algorithmdynamic-programmingcoin-change# Dynamic Programming Coin Change Limited Coins

**Dynamic Programming Change Problem (Limited Coins)**.
I'm trying to create a program that takes as **INPUT:**

```
int coinValues[]; //e.g [coin1,coin2,coin3]
int coinLimit[]; //e.g [2 coin1 available,1 coin2 available,...]
int amount; //the amount we want change for.
```

**OUTPUT:**

```
int DynProg[]; //of size amount+1.
```

And output should be an Array of size **amount+1** of which each cell represents the optimal number of coins we need to give change for the amount of the cell's index.

**EXAMPLE:** Let's say that we have the cell of Array at index: 5 with a content of 2.
This means that in order to give change for the amount of 5(**INDEX**), you need 2(**cell's content**) coins (Optimal Solution).

Basically I need exactly the output of the first array of this **video**(C[p])
. It's exactly the same problem with the big **DIFFERENCE** of **LIMITED COINS**.
Link to Video.

Note: See the video to understand, ignore the 2nd array of the video, and have in mind that I don't need the combinations, but the DP array, so then I can find which coins to give as change.

Thank you.

Solution

Consider the next pseudocode:

```
for every coin nominal v = coinValues[i]:
loop coinLimit[i] times:
starting with k=0 entry, check for non-zero C[k]:
if C[k]+1 < C[k+v] then
replace C[k+v] with C[k]+1 and set S[k+v]=v
```

Is it clear?

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