What is shortest path?

Shortest path

As explained in Modern C

A shortest path is a path between two graph nodes whose total distance is minimal among the available paths.

A shortest path connects two graph nodes with the least total distance among available routes. Represent direct distances in a distance matrix D. section 6.1.5

Represent the problem as follows:

Store the distance from point i to point j in D[i][j]. section 6.1.5
Represent the absence of a direct arc with a very large value such as SIZE_MAX. section 6.1.5
Given nodes x and y, find the shortest path between them using the distance information. section 6.1.5

liveBook manning.com

Read Modern C on liveBook Get the book at manning.com

Also explained in

liveBook manning.com

Classic Computer Science Problems in Swift: Essential techniques for practicing programmersA shortest path is a path between vertices whose total edge cost is minimal among the available paths.
liveBook manning.com

Graph Algorithms for Data ScienceNetwork distance is the minimum number of relationships along a path connecting two nodes, particularly when relationships are unweighted.
liveBook manning.com

Grokking Algorithms, Second EditionA shortest-path problem asks for a path between locations or nodes that minimizes the number of steps or another path cost.
liveBook manning.com

Advanced Algorithms and Data StructuresA shortest path is a path between graph vertices having minimum total edge distance or cost.
liveBook manning.com

Learn Haskell by ExampleA shortest path is a path between two graph nodes having minimal total length or cost.

Compare how 6 books explain shortest path →

Related concepts

breadth-first searchaddressed by · Breadth-first search is a graph or tree traversal algorithm that explores nodes in nondecreasing order of their distance from a starting node.
Dijkstra's algorithmaddressed by · Dijkstra's algorithm computes shortest paths from a source vertex in a weighted graph with nonnegative edge weights.
depth-first searchcontrasts with · Depth-first search is a graph or tree traversal algorithm that explores one branch as far as possible before backtracking to explore alternatives.
betweenness centralitymeasured by · Betweenness centrality is a graph metric that measures how frequently a node lies on shortest paths between other nodes.

This explainer was generated by Manning's knowledge graph from the text of Modern C. The section links point to the parts of the book it draws on.