How should I practice Count Routes Through a City Grid?

Start by reading the full statement, solve the visible examples, then compare the pattern against related IMC Trading phone screen problems in FastPrep.

Is Count Routes Through a City Grid associated with IMC Trading?

FastPrep tags this as a IMC Trading phone screen coding practice problem when the problem catalog has that company and stage context.

Count Routes Through a City Grid

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Problem statement

A city is represented by a rectangular grid with rows rows and columns columns. Start at the top-left cell and reach the bottom-right cell.

For this exercise, assume each step moves exactly one cell right or one cell down, every cell is open, and there is no wrapping. Count distinct step sequences that reach the destination. For this exercise, assume the grid dimensions are supplied as parameters and the result is an exact signed64-bit count with no modulus.

A one-cell grid has one route: the empty sequence. Complete countCityGridRoutes(rows, columns).

Function

countCityGridRoutes(rows: int, columns: int) → long

Examples

Example 1

rows = 3columns = 3return = 6

Each route has two right moves and two down moves. Choosing their order gives 6 routes. These dimensions are an authored practice example.

Example 2

rows = 1columns = 1return = 1

The start is already the destination, so the empty sequence is the single route.

Example 3

rows = 1columns = 5return = 1

Every step must go right, giving exactly one route.

Example 4

rows = 25columns = 40return = 156655690918541325

Choose positions of the24downmoves among63steps: C(63,24)=156655690918541325. This odd integer exceeds the exact-integer range of an IEEE754double, so keep the count in signed64-bit arithmetic.

Constraints

For this exercise, assume 1 <= rows <= 25 and 1 <= columns <= 40.
The largest result is 156655690918541325, which fits a signed64-bit integer.
Do not use floating-point rounding to count routes.