#0067

Unique Paths in a Grid

MediumDSA25 min20 XP

Problem

Given m rows and n columns, return the number of ways to move from the top-left cell to the bottom-right cell using only right and down moves.

Why This Matters

2D DP becomes less scary when you see that each cell only depends on the cell above and the cell to the left.

Function Signature

def unique_paths(m, n):

Examples

Example 1

Inputm = 3, n = 7

Output28

Every interior cell combines paths from above and left.

Constraints

m and n are positive integers.
No obstacles are present.
Return an integer count.

CodePython

def unique_paths(m, n):
    """
    Input example: m = 3, n = 7
    Return: 28
    Return the value from the function so the tests can compare it. Do not print unless the prompt asks.
    """
    # write your code here
    return 0

def unique_paths(m, n):
    """
    Input example: m = 3, n = 7
    Return: 28
    Return the value from the function so the tests can compare it. Do not print unless the prompt asks.
    """
    # write your code here
    return 0

Visible browser tests run here when available.

Testcases2 visible / 3 hidden categories

Three by seven grid

Input3, 7

Expected28

Classic small grid example.

Single row

Input1, 5

Expected1

Only keep moving right.

Hidden Test Categories

single columnsquare gridsmall 2x2 grid