Hackerrank Solution: Connecting Towns

Original Problem

Cities on a map are connected by a number of roads. The number of roads between each city is in an array and city \(0\) is the starting location. The number of roads from city \(0\) to city \(1\) is the first value in the array, from city \(1\) to city \(2\) is the second, and so on.

How many paths are there from city \(0\) to the last city in the list, modulo \(1234567\)?

Example

\(n=4\)
\(routes=[3,4,5]\)
There are \(3\) roads to city \(1\), \(4\) roads to city \(2\) and \(5\) roads to city \(3\). The total number of roads is \(3\times 4\times 5\mod 1234567 = 60\).

Note
Pass all the towns T_i for i=1 to n-1 in numerical order to reach T_n.

Function Description

Complete the connectingTowns function in the editor below.

connectingTowns has the following parameters:

• int n: the number of towns
• int routes[n-1]: the number of routes between towns

Returns

• int: the total number of routes, modulo 1234567.

Input Format
The first line contains an integer T, T test-cases follow.

Each test-case has 2 lines.
The first line contains an integer N (the number of towns).
The second line contains N - 1 space separated integers where the i^th integer denotes the number of routes, N_i, from the town T_i to T_i+1

Constraints
1 <= T<=1000
2< N <=100
1 <= routes[i] <=1000

Sample Input

2
3
1 3
4
2 2 2

Sample Output

3
8

Explanation
Case 1: 1 route from T₁ to T₂, 3 routes from T₂ to T₃, hence only 3 routes.
Case 2: There are 2 routes from each city to the next, hence 2 * 2 * 2 = 8.

Solution

The solution was given already by the problem statement. We have to multiply all number of routes and since the number can get quite large, we are required to get the result modulo 1234567. To not rely on bigint, we make use of multiplicative rules of modulo and can solve the problem with

function connectingTowns(n, routes) {
  var p = 1;
  for (var r of routes) {
    p = (r * p) % 1234567;
  }
  return p % 1234567;
}