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

**Constraints:**

- $1 \leq$ `coins.length` $\leq 12$

- $1 \leq$ `coins[i]` $\leq 10^4$

- $0 \leq$ `total` $\leq 900$

What's the minimum number of coins required to make up the given total with the following set of coins?


`coins` = [1, 2, 3, 4]. \
`total` = 11.

What’s the minimum number of coins required to make up the given total with the following set of coins?
<code>coins</code> = [1, 2, 3, 4]. 
<code>total</code> = 11.

Using **2** coins of denomination 4 and **1** coin of denomination 2

Which scenario would result in a valid solution for the given total and coins?


`coins` = [2, 4, 6]. \
`total` = 7.

Which scenario would result in a valid solution for the given total and coins?
<code>coins</code> = [2, 4, 6]. 
<code>total</code> = 7.

What’s the minimum number of coins required to make up the given total with the following set of coins?

`coins` = [1, 2, 3]. \
`total` = 0.

What’s the minimum number of coins required to make up the given total with the following set of coins?
<code>coins</code> = [1, 2, 3]. 
<code>total</code> = 0.

What’s the minimum number of coins required to make up the given total with the following set of coins?


`coins` = [4, 5, 6]. \
`total` = 10.

What’s the minimum number of coins required to make up the given total with the following set of coins?
<code>coins</code> = [4, 5, 6]. 
<code>total</code> = 10.

Coin Change

Coin Change

# 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: `coin_change`\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 `coin_change` 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 `coin_change`.\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) `coin_change`. \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) `coin_change`. \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 calculate_minimum_coins(coins, rem, counter): 
 if rem < 0: 
 return -1
 if rem == 0:
 return 0
 if counter[rem - 1] != float('inf'):
 return counter[rem - 1]
 minimum = float('inf')

 for s in coins: 
 result = calculate_minimum_coins(coins, rem - s, counter)
 if result >= 0 and result < minimum:
 minimum = 1 + result

 counter[rem - 1] = minimum if minimum != float('inf') else -1 
 return counter[rem - 1]

 def coin_change2(coins, total): 
 if total < 1:
 return 0
 return calculate_minimum_coins(coins, total, [float('inf')] * total)

 def compareResult(expected, actual_output):
 # expected.sort()
 # actual_output.sort()
 
 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 = coin_change2(self.__inputs[0], self.__inputs[1])
 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

def coin_change(coins, total):
    # Replace this placeholder return statement with your code
    return -1

coin-change.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1: [1,2,5]
    - 2: 11
    output: 
    - 1 : 3
  - name: "testcase 2"
    inputs:
    - 1: [2]
    - 2: 4
    output: 
    - 1 : 2
  - name: "testcase 3"
    inputs:
    - 1: [5]
    - 2: 3
    output: 
    - 1 : -1
  - name: "testcase 3"
    inputs:
    - 1: [1,2,5]
    - 2: 0
    output: 
    - 1 : 0
  - name: "testcase 5"
    inputs:
    - 1: [2,3,4,6,8]
    - 2: 23
    output: 
    - 1 : 4

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 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)

 coins_array = self.__inputs[0]
 
 if not is_valid_1d_array(coins_array):
 self.store_result ("Invalid 1D array", ValidationFunction.FAIL)
 elif not isinstance(coins_array, list):
 self.store_result ("Expected integer array", ValidationFunction.FAIL)
 elif any(num is None for num in coins_array):
 self.store_result ("Array should not contain null values", 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]) > 12:
 self.store_result ("Coins array length should be in range [1, 12]", ValidationFunction.FAIL)
 elif self.__inputs[1] < 0 or self.__inputs[1] > 900:
 self.store_result("Total amount should be in range [0, 900]", ValidationFunction.FAIL)
 elif any(x <= 0 or x > 10000 for x in self.__inputs[0]):
 self.store_result("Coin denomination should be in range [1, 10000]", ValidationFunction.FAIL)
 else:
 self.store_result("", ValidationFunction.PASS)

Greedy Techniques

Dynamic Programming

Conclusion

Coin Change

Statement

Examples

Understand the problem

Figure it out!

Try it yourself