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

Speedrun the Microsoft Coding Interview: Top Problems in C++

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

Given the following array, what is the maximum product we can obtain from a subarray?

`nums` = [1, 2, 3, 0, 4]

Given the following array, what is the maximum product we can obtain from a subarray?
<code>nums</code> = [1, 2, 3, 0, 4]

Given the following array, what is the maximum product we can obtain from a subarray?

`nums` = [7, 4, 1]

Given the following array, what is the maximum product we can obtain from a subarray?
<code>nums</code> = [7, 4, 1]

Given the following array, what is the maximum product we can obtain from a subarray?

`nums` = [-3, 4, -5, 10, -1, 0]

Given the following array, what is the maximum product we can obtain from a subarray?
<code>nums</code> = [-3, 4, -5, 10, -1, 0]

Maximum Product Subarray

Maximum Product Subarray

An integer in the array can be positive, zero, or negative. Think about how each will affect the product of a subarray?

The maximum product at any point depends on the maximum and minimum products found so far, so keep updating these as you go.

# 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: `MaxProduct`\n- Candidate's submitted solution code: USER_CODE\n- Error: ERROR_DESCRIPTION\n- Failed test case: FAILED_TEST_CASE\n- Coding language: `C++`\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 `MaxProduct` 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 `MaxProduct`.\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) `MaxProduct`. \n- While calculating time complexity, include the time complexity of built-in C++ 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) `MaxProduct`. \n- While calculating space complexity, include the space complexity of built-in C++ 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 max_product2(nums):
            if len(nums) == 0:
                return 0

            max_so_far = nums[0]
            min_so_far = nums[0]
            result = max_so_far

            for i in range(1, len(nums)):
                curr = nums[i]

                temp_max_so_far = max(curr, max_so_far * curr, min_so_far * curr)
                min_so_far = min(curr, max_so_far * curr, min_so_far * curr)
                max_so_far = temp_max_so_far

                result = max(max_so_far, result)

            return result
        
        def compareResult(expected, actual_output):
            
            if expected == actual_output:
                return True
            return False

        # 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 = max_product2(self.__inputs[0])
        expected_outputs.append(expected)

        actual_output = self.__actual_outputs[0]
        compare = compareResult(expected, actual_output)
        if compare:
            self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
        else:
            self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

        return self.__edu_result

int MaxProduct(std::vector<int> nums) {
 // Replace this placeholder return statement with your code
 return -1;
}

max_product.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [-2, 0, -1]
    output: 
    - 1 : 0
  - name: "testcase 2"
    inputs:
    - 1 : [2, 3, -2, 4]
    output: 
    - 1 : 6
  - name: "testcase 3"
    inputs:
    - 1 : [2, -5, 3, 1, -4, 0, -10, 2]
    output: 
    - 1 : 120
  - name: "testcase 4"
    inputs:
    - 1 : [1, 2, 3, 0, 4]
    output: 
    - 1 : 6
  - name: "testcase 5"
    inputs:
    - 1 : [5, 4, 3, 10, 4, 1]
    output: 
    - 1 : 2400
  

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

def validate_inputs(self) -> None:
 """
 self.__inputs is the list of inputs that are passed as input to function
 store the result using the self.store_result(error_msg, status)
 return : void
 """
 def max_product2(nums):
 if len(nums) == 0:
 return 0

 max_so_far = nums[0]
 min_so_far = nums[0]
 result = max_so_far

 for i in range(1, len(nums)):
 curr = nums[i]

 temp_max_so_far = max(curr, max_so_far * curr, min_so_far * curr)
 min_so_far = min(curr, max_so_far * curr, min_so_far * curr)
 max_so_far = temp_max_so_far

 result = max(max_so_far, result)

 return result

 def main(nums):
 res=max_product2(nums)
 if res < -2**31:
 res = -2**31
 elif res > 2**31 - 1:
 res = 2**31 - 1

 return res
 
 inp = self.__inputs[0]

 def is_valid_1d_array(arr):
 if not isinstance(arr, list):
 return False # Not a valid 1D array if it's not a list
 
 return all(isinstance(elem, int) and not isinstance(elem, bool) for elem in arr)
 

 if not (is_valid_1d_array(inp)):
 self.store_result ("Invalid test case", ValidationFunction.FAIL)
 elif max_product2(inp) > 2**31 - 1:
 self.store_result ("Subarray product exceeds 32-bit integer representation", ValidationFunction.FAIL)
 # inputs can be accessed using self.__inputs starting from 0 to len(self.__inputs) - 1
 elif len(self.__inputs[0]) < 1 or len(self.__inputs[0]) > 20000:
 self.store_result ("Array length should be in range [1, 20000]", ValidationFunction.FAIL)
 elif any(x < -10 or x > 10 for x in self.__inputs[0]):
 self.store_result("Arrays elements should be in range [-10, 10]", ValidationFunction.FAIL)
 else:
 self.store_result("", ValidationFunction.PASS)

Try to solve the Maximum Product Subarray problem.


Greedy Techniques

Dynamic Programming

Conclusion

Maximum Product Subarray

Statement

Example

Understand the problem

Figure it out

Try it yourself