Problem Description

In this problem, you are given the task of simulating the killing of processes in an operating system. Each process is identified by a unique ID. The relationships between processes are given in a tree-like structure, where every process is a node in the tree, and has one parent node except for the root process, which has no parent and is identified by ppid[i] = 0.

You are provided with two arrays: pid, which contains the ID of each process, and ppid, which contains the corresponding parent process ID for each process. The root of the tree is the process with no parent, and its ID is the one for which ppid[i] = 0.

Your task is to implement a function that, when given the ID of a process to kill, returns a list of all the process IDs that will be terminated. This includes the process itself and all of its descendant processes - in other words, its children, its children's children, and so on. The function should return the list of IDs in any order.

The problem statement implies that when a process is killed, it's not just that single process that stops - all processes that are 'below' it in the tree (its children) are also killed, recursively.

Flowchart Walkthrough

Let's analyze the problem from LeetCode 582. Kill Process using the described algorithm flowchart. You can refer to the flowchart directly here. Here’s a detailed step-by-step walkthrough based on the flowchart:

Is it a graph?

• Yes: The PID and PPID lists can be visualized as a graph where each PID is a node and each PPID is a connection to its parent PID.

Is it a tree?

• Yes: The structure of the process IDs where each PID (except the root) has exactly one parent PPID resembles a tree formation.

Since it is identified as a tree, the Depth-First Search (DFS) pattern is suggested as per the node right after confirming it is a tree in the flowchart. In the context of the problem, you'd use DFS to traverse through the nodes starting from the kill node and traversing all its descendants. This approach efficiently tracks all processes that need to be terminated.

Conclusion: The flowchart suggests using DFS since the problem representation aligns with a tree data structure, where DFS is ideal for traversing and handling each node starting from a specific node (the process to kill).

Intuition

To solve this problem, one intuitive approach is to map out the relationships between all processes in a way that allows you to easily identify a process's children. This can be effectively done using a graph data structure, where each process is a node and the edges represent the parent-child relationships.

First, construct a graph from the given pid and ppid arrays. In this graph, the key is the process ID of the parent, and the value is a list of IDs of its child processes. We represent this graph with a dictionary or a hashmap, where each entry corresponds to a process and its children. In Python, a defaultdict(list) is ideal for this because it automatically initializes a new list for each new key.

Once you have the graph, perform a Depth-First Search (DFS) starting from the process ID that needs to be killed. DFS is a suitable algorithm here because it allows us to explore all descendants of a node by going as deep as possible into the tree's branches before backtracking, thus ensuring that we find all processes that need to be terminated.

As you perform DFS, each time you visit a node (process), add its ID to the answer list. Once you exhaust all the child nodes of the process to be killed, the recursive DFS function will naturally backtrack, and the process is complete. The DFS ensures all child processes are visited and their IDs are added to the list, effectively giving us the full list of processes that will be killed.

The solution code implements this intuition, with the dfs function handling the actual traversal and the killProcess function preparing the graph and initiating the DFS call.

Learn more about Tree, Depth-First Search and Breadth-First Search patterns.

Solution Approach

The solution to the problem is implemented in Python using a Depth-First Search (DFS) on the graph representation of the processes. Here's an explanation of the steps taken in the given solution:

Data Structure: Graph

The graph is created as a hashmap (specifically, a defaultdict(list) in Python) where each key-value pair corresponds to a parent process ID (the key) and a list of its child process IDs (the value).

Graph Construction

Using the zip function, we iterate through both pid and ppid arrays in tandem. For each pair (i, p) from pid and ppid, we add process i to the graph under its parent p. The graph will store all the relations as adjacency lists.

DFS Function

The dfs function performs a classical depth-first search starting from the kill process ID. It takes an integer i as its argument, which is the process ID from where the search begins. The function works as follows:

1. The current node (process ID) i is added to the list ans of processes to be killed.
2. The function iterates over all the children of process i (if any) by looking up graph g[i]. For each child process j, the function calls itself recursively (dfs(j)), which leads to the child process and all its descendants being added to ans.

Initiating the Algorithm

We initialize an empty list ans which will eventually contain all process IDs to be killed.

We then call dfs(kill), which begins the depth-first search starting from the process we want to kill.

After the DFS completes, 'ans' contains all the process IDs that were visited during the recursive search. Since DFS was executed starting with the process ID of kill, this means it includes the kill process and all its descendant processes, recursively.

The solution code encapsulates this approach neatly and efficiently, making sure that by the end of the call to dfs(kill), the list ans includes every process that needs to be terminated as specified by the problem statement.

Example Walkthrough

Imagine we have a system with the following processes and parent-child relationships:

Processes: pid = [1, 3, 10, 5] Parent Processes:ppid = [0, 1, 3, 3]

The processes create a tree structure with their parent-child relationships like this:

     1        ppid[0]=0 (root process)
    / 
   3          ppid[1]=1
  / \
10   5        ppid[2]=3, ppid[3]=3

Here, process 1 is the root of the tree, and it has one child, process 3. Process 3, in turn, has two children, process 10 and process 5.

Let's walk through the solution if we want to kill process 3.

Step 1: Graph Construction First, we build the graph from pid and ppid arrays using a hashmap. Our graph would look like this:

• Key 1 will have a value [3], indicating that process 1's child is process 3.
• Key 3 will have a value [10, 5], indicating that process 3's children are processes 10 and 5.

This results in the graph representation being: {1: [3], 3: [10, 5]} with other processes linking to an empty list, since they don't have children.

Step 2: Depth-First Search (DFS) Function We want to kill process 3. So, we perform a depth-first search starting from process 3.

• We add process 3 to the ans list.
• We see that process 3 has two children: 10 and 5. We start a DFS for process 10.
  • We add process 10 to the ans list. This process has no children, so the DFS on process 10 ends.
• The DFS retraces its steps back to process 3 and starts a DFS for process 5.
  • We add process 5 to the ans list. This process has no children, so the DFS on process 5 ends.

The DFS has now visited all children and descendants of process 3. The process recursion completes and we have the list ans filled with the processes that were killed, which are [3, 10, 5].

Step 3: Return the Result The list ans is returned from the function, which contains all the processes that were killed when process 3 was terminated. In this case, the final output would be [3, 10, 5]. And so, the algorithm successfully solves the problem by identifying the process to kill along with all of its descendants using a DFS approach on the process tree.

Solution Implementation

Time and Space Complexity

The input lists pid and ppid are traversed once to build the graph g, contributing O(n) to the time complexity, where n is the number of processes. The depth-first search (DFS) dfs is called once for each node in the graph within its own subtree. Since each node will be visited exactly once, the total time for all DFS calls is also O(n). Thus, the total time complexity of the algorithm is O(n).

The space complexity is O(n) as well, primarily due to two factors: the space taken by the graph g, which can have at most n edges, and the space taken by the ans list. There is also the implicit stack space used by the DFS calls, which in the worst case (when the graph is a straight line), could be O(n). However, since this stack space does not exceed the size of the input, the overall space complexity remains O(n).

Learn more about how to find time and space complexity quickly using problem constraints.