Unique Paths

Problem

Count the number of paths from the top-left to the bottom-right corner of an m by n grid when each move goes one cell right or one cell down.

Use dynamic programming where the first row and column are all 1 and every other cell is the sum of the cell above and the cell to the left. Assume m >= 1 and n >= 1.

Hint

Each cell is reachable only from the cell above and the cell to the left.

Test cases

case 1

in: [3,7]

expected: 28

case 2

in: [3,3]

expected: 6

case 3

in: [1,1]

expected: 1

case 4

in: [1,5]

expected: 1

case 5

in: [5,5]

expected: 70

Starter codePython

def unique_paths(m, n):
    # Your code here
    pass

5 test cases · run your code against them in the editor