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Tree Node - Problem

Database Medium

Imagine you're building a family tree analyzer! You have a database table containing information about nodes in a tree structure, where each node has an id and a p_id (parent ID).

Your mission: Classify each node as one of three types:

"Root" - The ancestor of all nodes (has no parent, p_id is null)
"Leaf" - A node with no children (appears as p_id for no other nodes)
"Inner" - A node that has both a parent and at least one child

The tree structure is guaranteed to be valid, meaning there are no cycles and exactly one root node.

Table Structure:

Tree
+-------------+------+
| Column Name | Type |
+-------------+------+
| id          | int  |
| p_id        | int  |
+-------------+------+

Return the result showing each node's id and its corresponding type, in any order.

Input & Output

example_1.sql — Basic Tree

$ Input: Tree table: +----+------+ | id | p_id | +----+------+ | 1 | NULL | | 2 | 1 | | 3 | 1 | | 4 | 2 | +----+------+

› Output: +----+-------+ | id | type | +----+-------+ | 1 | Root | | 2 | Inner | | 3 | Leaf | | 4 | Leaf | +----+-------+

💡 Note: Node 1 is the root (p_id is NULL). Node 2 has both parent (1) and child (4), so it's Inner. Nodes 3 and 4 have parents but no children, so they're Leaf nodes.

example_2.sql — Single Node Tree

$ Input: Tree table: +----+------+ | id | p_id | +----+------+ | 1 | NULL | +----+------+

› Output: +----+------+ | id | type | +----+------+ | 1 | Root | +----+------+

💡 Note: A single node tree has only one node, which is the root by definition (p_id is NULL).

example_3.sql — Linear Tree

$ Input: Tree table: +----+------+ | id | p_id | +----+------+ | 1 | NULL | | 2 | 1 | | 3 | 2 | | 4 | 3 | +----+------+

› Output: +----+-------+ | id | type | +----+-------+ | 1 | Root | | 2 | Inner | | 3 | Inner | | 4 | Leaf | +----+-------+

💡 Note: This is a linear tree (like a linked list). Node 1 is Root, nodes 2 and 3 are Inner (have both parent and child), and node 4 is Leaf (has parent but no children).

Constraints

1 ≤ Number of nodes ≤ 10⁴
1 ≤ Node ID ≤ 10⁹
Parent ID (p_id) can be NULL for root node only
The tree structure is guaranteed to be valid (no cycles, single root)
Each node ID appears exactly once in the table

Visualization

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Understanding the Visualization

Identify Root

Find the node with p_id = NULL - this is the tree root

Map Relationships

Create parent-child mappings to understand tree structure

Count Children

For each node, count how many children it has

Classify Nodes

Apply rules: Root (no parent), Inner (has children), Leaf (no children)

Key Takeaway

🎯 Key Insight: Use SQL JOINs and aggregation to efficiently determine parent-child relationships and classify nodes based on whether they have parents and children.

Asked in

a Amazon 45 ⊞ Microsoft 35 G Google 30 f Meta 25

The optimal solution uses SQL LEFT JOIN with GROUP BY to efficiently classify tree nodes. By joining the table with itself on parent-child relationships and counting children, we can determine node types in a single pass: Root (p_id IS NULL), Inner (has children), or Leaf (no children). This approach leverages database optimization for O(n log n) performance.

Common Approaches

Approach	Time	Space	Notes
✓ SQL JOIN with Aggregation (Optimal)	O(n log n)	O(n)	Use LEFT JOIN and COUNT to efficiently determine node types in one pass
Brute Force (Multiple Subqueries)	O(n²)	O(1)	Use nested subqueries to check each node's relationships individually

SQL JOIN with Aggregation (Optimal) — Algorithm Steps

LEFT JOIN the Tree table with itself (parent-child relationship)
GROUP BY the main node id to aggregate child counts
Use CASE statement with COUNT to classify nodes
NULL p_id = Root, COUNT > 0 = Inner, COUNT = 0 = Leaf

Visualization

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Step-by-Step Walkthrough

LEFT JOIN

Join Tree with itself to find parent-child relationships

GROUP BY

Group by node ID to count children for each node

CASE Classification

Use p_id NULL and child count to determine node type

Code -

solution.c — C

// Optimal SQL solution for Tree Node classification
const char* sqlQuery = 
"SELECT \n"
"    t1.id,\n"
"    CASE \n"
"        WHEN t1.p_id IS NULL THEN 'Root'\n"
"        WHEN COUNT(t2.id) > 0 THEN 'Inner'\n"
"        ELSE 'Leaf'\n"
"    END AS type\n"
"FROM Tree t1\n"
"LEFT JOIN Tree t2 ON t1.id = t2.p_id\n"
"GROUP BY t1.id, t1.p_id\n"
"ORDER BY t1.id;";

// Simulating the optimal logic in C
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

typedef struct {
    int id;
    int p_id;
    int has_parent;
} Node;

typedef struct {
    int id;
    char type[10];
} Result;

int compare_results(const void *a, const void *b) {
    Result *ra = (Result *)a;
    Result *rb = (Result *)b;
    return ra->id - rb->id;
}

int classifyTreeNodesOptimal(Node* nodes, int count, Result* results) {
    // Build children tracking
    int* hasChildren = (int*)calloc(1000, sizeof(int)); // Assuming max id < 1000
    
    // Mark which nodes have children
    for (int i = 0; i < count; i++) {
        if (nodes[i].has_parent) {
            hasChildren[nodes[i].p_id] = 1;
        }
    }
    
    // Classify each node
    for (int i = 0; i < count; i++) {
        results[i].id = nodes[i].id;
        
        if (!nodes[i].has_parent) {
            strcpy(results[i].type, "Root");
        } else if (hasChildren[nodes[i].id]) {
            strcpy(results[i].type, "Inner");
        } else {
            strcpy(results[i].type, "Leaf");
        }
    }
    
    // Sort results by id
    qsort(results, count, sizeof(Result), compare_results);
    
    free(hasChildren);
    return count;
}

Time & Space Complexity

Time Complexity

⏱️

O(n log n)

JOIN operation with GROUP BY, optimized by database engine

⚡ Linearithmic

Space Complexity

O(n)

Temporary space for JOIN results and grouping

⚡ Linearithmic Space

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Medium Frequency

~15 min Avg. Time

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

SQL JOIN with Aggregation (Optimal) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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