# Unique Paths

Category

DP - Multidimensional

Checkbox

Checkbox

Difficulty

Medium

Index

63

Key Ideas

The key idea to solve this problem is to use dynamic programming to calculate the number of unique paths from the top-left corner to the bottom-right corner in a grid.

Problem Number

62

Problem Summary

The Unique Paths problem is a medium difficulty problem in the field of dynamic programming. It involves finding the number of unique paths from the top-left corner to the bottom-right corner of a grid, given certain constraints. Some key pitfalls to watch out for include not considering all possible moves and not properly initializing the dynamic programming array.

Solution Summary

The best solution to solve the Unique Paths problem is to use dynamic programming. We can create a 2D grid and initialize the first row and first column with a value of 1, representing that there is only one way to reach each cell in the first row and first column. Then, for each cell (i, j), we can calculate the number of unique paths to reach that cell by summing the number of unique paths from the cell above (i-1, j) and the cell to the left (i, j-1). Finally, the value in the bottom-right cell of the grid represents the total number of unique paths from the top-left cell to the bottom-right cell, which is the desired output of the problem.
This dynamic programming approach has a time complexity of O(m*n), where m is the number of rows and n is the number of columns in the grid. By using this solution, we can efficiently find the number of unique paths in a grid and solve the Unique Paths problem.

Tags

Math

Dynamic Programming

Combinatorics