All Valid Triplets That Can Represent a Country

All Valid Triplets That Can Represent a Country - Problem

Database Easy

All Valid Triplets That Can Represent a Country

A country with three schools - SchoolA, SchoolB, and SchoolC - is preparing for an international competition. Each student is enrolled in exactly one school, and the country needs to select one student from each school to form a representative team.

The selection criteria are strict:
• Select exactly one student from each school (member_A, member_B, member_C)
• No two students can share the same ID
• No two students can share the same name

Given three database tables representing the students in each school, find all possible valid triplets that can represent the country under these constraints.

Goal: Return all valid combinations where student IDs and names are pairwise distinct across the three selected students.

Input & Output

example_1.sql — Basic Case

$ Input: SchoolA: [(1, Alice), (2, Bob)] SchoolB: [(3, Charlie), (1, David)] SchoolC: [(2, Eve), (4, Frank)]

› Output: [(1, 3, 2), (1, 3, 4), (2, 1, 4)]

💡 Note: Valid triplets where no two students share the same ID or name. (1,Alice) + (3,Charlie) + (2,Eve) works because all IDs and names are unique.

example_2.sql — Name Conflicts

$ Input: SchoolA: [(1, Alice), (2, Bob)] SchoolB: [(3, Alice), (4, Charlie)] SchoolC: [(5, David), (6, Eve)]

› Output: [(1, 4, 5), (1, 4, 6), (2, 3, 5), (2, 3, 6), (2, 4, 5), (2, 4, 6)]

💡 Note: Alice from SchoolA cannot be paired with Alice from SchoolB due to name conflict, but other combinations are valid.

example_3.sql — No Valid Triplets

$ Input: SchoolA: [(1, Alice)] SchoolB: [(1, Bob)] SchoolC: [(2, Charlie)]

› Output: []

💡 Note: Students from SchoolA and SchoolB have the same ID (1), so no valid triplet can be formed.

Visualization

Tap to expand

Understanding the Visualization

List All Athletes

Gather rosters from all three training camps

Generate Combinations

Create all possible team lineups (one from each camp)

Check Jersey Numbers

Eliminate teams where athletes share the same jersey number

Check Name Conflicts

Remove teams with athletes having identical names

Final Valid Teams

Return all qualifying team combinations

Key Takeaway

🎯 Key Insight: Use CROSS JOIN to generate all combinations, then filter with WHERE conditions to ensure uniqueness constraints are met

Time & Space Complexity

Time Complexity

⏱️

O(n³)

Cross join creates n³ combinations where n is average table size, then filters each

⚠ Quadratic Growth

Space Complexity

O(n³)

Intermediate result set can be as large as the full Cartesian product

⚠ Quadratic Space

Constraints

1 ≤ Number of students in each school ≤ 1000
1 ≤ student_id ≤ 10⁹
1 ≤ student_name.length ≤ 20
All student_name values are distinct within each school
All student_id values are unique within each school

Asked in

A Amazon 35 ⊞ Microsoft 28 G Google 22 f Meta 18

This database problem is solved using CROSS JOIN to generate all possible student combinations from three schools, then applying WHERE conditions to filter out triplets with duplicate IDs or names. The key insight is leveraging SQL's set operations to efficiently handle the constraint checking across multiple tables.

Common Approaches

Approach	Time	Space	Notes
✓ Cross Join with Filtering	O(n³)	O(n³)	Generate all possible combinations and filter out invalid ones

Cross Join with Filtering — Algorithm Steps

Perform CROSS JOIN on all three school tables
Add WHERE conditions to ensure student_id uniqueness across triplets
Add WHERE conditions to ensure student_name uniqueness across triplets
Return all valid combinations

Visualization

Tap to expand

Step-by-Step Walkthrough

Generate Cartesian Product

CROSS JOIN creates all possible combinations of students from three schools

Apply ID Constraints

Filter out triplets where any two students share the same ID

Apply Name Constraints

Filter out triplets where any two students share the same name

Return Valid Triplets

Only combinations meeting both constraints remain

Code -

solution.c — C

// SQL Solution for Valid Country Triplets
const char* sqlQuery = 
"SELECT \n"
"    a.student_id as member_A,\n"
"    b.student_id as member_B, \n"
"    c.student_id as member_C\n"
"FROM SchoolA a\n"
"CROSS JOIN SchoolB b \n"
"CROSS JOIN SchoolC c\n"
"WHERE \n"
"    a.student_id != b.student_id AND\n"
"    a.student_id != c.student_id AND \n"
"    b.student_id != c.student_id AND\n"
"    a.student_name != b.student_name AND\n"
"    a.student_name != c.student_name AND\n"
"    b.student_name != c.student_name\n"
"ORDER BY member_A, member_B, member_C;";

// For testing with sample data
int solveTriplets(Student* schoolA, int sizeA, Student* schoolB, int sizeB, 
                  Student* schoolC, int sizeC, int result[][3]) {
    int count = 0;
    for (int i = 0; i < sizeA; i++) {
        for (int j = 0; j < sizeB; j++) {
            for (int k = 0; k < sizeC; k++) {
                if (schoolA[i].id != schoolB[j].id && schoolA[i].id != schoolC[k].id && 
                    schoolB[j].id != schoolC[k].id && 
                    strcmp(schoolA[i].name, schoolB[j].name) != 0 &&
                    strcmp(schoolA[i].name, schoolC[k].name) != 0 &&
                    strcmp(schoolB[j].name, schoolC[k].name) != 0) {
                    result[count][0] = schoolA[i].id;
                    result[count][1] = schoolB[j].id;
                    result[count][2] = schoolC[k].id;
                    count++;
                }
            }
        }
    }
    return count;
}

Time & Space Complexity

Time Complexity

⏱️

O(n³)

Cross join creates n³ combinations where n is average table size, then filters each

⚠ Quadratic Growth

Space Complexity

O(n³)

Intermediate result set can be as large as the full Cartesian product

⚠ Quadratic Space

Constraints

1 ≤ Number of students in each school ≤ 1000
1 ≤ student_id ≤ 10⁹
1 ≤ student_name.length ≤ 20
All student_name values are distinct within each school
All student_id values are unique within each school

28.9K Views

Medium Frequency

~12 min Avg. Time

847 Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen

Input & Output

Visualization

Time & Space Complexity

Related Problems

Constraints

Common Approaches

Cross Join with Filtering — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Constraints

Select Compiler