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

What is the output of the following code?
```python
def foo(x, p) :
    if (p == 0):
      return 1;
    else :
      return (x * foo(x, p - 1))
    
# Driver Code
print(foo(2, 5))
```


What is the output of the following code?
<pre><code class="language-python">def foo(x, p) :
 if (p == 0):
 return 1;
 else :
 return (x * foo(x, p - 1))
 
# Driver Code
print(foo(2, 5))
</code></pre>

What is the output of the following code?
```python
def foo(n) :
    if n == 12 :
        return n
    else :
        return foo(n + 1)

# Driver code
print(foo(3))
```

What is the output of the following code?
<pre><code class="language-python">def foo(n) :
 if n == 12 :
 return n
 else :
 return foo(n + 1)

# Driver code
print(foo(3))
</code></pre>

What is the output of the following code?
```python
def foo(n):
    if n == 0 :
        print("False")
        return
      
    if n == 1 :
        print("True")
        return
    
    if n % 2 == 0 :
        foo(n / 2)
    else :
        print("False")
        return

# Driver Code
foo(64)
```

What is the output of the following code?
<pre><code class="language-python">def foo(n):
 if n == 0 :
 print(&quot;False&quot;)
 return
 
 if n == 1 :
 print(&quot;True&quot;)
 return
 
 if n % 2 == 0 :
 foo(n / 2)
 else :
 print(&quot;False&quot;)
 return

# Driver Code
foo(64)
</code></pre>

What is the output of the following piece of code?
```python
def foo(i, j):
    if i == 0 :
        return j
    else :
        return foo(i - 1, i + j)
      
# Driver Code
print(foo(4, 7))
```

What is the output of the following piece of code?
<pre><code class="language-python">def foo(i, j):
 if i == 0 :
 return j
 else :
 return foo(i - 1, i + j)
 
# Driver Code
print(foo(4, 7))
</code></pre>

What is the output of the following piece of code?
```python
def foo(n):
    if n > 100 :
      return n - 5
    return foo(foo(n + 11))
  
# Driver Code
print(foo(45))
```

What is the output of the following piece of code?
<pre><code class="language-python">def foo(n):
 if n &gt; 100 :
 return n - 5
 return foo(foo(n + 11))
 
# Driver Code
print(foo(45))
</code></pre>

What is the greatester common divisor of $5$ and $2$?

What is the greatester common divisor of <math><semantics><mrow><mn>5</mn></mrow><annotation encoding="application/x-tex">5</annotation></semantics></math>5 and <math><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math>2?

What should be the value of `testVariable` to satisfy the base case?
```python
def printPascal(testVariable) :
    if testVariable == 0 :
        return []
    if testVariable == 1 :
        return [1]

    else :
        line = [1]
        previousLine = printPascal(testVariable - 1)
        for i in range(len(previousLine) - 1):
            line.append(previousLine[i] + previousLine[i + 1])
        line += [1]
    return line
  ```

What should be the value of <code>testVariable</code> to satisfy the base case?
<pre><code class="language-python">def printPascal(testVariable) :
 if testVariable == 0 :
 return []
 if testVariable == 1 :
 return [1]

 else :
 line = [1]
 previousLine = printPascal(testVariable - 1)
 for i in range(len(previousLine) - 1):
 line.append(previousLine[i] + previousLine[i + 1])
 line += [1]
 return line
</code></pre>

The sum of integers from $1$ to $9$ is $9$.

The sum of integers from <math><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math>1 to <math><semantics><mrow><mn>9</mn></mrow><annotation encoding="application/x-tex">9</annotation></semantics></math>9 is <math><semantics><mrow><mn>9</mn></mrow><annotation encoding="application/x-tex">9</annotation></semantics></math>9.

The output of the following code is:
```python
print(11 // 2)
```

The output of the following code is:
<pre><code class="language-python">print(11 // 2)
</code></pre>

The power of a number can be calculated recursively.

The power of a number can be calculated recursively.

This Quiz will take maximum 10 minutes.

This Quiz will take maximum 10 minutes.

---
In the next chapter, we will be dealing with strings using recursion.

Recursion Fundamentals

Iteration Vs. Recursion

Recursion with Numbers

Recursion with Strings

Recursion with Arrays

Recursion with Data Structures

Conclusion

Test Your Knowledge 3

Quiz on Recursion with Numbers