How to calculate shortest possible route between nodes?

Question

I have the following variable input array to my program, for example: [AB3, EC10]

It can be any length, and the first-second characters are origin and destination of a route, respectively. The number following is the distance between the first and second characters (the nodes).

How would I go about calculating the shortest possible route from one point to another, if you can only advance from one node to another by steps (to go from A to D, you would have to go AB, BC, CD, ED) and the distance is variable between the nodes?

const routesInfo = ["AB5", "BC4", "CD8", "DC8", "DE6", "AD5", "CE2", "EB3", "AE7"]

  const stop1 = 'A',
  stop2 = 'B',
  stop3 = 'C',
  stop4 = '',
  stop5 = ''

  var trip1dist = 0,
    trip2dist = 0,
    trip3dist = 0,
    trip4dist = 0,
    dist = 0

  // for 3 stations
  if (stop1 && stop2 && stop3 && (!stop4) && (!stop5)) {
    var foundFirst = false,
    foundSecond = false
    for (var i = 0; i<routesInfo.length;i++) {
      var origin = routesInfo[i].charAt(0),
      destination = routesInfo[i].charAt(1)
      if (origin == stop1 && destination == stop2) {
        distance = routesInfo[i].charAt(2)
        trip1dist = distance
        foundFirst = true
      }
      if (origin == stop2 && destination == stop3) {
        distance = routesInfo[i].charAt(2)
        trip2dist = distance
        foundSecond = true
      }
    }
    // REFACTOR CHECKING FOR IMPOSSIBLE ROUTE
    if (foundFirst && !foundSecond) {
      console.log(null)
    }
    if (!foundFirst && foundSecond) {
      console.log(null)
    }
    if (!foundFirst && !foundSecond) {
      console.log(null)
    }
    var total = Number(trip1dist) + Number(trip2dist)
    console.log('The distance of the trip was: '+total)
  }

Answer 1

If you know the start and end points beforehand, you could run Dijkstra's algorithm to find the shortest path between the start and end point. Dijkstra's algorithm is a well-known solution for the shortest path problem in a graph. You can read more about it here. Also, you can find implementations of it quite easily.

If you want to know the shortest distance between any two given points, you should take a look into the Floyd-Warshall algorithm. You can read more about it here.