Advanced Graphs Cheat Sheet

What is Advanced Graphs?

Master complex graph algorithms like shortest paths and minimum spanning trees.

Template Code

import heapq

def minCostConnectPoints(points: List[List[int]]) -> int:
    n = len(points)
    if n <= 1:
        return 0
    
    # Prim's algorithm
    visited = set()
    min_heap = [(0, 0)]  # (cost, point_index)
    total_cost = 0
    
    while len(visited) < n:
        cost, i = heapq.heappop(min_heap)
        
        if i in visited:
            continue
        
        visited.add(i)
        total_cost += cost
        
        # Add edges to all unvisited points
        for j in range(n):
            if j not in visited:
                dist = abs(points[i][0] - points[j][0]) + abs(points[i][1] - points[j][1])
                heapq.heappush(min_heap, (dist, j))
    
    return total_cost

Complexity

Common Variations

• Basic Advanced Graphs
• Advanced Graphs with constraints
• Optimized Advanced Graphs

Practice Problems