smaller problems, say we call it as coinReq[]. Since we are using Bottom-up approachso will start filling the coinReq[] from 0 to n.

Like this: Like LoadingCoin change problem is the last algorithm we are going to discuss in this section of dynamic programming.

Now, we have to make an amount by using these coins such that a minimum number of coins are used. Like the rod cutting problemcoin change problem also has the property of the optimal substructure i. For example, we are making an optimal solution for an amount of 8 by using two values - 5 and 3. So, the optimal solution will be the solution in which 5 and 3 are also optimally made, otherwise, we can reduce the total number of coins of optimizing the values of 5 and 8.

The reason we are checking if the problem has optimal substructure or not because if there is optimal substructure, then the chances are quite high that using dynamic programming will optimize the problem.

Let's start by picking up the first coin i. We can repeat the process with all the k coins and then the minimum value of all these will be our answer. The above process can also be understood in a different way. Suppose, we have picked a coin with value x and we know that this coin is going to be in the solution.

So, our next task is to find the minimum number of coins needed to make the change of value n-x i. Also, by choosing the coin with value x, we have already increased the total number of coins needed by 1. But the real problem is that we don't know the value of x. So, we will try every coin for the value of x and then we will select the minimum among those.

You can see that there are overlapping subproblems in our solution and thus, we can use dynamic programming to optimize this. So, let's look at the coding implementation of the formula we derived above.

Our function is going to need the denomination vectors of coin dthe value for which change has to be made n and number of denominations we have k or number of elements in the array d i.

L07 : Coin Change - Dynamic Programming - LeetCode

Let's start by making an array to store the minimum number of coins needed for each value i. Now, we need to iterate for each value in array the M and fill it up. Let's suppose we know the first coin needed to get the optimal solution of each value. So, the point is we only need to store the first coin needed for each value and then we can get the optimal coins for any value.

In this case, we are also assigning the value of i to the variable 'coin' because this coin 'i' is giving us the minimum value and thus, it will be the coin to be stored in the array S. As said above, we are first printing the value of the coin S[l] will give us the coin and d[S[l]] is the value of that coin. After this, our initial value has decreased by the value of the coin i. The last loop will also run a total of n times in worst case it can run faster depending upon the value of l-d[S[l]]. Now, there is also a nested loop. All the other statements are constant time taking statements. There are many other interesting algorithms which are optimized by dynamic programming.

You can write about them on BlogsDope or can download the BlogsDope app to never miss any new articles. By signing up or logging in, you agree to our Terms of service and confirm that you have read our Privacy Policy. Approach to Solve the Coin Change Problem Like the rod cutting problemcoin change problem also has the property of the optimal substructure i. Code for Coin Change Problem We are going to use the bottom-up implementation of the dynamic programming to the code.

We know that for a value of 0, no coins are needed at all. Now we just need to change the value of the array M to the calculated minimum and return it. New Questions error: can't find main String[] method in class: - Java. We want to calculate the total marks of each student of a class in Physics,Chemistry and Mathematics and the average marks of the class. The number of - Cpp. Please provide the solution of Problem 8 given below: Thank you - Java. I am working on a project in C language and I want to do one way hashing of passwords but cannot find anything relevant on the internet.

Ask Yours.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I was trying to do this problem, where given coins of certain denomination, I want to find the maximum number of coins to make change.

Learn more. Asked 4 years, 9 months ago. Active 4 years, 9 months ago. Viewed 2k times. ArrayList; import java. However, how can I modify the above to find the maximum number of coins. JoSSte, yes sorry. Editing it so as to not confuse people. I would probably look at factoring. For each value find the biggest number divisible by the smallest coin denomination, and look at the remainder.

Input: The first line of input contains an integer T denoting the number of test cases. Each test case consist of an Integer value N denoting the amount to get change for. Output: Print all the denominations needed to make the change in a separate line. Example: Input: 1 If you have purchased any course from GeeksforGeeks then please ask your doubt on course discussion forum. You will get quick replies from GFG Moderators there. Please choose 'ReadOnlyMode' if you needn't to 'Edit' the problem e.

## Coin Change Problem | Dynamic Programming

EditMode ReadOnlyMode. Close Run Code. Close See Output. Login to report an issue on this page. Attach Screenshot optional. Send Close.Given a value V. Find the minimum number of coins to make the change. Input: The first line of input contains an integer T denoting the number of test cases.

The first line of each test case is V and N, V is the value of cents and N is the number of coins. The second line of each test case contains N input C[i], value of available coins.

Output: Print the minimum number of coins to make the change, if not possible print "-1". Example: Input : 1 7 2 2 1. Explanation : Testcase 1: We can use coin with value 2 three times, and coin with value 1 one times to change a total of 7. If you have purchased any course from GeeksforGeeks then please ask your doubt on course discussion forum.

You will get quick replies from GFG Moderators there. Please choose 'ReadOnlyMode' if you needn't to 'Edit' the problem e. Please note that Custom Input s should be mentioned in the same order format as stated in the problem description.

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### What is the minimum number of coins that must be reversed

Close See Output. Login to report an issue on this page. Attach Screenshot optional. Send Close. Ibrahim Nash.If you have only one more dime, that leaves cents in nickels or quarters, which is impossible. Coin Change Problem: Given an unlimited supply of coins of given denominations, find the total number of distinct ways to get a desired change The idea is to use recursion to solve this problem.

For example, given array A consisting of eight numbers, such that: The triangle is arranged so that the first row has 1 counter, second row has 2 counters, third row as 3 counters, fourth row as 4 counters and so on. What is the smallest number of trips needed to make the crossing? When I arrange the members of a marching band in rows of 2, 3, or 4, there is always 1 person left over.

After 24 days and 24 nights, the sloth is 24 feet up. It is common for six confirmations to be required which takes about an hour. The United States Mint does not sell its bullion coins directly to the public. Given three positive integers N, L and R, find the number of non-decreasing sequences of size at least 1 and at most N, such that each element of the sequence lies between L and R, both inclusive.

You may use the balance twice. Consecutive elements of array A represent: consecutive coins in the row. Reversing coins there are n coins, each showing either heads or tails. Learn vocabulary, terms, and more with flashcards, games, and other study tools. If the first toss is Tails then the second toss must be Heads and the third toss must be Tails. N, and there is infinite supply of each of the denominations in Indian currency, i.

Peter has one of each of the following coins in his pocket: a penny, a nickel, a dime, a quarter, and a half-dollar.

Complete the getWays function in the editor below. The Reversed Emperor must sleep with one eye open. If you have two dimes, that leaves cents for nickels or quarters, which is again impossible. C program to find minimum or the smallest element in an array. The minimum User-to-user transactions within bitcoinwallet. It is a special case of the integer knapsack problemand has applications wider than just currency.