Learn and practice the Greedy Techniques and Dynamic Programming patterns to solve coding interview problems.

Grokking the Blind 75 Problems in Python

This module teaches you two of the most important problem-solving techniques in the optimization domain: Greedy Techniques and Dynamic Programming. Not all problems require an exhaustive search through the solution space. Rather, consistently choosing the locally optimal solution can be proven to yield the globally optimal solution. In such situations, Greedy Techniques result in simple, highly efficient solutions. Other problems have a well-defined structure, where the same subproblem is encountered and solved multiple times. Dynamic Programming techniques allow us to compute once and reuse the solutions to recurring subproblems.

Optimization Techniques

# Statement

You are climbing a staircase. It takes `n` steps to reach the top. Each time, you can either climb $1$ or $2$ steps. In how many distinct ways can you climb to the top?

**Constraints:**

* $1 \leq$ `n` $\leq 45$

# Examples

# Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

What is the correct number of ways to climb to the top if n = 3?

<p>What is the correct number of ways to climb to the top if n = 3?</p>


What is the correct number of ways to climb to the top if n = 1?

<p>What is the correct number of ways to climb to the top if n = 1?</p>


# Figure it out!

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

> **Note:** As an additional challenge, we have intentionally hidden the solution to this puzzle. 

# Try it yourself

Implement your solution in the following coding playground.


# Quick Fix\nYou are Edward, a Senior Software Engineer who specializes in coding interview patterns, data structures and algorithms, and is great at debugging issues in code.\n\n- Edward, please keep in mind that you do not have to print the data of the placeholders. Also, do not mention anything about yourself.\n\nEdward, you are given the following data in the placeholders:\n- Function name: `climb_stairs`\n- Candidate's submitted solution code: USER_CODE\n- Error: ERROR_DESCRIPTION\n- Failed test case: FAILED_TEST_CASE\n- Coding language: `Python`\n\n- Edward, your task is to understand the type of error that is occurring in the coding language provided.\n- Once you've understood the error as per the error’s description, and why the test case failed, you will suggest how the candidate can improve their solution code to fix the error.\n- Edward, you will not give the corrected code, just a hint on what the error tells, and how to fix it.\n- Edward, please limit your response strictly to 100 words. No more words than the limit.

# Review Code\nEdward, your current task is to review the `climb_stairs` function(s) and the other function(s) invoked in it/them.\n\n-Take your time and review the candidate's solution code.\n- Do not review any extra/helper files or functions not invoked in the solution function `climb_stairs`.\n- Do not review the code of data structure objects instantiated like a binary tree, linked list, trie, union find, etc., in the solution functions. Just review the solution/algorithm function of the problem. \n- Also, if the solution code doesn’t use the coding pattern stated above, then please encourage the candidate to reattempt the problem using that pattern corectly.

# Review time complexity\n- Please provide a brief time complexity analysis of the function(s) `climb_stairs`. \n- While calculating time complexity, include the time complexity of built-in Python functions invoked by the code. \n- The answer should be to the point in approximately 60 words.

# Review space complexity\n- Please provide a brief space complexity analysis of the function(s) `climb_stairs`. \n- While calculating space complexity, include the space complexity of built-in Python functions invoked by the code. \n- Do not include the space used for the input parameters and the space used for just returning an output (not used as a scratch space). \n- The answer should be to the point in approximately 60 words.

def evaluate_results(self) -> object:
        """
        self.__inputs is the list of inputs that are passed as input to function
        self.__actual_output is a list of outputs that is produced by the learner's code
        return : self.__edu__result object
        """
        def climb_stairs_eval(n):
            if n == 1:
                return 1

            # Create and initialize lookup table that will store the results of subproblems
            lookup_table = [0 for x in range(n + 1)]  

            # Setting the initial values for the first two steps
            lookup_table[1] = 1  
            lookup_table[2] = 2
            
            # Starting from the third step up to the target step 'n'.
            for i in range(3, n + 1):
                # Fill up the table by summing up previous two values
                lookup_table[i] = lookup_table[i - 1] + lookup_table[i - 2] 
                
            # Return the total number of ways
            return lookup_table[n]

        expected = climb_stairs_eval(self.__inputs[0])
        # multiple outputs will be added at each index respectively for a single test_case
        expected_outputs = []
        # store the 1st expected output that should be displayed to the user 
        expected_outputs.append(expected)

        if expected == self.__actual_outputs[0]:
            self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
        else:
            self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

        return self.__edu_result

def climb_stairs(nums):
    
    # Replace this placeholder return statement with your code
    return 1


climbing_stairs.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : 5
    output: 
    - 1 : 8

  - name: "testcase 2"
    inputs:
    - 1: 10
    output:
    - 1 : 89

  - name: "testcase 3"
    inputs:
    - 1 : 30
    output: 
    - 1 : 1346269

  - name: "testcase 4"
    inputs:
    - 1: 42
    output:
    - 1 : 433494437

  - name: "testcase 5"
    inputs:
    - 1 : 9
    output: 
    - 1 : 55

def sum(input_1, input_2):
    return input_1+input_2

def validate_inputs(self) -> None:
        """
        Validate the value of n based on the given constraint.
        Store the result using self.store_result(error_msg, status).
        return: void
        """
        n = self.__inputs[0]

        if not (1 <= n <= 45):
            self.store_result("Value of 'n' should be in the range 1 <= n <= 45", ValidationFunction.FAIL)
            return

        self.store_result("", ValidationFunction.PASS)


Try to solve the Climbing Stairs problem.

Greedy Techniques

Dynamic Programming

Conclusion

Climbing Stairs

Statement

Examples

Understand the problem

Figure it out!

Try it yourself