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OpenAI VO Interview Question #3: Spreadsheet Cell Dependency Calculation with DFS - Complete Recursion & Caching Optimization Guide

2025-12-26

OAVOService Technical Deep Dive

This OpenAI spreadsheet system design question is a typical combination of graph theory and recursion examination, medium-high difficulty with numerous detail traps. Many candidates fail at dependency relationship handling, cycle detection, and cache optimization.

OAVOService Professional Reminder: This type of question appears to be a data structure problem but actually examines engineering thinking and system design capabilities. Our interview assistance team maintains a 98% pass rate on this question, with the key being comprehensive technical solutions and clear code implementation.

Complete Problem Statement

Design a simple spreadsheet system supporting inter-cell dependency calculations.

Core Requirements

Cell Types:

System Interface:

Cell Object Definition

class Cell:
    def __init__(self, value=None, child1=None, child2=None):
        self.value = value      # Numerical value (if constant cell)
        self.child1 = child1    # First dependency cell key
        self.child2 = child2    # Second dependency cell key

Example Scenarios

Basic Example:

A = B + C
B = 3  
C = 5
getCellValue("A") → 8

Nested Dependencies:

A = B + C
B = D + E  
C = 2
D = 4
E = 1
getCellValue("A") → 7  # (D+E) + C = (4+1) + 2 = 7

OAVOService Expert-Level Solutions

Solution 1: Basic DFS Recursive Implementation

class BasicSpreadsheet:
    def __init__(self):
        self.cells = {}  # key -> Cell object
    
    def setCell(self, key, cell):
        """Set cell"""
        self.cells[key] = cell
    
    def getCellValue(self, key):
        """Get cell value (DFS recursion)"""
        if key not in self.cells:
            raise KeyError(f"Cell {key} not found")
        
        cell = self.cells[key]
        
        # If value cell, return value directly
        if cell.value is not None:
            return cell.value
        
        # If dependency cell, recursively calculate
        result = 0
        
        if cell.child1:
            result += self.getCellValue(cell.child1)
        
        if cell.child2:
            result += self.getCellValue(cell.child2)
        
        return result

Solution 2: Memoized Optimization Version

class OptimizedSpreadsheet:
    def __init__(self):
        self.cells = {}
        self.cache = {}  # Cache computation results
    
    def setCell(self, key, cell):
        """Set cell and clear related cache"""
        self.cells[key] = cell
        
        # Clear affected cache
        self._invalidateCache(key)
    
    def getCellValue(self, key):
        """Get cell value (with cache optimization)"""
        # Check cache
        if key in self.cache:
            return self.cache[key]
        
        if key not in self.cells:
            raise KeyError(f"Cell {key} not found")
        
        cell = self.cells[key]
        
        # Calculate value
        if cell.value is not None:
            # Value cell
            result = cell.value
        else:
            # Dependency cell
            result = 0
            if cell.child1:
                result += self.getCellValue(cell.child1)
            if cell.child2:
                result += self.getCellValue(cell.child2)
        
        # Cache result
        self.cache[key] = result
        return result
    
    def _invalidateCache(self, key):
        """Recursively clear affected cache"""
        if key not in self.cache:
            return
        
        # Clear current key's cache
        del self.cache[key]
        
        # Find all cells depending on current key
        for cell_key, cell in self.cells.items():
            if (cell.child1 == key or cell.child2 == key):
                self._invalidateCache(cell_key)

Solution 3: Complete Production Version (with Cycle Detection)

class ProductionSpreadsheet:
    def __init__(self):
        self.cells = {}
        self.cache = {}
        self.dependency_graph = {}  # key -> [keys depending on it]
    
    def setCell(self, key, cell):
        """Set cell (complete version)"""
        # Update dependency graph
        self._updateDependencyGraph(key, cell)
        
        # Detect circular dependencies
        if self._hasCycle(key):
            raise ValueError(f"Circular dependency detected involving {key}")
        
        # Set cell
        self.cells[key] = cell
        
        # Clear affected cache
        self._invalidateCache(key)
    
    def getCellValue(self, key):
        """Get cell value (production-grade version)"""
        return self._getCellValueWithPath(key, set())
    
    def _getCellValueWithPath(self, key, path):
        """Value calculation with path tracking (prevent runtime cycles)"""
        if key in path:
            raise ValueError(f"Circular dependency detected: {path} -> {key}")
        
        # Check cache
        if key in self.cache:
            return self.cache[key]
        
        if key not in self.cells:
            raise KeyError(f"Cell {key} not found")
        
        cell = self.cells[key]
        path.add(key)
        
        try:
            if cell.value is not None:
                # Value cell
                result = cell.value
            else:
                # Dependency cell
                result = 0
                if cell.child1:
                    result += self._getCellValueWithPath(cell.child1, path)
                if cell.child2:
                    result += self._getCellValueWithPath(cell.child2, path)
            
