If you’ve ever struggled with solving problems using recursion, or if you have to brush up your skills for an interview, this course is for you.

We'll start with the basics of what recursion is and why it’s important before diving into practicing solving actual questions. You’ll have access to detailed explanations and visualizations for each problem to help you along the way. 

By the time you have completed this course, you’ll be able to use all the concepts to solve complex real-world problems. We hope that through practicing recursion, you will be able to ace all recursion related questions in interviews at top tech companies.

Solving Problems with Recursion in Python

```python
if startIndex >= length :
  return
```

```python
if startIndex <= length :
 return
```

```python
if startIndex >= length/2 :
   return
```

```python
if startIndex >= 0 :
   return
```

The function below prints a string recursively, such that one character is printed in each recursive call.
```python
def printArray(array, startIndex, length) :
  # Base case
  _______________________________
  
  print(arr[startIndex] + "\t")
  
  #Recursively calling printArray to print next element in the array
  printArray(array, startIndex + 1, length)
```
What should be the base case of the following code?

The function below prints a string recursively, such that one character is printed in each recursive call.
<pre><code class="language-python">def printArray(array, startIndex, length) :
 # Base case
 _______________________________
 
 print(arr[startIndex] + &quot;\t&quot;)
 
 #Recursively calling printArray to print next element in the array
 printArray(array, startIndex + 1, length)
</code></pre>
What should be the base case of the following code?

```python
return array[0] + arraySum(array[1:]) 
```

```python
return (array[0], arraySum(array))
```

The function below prints the **sum** of array elements using recursion.
```python
def arraySum(array):
    # Base Case
    if len(array) == 0 :
        return 0

    # Recursive Case    
    else:
       ___________________________
```

What should be the **recursive case** of the following code?


The function below prints the sum of array elements using recursion.
<pre><code class="language-python">def arraySum(array):
 # Base Case
 if len(array) == 0 :
 return 0

 # Recursive Case 
 else:
 ___________________________
</code></pre>
What should be the recursive case of the following code?

```python
helperFunction(array, key, low, high)
```

```python
return helperFunction(array, key, low + 1, high - 1)
```

```python
helperFunction(array, key, low - 1, high + 1)
```

```python
return helperFunction(array, key, low, high)
```

Fill in the code to complete the following function for **binary search** that returns the index of the element being serached.
```python
def recursiveBinarySearch(array, key) :
 low = 0
 high = len(array) - 1
 ________________________________________

def helperFunction(array, key, low, high):
 if low > high: # The key was not found in the array
 return -1

 mid = (low + high) // 2
 
 if key < array[mid]:
 return helperFunction(array, key, low, mid - 1)
 
 elif key == array[mid]:
 return mid
 
 else:
 return helperFunction(array, key, mid + 1, high)
 ```

Fill in the code to complete the following function for binary search that returns the index of the element being serached.
<pre><code class="language-python">def recursiveBinarySearch(array, key) :
 low = 0
 high = len(array) - 1
 ________________________________________

def helperFunction(array, key, low, high):
 if low &gt; high: # The key was not found in the array
 return -1

 mid = (low + high) // 2
 
 if key &lt; array[mid]:
 return helperFunction(array, key, low, mid - 1)
 
 elif key == array[mid]:
 return mid
 
 else:
 return helperFunction(array, key, mid + 1, high)
</code></pre>

This Quiz will take maximum 10 minutes.

This Quiz will take maximum 10 minutes.

---
In the next chapter, we will be using recursion to solve problems dealing with data structures.

Recursion Fundamentals

Iteration Vs. Recursion

Recursion with Numbers

Recursion with Strings

Recursion with Arrays

Recursion with Data Structures

Conclusion

Test Your Knowledge 5

Quiz on Arrays