DEV Community

Cover image for 1334. Find the City With the Smallest Number of Neighbors at a Threshold Distance
MD ARIFUL HAQUE
MD ARIFUL HAQUE

Posted on

3

1334. Find the City With the Smallest Number of Neighbors at a Threshold Distance

1334. Find the City With the Smallest Number of Neighbors at a Threshold Distance

Medium

There are n cities numbered from 0 to n-1. Given the array edges where edges[i] = [fromi, toi, weighti] represents a bidirectional and weighted edge between cities fromi and toi, and given the integer distanceThreshold.

Return the city with the smallest number of cities that are reachable through some path and whose distance is at most distanceThreshold, If there are multiple such cities, return the city with the greatest number.

Notice that the distance of a path connecting cities i and j is equal to the sum of the edges' weights along that path.

Example 1:

find_the_city_01

  • Input: n = 4, edges = [[0,1,3],[1,2,1],[1,3,4],[2,3,1]], distanceThreshold = 4
  • Output: 3
  • Explanation: The figure above describes the graph.
    • The neighboring cities at a distanceThreshold = 4 for each city are:
  City 0 -> [City 1, City 2]
  City 1 -> [City 0, City 2, City 3]
  City 2 -> [City 0, City 1, City 3]
  City 3 -> [City 1, City 2]
Enter fullscreen mode Exit fullscreen mode

Cities 0 and 3 have 2 neighboring cities at a distanceThreshold = 4, but we have to return city 3 since it has the greatest number.

Example 2:

find_the_city_02

  • Input: n = 5, edges = [[0,1,2],[0,4,8],[1,2,3],[1,4,2],[2,3,1],[3,4,1]], distanceThreshold = 2
  • Output: 0
  • Explanation: The figure above describes the graph.
    • The neighboring cities at a distanceThreshold = 2 for each city are:
  City 0 -> [City 1]
  City 1 -> [City 0, City 4]
  City 2 -> [City 3, City 4]
  City 3 -> [City 2, City 4]
  City 4 -> [City 1, City 2, City 3]
Enter fullscreen mode Exit fullscreen mode

The city 0 has 1 neighboring city at a distanceThreshold = 2.

Constraints:

  • 2 <= n <= 100
  • 1 <= edges.length <= n * (n - 1) / 2
  • edges[i].length == 3
  • 0 <= fromi < toi < n
  • 1 <= weighti, distanceThreshold <= 10^4
  • All pairs (fromi, toi) are distinct.

Hint:

  1. Use Floyd-Warshall's algorithm to compute any-point to any-point distances. (Or can also do Dijkstra from every node due to the weights are non-negative).
  2. For each city calculate the number of reachable cities within the threshold, then search for the optimal city.

Solution:

To solve this problem, we can follow these steps:

  1. Initialize the Distance Matrix: Create a distance matrix dist where dist[i][j] represents the shortest distance between city i and city j. Initialize the matrix with INF (a large number representing infinity) and set dist[i][i] to 0 for all i.

  2. Populate the Distance Matrix with Given Edges: Set the distances based on the given edges.

  3. Floyd-Warshall Algorithm: Update the distance matrix using the Floyd-Warshall algorithm to find the shortest paths between all pairs of cities.

  4. Calculate Reachable Cities: For each city, count the number of cities that can be reached within the distanceThreshold.

  5. Find the Desired City: Identify the city with the smallest number of reachable cities. If there are multiple such cities, return the one with the greatest number.

Let's implement this solution in PHP: 1334. Find the City With the Smallest Number of Neighbors at a Threshold Distance

<?php
// Example usage:
$n1 = 4;
$edges1 = [[0,1,3],[1,2,1],[1,3,4],[2,3,1]];
$distanceThreshold1 = 4;
echo findTheCity($n1, $edges1, $distanceThreshold1); // Output: 3

$n2 = 5;
$edges2 = [[0,1,2],[0,4,8],[1,2,3],[1,4,2],[2,3,1],[3,4,1]];
$distanceThreshold2 = 2;
echo findTheCity($n2, $edges2, $distanceThreshold2); // Output: 0

?>
Enter fullscreen mode Exit fullscreen mode

Contact Links

If you found this series helpful, please consider giving the repository a star on GitHub or sharing the post on your favorite social networks 😍. Your support would mean a lot to me!

If you want more helpful content like this, feel free to follow me:

Image of AssemblyAI tool

Transforming Interviews into Publishable Stories with AssemblyAI

Insightview is a modern web application that streamlines the interview workflow for journalists. By leveraging AssemblyAI's LeMUR and Universal-2 technology, it transforms raw interview recordings into structured, actionable content, dramatically reducing the time from recording to publication.

Key Features:
🎥 Audio/video file upload with real-time preview
🗣️ Advanced transcription with speaker identification
⭐ Automatic highlight extraction of key moments
✍️ AI-powered article draft generation
📤 Export interview's subtitles in VTT format

Read full post

Top comments (0)

AWS Security LIVE!

Tune in for AWS Security LIVE!

Join AWS Security LIVE! for expert insights and actionable tips to protect your organization and keep security teams prepared.

Learn More

👋 Kindness is contagious

Discover a treasure trove of wisdom within this insightful piece, highly respected in the nurturing DEV Community enviroment. Developers, whether novice or expert, are encouraged to participate and add to our shared knowledge basin.

A simple "thank you" can illuminate someone's day. Express your appreciation in the comments section!

On DEV, sharing ideas smoothens our journey and strengthens our community ties. Learn something useful? Offering a quick thanks to the author is deeply appreciated.

Okay