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Topological Sort

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Behavioral

Given the following input:

* parent = `[-1, 0, 0, 1, 1]`
* s = `"abaca"`

What is the length of the longest valid path where adjacent nodes have distinct characters?

Given the following input:
<ul>
<li>parent = <code>[-1, 0, 0, 1, 1]</code></li>
<li>s = <code>&quot;abaca&quot;</code></li>
</ul>
What is the length of the longest valid path where adjacent nodes have distinct characters?

```
         0(a)
       /      \
     2(d)     1(b)
    /            \
  4(c)           3(e)
```

```
         0(a)
       /      \
     2(d)     1(b)
    /   \
  4(c)  3(e)
```

```
         0(a)
       /      \
     2(d)     1(b)
              /   \
            4(c)  3(e)
```

How would a tree look like if the following values are given as input?

* parent = `[-1, 0, 0, 1, 2]`
* s = `"abdec"`

How would a tree look like if the following values are given as input?
<ul>
<li>parent = <code>[-1, 0, 0, 1, 2]</code></li>
<li>s = <code>&quot;abdec&quot;</code></li>
</ul>

$2 \rightarrow 1 \rightarrow 0 \rightarrow 3 \rightarrow 4$

$2 \rightarrow 1 \rightarrow 0 \rightarrow 3 \rightarrow 5$

$4 \rightarrow 3 \rightarrow 1 \rightarrow 0 \rightarrow 5$

$5 \rightarrow 3 \rightarrow 1 \rightarrow 0 \rightarrow 4$

$2 \rightarrow 0 \rightarrow 1 \rightarrow 3 \rightarrow 4$

$2 \rightarrow 0 \rightarrow 1 \rightarrow 3 \rightarrow 5$

$1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 5$

$1 \rightarrow 2 \rightarrow 5 \rightarrow 4 \rightarrow 3$

Given the following input:

* parent = `[-1, 0, 0, 1, 3, 3]`
* s = `"abcaba"`

What is the length of the longest valid path where adjacent nodes have distinct characters?

Given the following input:
<ul>
<li>parent = <code>[-1, 0, 0, 1, 3, 3]</code></li>
<li>s = <code>&quot;abcaba&quot;</code></li>
</ul>
What is the length of the longest valid path where adjacent nodes have distinct characters?

Longest Path With Different Adjacent Characters

Longest Path With Different Adjacent Characters

# 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: `longest_path`\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 `longest_path` 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 `longest_path`.\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) `longest_path`. \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) `longest_path`. \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
        """
        from collections import deque

        def longest_path_evaluation(parent, s):
            n = len(parent)
        
            in_degree = [0] * n
            for node in range(1, n):
                in_degree[parent[node]] += 1
        
            queue = deque()
            longest_chains = [[0, 0] for _ in range(n)]
            longest_path = 1
        
            for node in range(n):
                if in_degree[node] == 0:
                    longest_chains[node][0] = 1
                    queue.append(node)
        
            while queue:
                current_node = queue.popleft()
                par = parent[current_node]
        
                if par != -1:
                    longest_chain_from_current = longest_chains[current_node][0]
        
                    if s[current_node] != s[par]:
                        if longest_chain_from_current > longest_chains[par][0]:
                            longest_chains[par][1] = longest_chains[par][0]
                            longest_chains[par][0] = longest_chain_from_current
                        elif longest_chain_from_current > longest_chains[par][1]:
                            longest_chains[par][1] = longest_chain_from_current

                    longest_path = max(longest_path, longest_chains[par][0] + longest_chains[par][1] + 1)

                    in_degree[par] -= 1
                    if in_degree[par] == 0:
                        longest_chains[par][0] += 1
                        queue.append(par)

            return longest_path

        expected = longest_path_evaluation(self.__inputs[0], self.__inputs[1])
        actual = self.__actual_outputs[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 json.dumps(expected) == json.dumps(actual):
            self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
        else:
            self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

        return self.__edu_result

from collections import deque

def longest_path(parent, s):
    
    # Replace the following placeholder statement with your code
    return -1


parent-string-test-cases.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [-1, 0, 0, 1, 1, 2, 2]
    - 2 : "abcdefg"
    output: 
    - 1 : 5
  - name: "testcase 2"
    inputs:
    - 1: [-1, 0, 0, 0]
    - 2: "aabc"
    output:
    - 1 : 3
  - name: "testcase 3"
    inputs:
    - 1 : [-1, 0, 0, 1, 1, 2]
    - 2 : "abacbe"
    output: 
    - 1 : 3
  - name: "testcase 4"
    inputs:
    - 1: [-1]
    - 2: "a"
    output:
    - 1 : 1
  - name: "testcase 5"
    inputs:
    - 1: [-1, 0, 1, 2]
    - 2: "aaaa"
    output:
    - 1 : 1

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
 """
 parent = self.__inputs[0] # The parent array.
 s = self.__inputs[1] # The string of characters.
 
 n = len(parent)
 
 # Check if n == len(s)
 if n != len(s):
 self.store_result("parent and s must have the same length", ValidationFunction.FAIL)
 return
 
 # Check if n is within the allowed range
 if not (1 <= n <= 10**5):
 self.store_result("n must be between 1 and 100000", ValidationFunction.FAIL)
 return
 
 # Check the first element of parent
 if parent[0] != -1:
 self.store_result("parent[0] must be -1 as the root node", ValidationFunction.FAIL)
 return
 
 # Check the remaining elements of parent
 for i in range(1, n):
 if not (0 <= parent[i] < n):
 self.store_result(f"parent[{i}] must be between 0 and {n-1}", ValidationFunction.FAIL)
 return
 
 # Check if s consists only of lowercase English letters
 if not all('a' <= ch <= 'z' for ch in s):
 self.store_result("s must consist of only lowercase English letters", ValidationFunction.FAIL)
 return
 
 # Check if the parent array represents a valid tree.
 # If n == 1, it is a valid single-node tree.
 if n == 1:
 if parent[0] == -1 and len(s) == 1:
 self.store_result("", ValidationFunction.PASS)
 return
 
 # Initialize an array to track if we have visited a node.
 visited = [False] * n
 children_count = [0] * n
 
 # Visit all nodes and count their children
 for i in range(1, n):
 parent_node = parent[i]
 children_count[parent_node] += 1
 
 # If a node already has 0 parents (not the root), there's a problem.
 if visited[i]:
 self.store_result("Cycle detected or disconnected component", ValidationFunction.FAIL)
 return
 visited[i] = True
 
 # Ensure there's only one root and that it's connected
 root_count = 0
 for i in range(n):
 if parent[i] == -1:
 root_count += 1
 
 if root_count != 1:
 self.store_result("There must be exactly one root node", ValidationFunction.FAIL)
 return
 
 # If tree passes all checks
 self.store_result("", ValidationFunction.PASS)

Try to solve the Longest Path With Different Adjacent Characters problem.

Problem: Longest Path With Different Adjacent Characters

Statement

Examples

Understand the problem

Figure it out!