Globe
difference between shortest path and alternate path
a straight line ^Wrong. A straight line is NOT the shortest distance between two places when you're on a globe. http://en.wikipedia.org/wiki/Great_circle This is mathematically proven using calculus. Another way to prove this is to take a globe, and get some string. Pick two points, and make a straight line with the string to measure the distance. Cut off the extra string so you are using the exact amount needed for a straight line. Now, use the great circle, and you will be able to reach the same point, and have extra string left over, proving that the great circle is shorter than the straight line.
The shortest path in an undirected graph is the path between two vertices that has the smallest total sum of edge weights.
The shortest path in a directed graph between two nodes is the path with the fewest number of edges or connections between the two nodes. This path is determined by algorithms like Dijkstra's or Bellman-Ford, which calculate the shortest distance between nodes based on the weights assigned to the edges.
The shortest path with at most k edges between two points in a graph is known as the k-shortest path. It is the path that has the fewest number of edges while still connecting the two points.
a segment of a strate line
The distance between these two places vary according to the path chosen. However, This is the shortest distance between the two places. The distance between the above places is 80 miles ( Approximately ).
The shortest path between two points is called a geodesic. In flat (Euclidean) space it is simply a straight line.
The distance between these two places vary according to the path chosen. However, This is the shortest distance between the two places. The distance between the above places is 70 miles ( Approximately ).
The fastest shortest path algorithm for finding the most efficient route between two points is Dijkstra's algorithm.
2D line.