            # Cache result
            self.cache[key] = result
            return result
        
        finally:
            path.remove(key)
    
    def _updateDependencyGraph(self, key, cell):
        """Update dependency relationship graph"""
        # Clear old dependencies
        for dep_key in list(self.dependency_graph.keys()):
            if key in self.dependency_graph[dep_key]:
                self.dependency_graph[dep_key].remove(key)
                if not self.dependency_graph[dep_key]:
                    del self.dependency_graph[dep_key]
        
        # Add new dependencies
        if cell.child1:
            if cell.child1 not in self.dependency_graph:
                self.dependency_graph[cell.child1] = []
            self.dependency_graph[cell.child1].append(key)
        
        if cell.child2:
            if cell.child2 not in self.dependency_graph:
                self.dependency_graph[cell.child2] = []
            self.dependency_graph[cell.child2].append(key)
    
    def _hasCycle(self, start_key):
        """Detect if cycle exists starting from specified node"""
        def dfs(key, visited, rec_stack):
            if key not in self.cells:
                return False
            
            visited.add(key)
            rec_stack.add(key)
            
            cell = self.cells[key]
            children = [child for child in [cell.child1, cell.child2] if child]
            
            for child in children:
                if child not in visited:
                    if dfs(child, visited, rec_stack):
                        return True
                elif child in rec_stack:
                    return True
            
            rec_stack.remove(key)
            return False
        
        return dfs(start_key, set(), set())
    
    def _invalidateCache(self, key):
        """Smart cache invalidation"""
        if key not in self.cache:
            return
        
        # Use BFS to clear all affected cache
        queue = [key]
        invalidated = set()
        
        while queue:
            current = queue.pop(0)
            
            if current in invalidated:
                continue
            
            invalidated.add(current)
            
            # Clear current cache
            self.cache.pop(current, None)
            
            # Find all cells depending on current cell
            if current in self.dependency_graph:
                queue.extend(self.dependency_graph[current])

Common Interviewer Follow-ups & OAVOService Standard Responses

Q1: How to optimize performance for frequent queries?

Professional Answer:

Q2: How to handle large-scale data?

System Design Approach:

Q3: How to support more complex formulas?

Extension Solutions:

Advanced Optimization: Reverse Dependency Graph Maintenance

class AdvancedSpreadsheet:
    def __init__(self):
        self.cells = {}
        self.cache = {}
        self.dependents = {}    # key -> set of keys depending on it
        self.dependencies = {}  # key -> set of keys it depends on
    
    def setCell(self, key, cell):
        # Update bidirectional dependency graph
        old_deps = self.dependencies.get(key, set())
        new_deps = set()
        
        if cell.child1:
            new_deps.add(cell.child1)
        if cell.child2:
            new_deps.add(cell.child2)
        
        # Remove old dependencies
        for dep in old_deps:
            if dep in self.dependents:
                self.dependents[dep].discard(key)
        
        # Add new dependencies
        for dep in new_deps:
            if dep not in self.dependents:
                self.dependents[dep] = set()
            self.dependents[dep].add(key)
        
        self.dependencies[key] = new_deps
        self.cells[key] = cell
        
        # Smart cache invalidation
        self._smartInvalidate(key)
    
    def _smartInvalidate(self, key):
        """Smart cache invalidation strategy"""
        to_invalidate = set()
        queue = [key]
        
        while queue:
            current = queue.pop(0)
            if current in to_invalidate:
                continue
                
            to_invalidate.add(current)
            
            # Add all keys depending on current key
            if current in self.dependents:
                queue.extend(self.dependents[current])
        
        # Batch clear cache
        for k in to_invalidate:
            self.cache.pop(k, None)

OAVOService Exclusive Interview Techniques

Code Implementation Key Points

  1. Error Handling: Non-existent keys, circular dependencies, and other exceptions
  2. Performance Analysis: Time and space complexity trade-offs
  3. Extensibility: How to support more operations and complex scenarios

Communication Strategies

  1. Overall then Details: Explain overall architecture first, then dive into implementation
  2. Proactive Optimization: Propose performance improvements without waiting for prompts
  3. Engineering Mindset: Consider edge conditions in real-world scenarios

Related Algorithm Problems

Summary

Spreadsheet dependency calculation is a comprehensive system design question examining:

OAVOService Interview Assistance Core Values: ✅ Thinking Guidance: Avoid design direction errors, ensure reasonable architecture ✅ Code Assistance: Real-time error correction and optimization suggestions, code quality guarantee ✅ Follow-up Response: Deep technical Q&A, demonstrate engineering experience ✅ Performance Tuning: Algorithm complexity analysis, system scalability considerations

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