How do you solve Design Graph With Shortest Path Calculator on LeetCode?

Design Graph With Shortest Path Calculator (LeetCode #2642) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O((E + V) log V) time complexity and O(V) space complexity. Key insight: Dijkstra's algorithm is efficient for finding the shortest path in weighted graphs.

What is the brute force solution for Design Graph With Shortest Path Calculator?

The brute force approach for Design Graph With Shortest Path Calculator is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves exploring all possible paths from the starting node to the destination node and calculating the total cost for each path. This method is straightforward but inefficient for larger graphs. The optimal Optimal Solution approach improves this to O((E + V) log V).

What algorithm or data structure is used to solve Design Graph With Shortest Path Calculator?

Design Graph With Shortest Path Calculator uses the following concepts: Graph Theory, Design, Heap (Priority Queue), Shortest Path. The recommended patterns to study are: Graph Traversal, Priority Queue, Dijkstra's Algorithm.

What are the interview tips for Design Graph With Shortest Path Calculator?

Always clarify the input constraints and edge cases with the interviewer. Explain your thought process and approach before jumping into coding. Practice implementing Dijkstra's algorithm, as it's a common interview topic.

What are common mistakes when solving Design Graph With Shortest Path Calculator?

Not updating the priority queue correctly after finding a shorter path. Confusing the use of visited nodes in Dijkstra's algorithm compared to DFS.

#2642

Design Graph With Shortest Path Calculator

Hard

Graph TheoryDesignHeap (Priority Queue)Shortest PathGraph TraversalPriority QueueDijkstra's Algorithm

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O((E + V) log V)
Space	O(1)	O(V)

💡

Intuition

Time O((E + V) log V)Space O(V)

Using Dijkstra's algorithm allows us to efficiently find the shortest path in a weighted graph. It systematically explores the nearest nodes first, ensuring we find the minimum cost path without exploring every possible route.

⚙️

Algorithm

4 steps

1Step 1: Initialize a priority queue (min-heap) and a distance array to track the minimum cost to reach each node.
2Step 2: Start from node1, add it to the priority queue with a cost of 0.
3Step 3: While the priority queue is not empty, extract the node with the smallest cost, update its neighbors, and push them into the queue if a shorter path is found.
4Step 4: If we reach node2, return the cost; if the queue is empty and node2 is not reached, return -1.

solution.py29 lines

1import heapq
2class Graph:
3    def __init__(self, n, edges):
4        self.graph = {}
5        for u, v, cost in edges:
6            if u not in self.graph:
7                self.graph[u] = []
8            self.graph[u].append((v, cost))
9
10    def addEdge(self, edge):
11        u, v, cost = edge
12        if u not in self.graph:
13            self.graph[u] = []
14        self.graph[u].append((v, cost))
15
16    def shortestPath(self, node1, node2):
17        pq = [(0, node1)]
18        distances = {i: float('inf') for i in range(len(self.graph))}
19        distances[node1] = 0
20        while pq:
21            current_cost, current_node = heapq.heappop(pq)
22            if current_node == node2:
23                return current_cost
24            for neighbor, cost in self.graph.get(current_node, []):
25                new_cost = current_cost + cost
26                if new_cost < distances[neighbor]:
27                    distances[neighbor] = new_cost
28                    heapq.heappush(pq, (new_cost, neighbor))
29        return -1

ℹ

Complexity note: The time complexity is derived from the priority queue operations, where E is the number of edges and V is the number of vertices. Each edge is processed once, and each vertex is added to the queue at most once.

1Dijkstra's algorithm is efficient for finding the shortest path in weighted graphs.
2Understanding how to use priority queues can significantly optimize pathfinding problems.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.