How many ways across the yard
A forklift crosses a rectangular yard from the top-left bay to the bottom-right one, and may only ever drive right or down. Planning wants the number of distinct routes.
- Movement is only ever one bay right or one bay down.
- Return how many distinct routes reach the far corner.
- A yard with no rows or no columns has no routes.
- A single bay is already the destination: one route.
RoutesAcross(rows: int, columns: int) → int
C# needs a compiler and Drill does not host one yet, so this page is the reference rather than an exercise: the problem, worked examples, and the solution in full. To type it out, the same problem runs in Python.
Where you start
public int RoutesAcross(int rows, int columns) {
}Worked examples
| Call | Result |
|---|---|
RoutesAcross(3, 3) | 6 |
RoutesAcross(1, 1) | 1 |
RoutesAcross(2, 3) | 3 |
RoutesAcross(0, 5) | 0 |
Hint
The routes into a bay are the routes into the bay above plus the routes into the bay to its left. The top row and left column have exactly one each.
Reference solution in C#
public int RoutesAcross(int rows, int columns) {
if (rows <= 0 || columns <= 0) return 0;
var ways = new int[rows, columns];
for (int r = 0; r < rows; r++) {
for (int c = 0; c < columns; c++) {
ways[r, c] = (r == 0 || c == 0) ? 1 : ways[r - 1, c] + ways[r, c - 1];
}
}
return ways[rows - 1, columns - 1];
}