Peter Cao

- 5-7.5% of the test
- Roughly
**2 to 3**multiple-choice questions

Sometimes, you can break down a large problem or task by doing a subproblem repeatedly. This is called **recursion**. If this sounds like loops and iteration, it's because all recursive (the adjective form of recursion) methods can be written as a loop! We will learn how to use recursion effectively and see how this will simplify our code!

When writing recursion, notice how the code is much more simplified than if we were using loops. But, they will run slower, so we will sacrifice speed for conciseness in code. Recursive code has two main parts, the **repeating/recursive part** and the **base case** which makes sure we don't create an infinite loop in which our programs never stop.

- Intro to Recursion
- How to code recursive methods
- Recursive Algorithms

Here is its anatomy:

```
public static void recursiveMethod()
if (baseCaseCondition) { // base case
base case steps
} else {
do something
recursiveMethod(); // recursive call
}
}
```

The base case is the last recursive call. When the base case is reached, the recursion is stopped and a value is returned. The base case is the easiest part of the recursive call to write and should be written first to make sure that the program doesn't run forever.

The recursive calls are the different calls to the method. Each of the different recursive calls has different parameter values and leads up to the base case being reached. To write efficient recursion, recognize what the subtask is and what is different between each time the subtask is done. The subtask is the recursive call and what is different and stays the same are the parameters.

Whenever we have a recursive method, we have a **call stack** that keeps track of all the times that the recursive function is called, as well as their individual parameters. This is useful for when we have a function that has a recursive call in its return statement where the results of later recursive calls are used in past calls. Here is a picture demonstrating the call stack for recursion.

In this, x and e are the parameters of the recursive calls, and h is the result of the recursion that is passed back up. The recursive calls are made from top to bottom, while the recursive returns are passed from bottom to top. This is where tracing comes in handy, as shown in the picture above!

All recursion can be written as a loop, that is, all recursive code can be written iteratively. If we can just use iteration, why use recursion? The main answer? Simplicity. Recursive code is usually easier to read than iterative code. Is there a trade-off? Yes. This comes in the form of speed and memory. This is because the call stack takes up memory in your computer when running the program, and it takes time to pass up the recursive return values.

Here is an example of an iterative and recursive method to do multiplication using repeated addition:

```
public static int multiply(int a, int b) {
int sum = 0;
for (int i = 0; i < b; i++) {
sum += a;
}
return sum;
}
```

```
public static int multiply(int a, int b) {
if (b == 0) {
return 0;
} else {
return multiply(a, b - 1) + a;
}
}
```

On the AP test FRQs, you can choose whether to write code iteratively or recursively, but you still have to know how recursion works for the AP exam!

We can write ArrayList traversal using recursion. As a reminder, here is the iterative code:

```
for (int i = 0; i < arrayList.size(); i++) {
System.out.println(arrayList);
}
```

Meanwhile, here is the recursive code:

```
public static void traverseArray(ArrayList<Integer> array, int startIndex) {
if (startIndex == array.size() - 1) { // base case
System.out.println(array.get(0));
} else { // recursive case
System.out.println(array.subList(startIndex, array.size()).get(0));
traverseArray(array, startIndex + 1)
}
}
//to use the above method
traverseArray(array, 0)
```

The recursion is actually getting the sublist of the big ArrayList with the first item in the sublist acting as the next item to be printed, and the last item in the sublist acts as the last item in the ArrayList. The base case is when there is only one item left in the sublist, at which point the last item is printed and the method stopped.

Browse Study Guides By Unit

➕Unit 1 – Primitive Types

📱Unit 2 – Using Objects

🖥Unit 3 – Boolean Expressions & if Statements

🕹Unit 4 – Iteration

⚙️Unit 5 – Writing Classes

⌚️Unit 6 – Array

💾Unit 7 – ArrayList

💻Unit 8 – 2D Array

🖲Unit 9 – Inheritance

🖱Unit 10 – Recursion

- The Big Takeaway of this Unit
- Exam Weighting
- Enduring Understanding
- Building Computational Thinking
- Main Ideas for the Unit 💡
- 10.1 Recursion
- 10.2 Recursive Searching and Sorting
- Merge Sort
- The Base Case
- Recursive Calls and the Call Stack
- Recursion vs. Loops
- Iterative Code:
- Recursive Code:
- Recursive Traversals
- What This Method Is Doing
- The Big Takeaway Of This Unit
- Unit Overview
- Exam Weighting
- Enduring Understanding
- Building Computational Thinking
- Main Ideas for This Unit
- 10.1: Recursion
- Intro to Recursion
- The Base Case
- Recursive Calls and the Call Stack
- Recursion vs. Loops
- Recursive Traversals

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