Dynamic Programming freeCodeCamp

• What is dynamic programming often perceived as?

  A very difficult topic
• Why is dynamic programming important for interviews?

  It is essential for data structure interviews
• Why does dynamic programming have a bad reputation?

  Problems vary greatly and seem unrelated
• What will students analyze in their solutions?

  Time and space complexity
• What are the first two numbers in the Fibonacci sequence?

  Both are one
• How is the next number in the Fibonacci sequence generated?

  By summing the previous two numbers
• What is the seventh Fibonacci number?

  13
• What is the time complexity of the classic recursive Fibonacci function?

  Exponential, specifically $O(2^n)$
• Why is the recursive Fibonacci function slow for large values of n?

  It has many repeated calculations
• What is a common mistake students make when visualizing problems?

  Trying to picture everything mentally
• What should students do to visualize complex problems?

  Draw on paper or a whiteboard
• What does the base case in the Fibonacci function return?

  One for inputs less than or equal to two
• How does the Fibonacci function calculate its result?

  By summing the results of previous calls
• What does the visualization of the Fibonacci function resemble?

  A recursive tree structure
• What do the nodes in the recursive tree represent?

  The values of n passed into the function
• What happens when a base case is reached in the Fibonacci function?

  It returns one to its parent node
• How does the final result of the Fibonacci function get calculated?

  By adding values from child nodes
• What is the final result of the Fibonacci function for the seventh number?

  13
• What is the time complexity of the Fibonacci function based on its recursive structure?

  Exponential, $O(2^n)$
• What is the purpose of visualizing the Fibonacci function?

  To understand its recursive structure
• What does the foo function illustrate in terms of recursion?

  It shows how recursive calls are made
• What happens when the foo function is called with a non-base case?

  It makes further recursive calls
• What is the significance of the base case in recursive functions?

  It prevents infinite recursion
• How does the recursive structure of the foo function behave?

  It creates a chain of calls until a base case
• What is the first step when visualizing a recursive function?

  Identify the base case
• What is the goal of the Fibonacci function?

  To return the nth Fibonacci number
• What is the expected output for fib(6)?

  8
• What is the expected output for fib(7)?

  13
• What is the expected output for fib(8)?

  21
• What is the expected output for fib(15)?

  610
• What is the significance of drawing the recursive tree?


  It helps visualize the recursive calls
• What does the recursive tree reveal about the Fibonacci function?

  It shows overlapping subproblems
• What is the relationship between the Fibonacci function and recursion?

  Fibonacci is a classic example of recursion
• What is the purpose of analyzing time complexity?

  To understand the efficiency of algorithms
• What is the expected behavior of the foo function?

  It will call itself recursively
• What is the first step in analyzing a recursive function?

  Identify the base case and recursive calls
• What is the expected output for foo(5)?

  It will call foo(4), foo(3), etc.
• What is the significance of the Fibonacci sequence in programming?

  It illustrates recursion and dynamic programming
• What is the expected output for fib(0)?

  1
• What is the expected output for fib(1)?


  1