beginner

What is the problem statement of Unique Paths in Grid DP?

Find the number of ways to move from the top-left corner to the bottom-right corner of a grid, moving only right or down.

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beginner

What does the DP state represent in Unique Paths problem?

DP[i][j] represents the number of unique paths to reach cell (i, j) from the start.

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intermediate

What is the recurrence relation used in Unique Paths DP?

DP[i][j] = DP[i-1][j] + DP[i][j-1], summing paths from the top and left cells.

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beginner

Why do we initialize the first row and first column with 1 in Unique Paths DP?

Because there is only one way to reach any cell in the first row (all moves right) or first column (all moves down).

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intermediate

How does Unique Paths DP handle obstacles in the grid?

Cells with obstacles have 0 paths; DP skips adding paths through those cells.

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In Unique Paths DP, what does DP[i][j] represent?

AMaximum value in row i

BMinimum steps to cell (i, j)

CNumber of unique paths to cell (i, j)

DSum of all cells in column j

What is the base case for the first row in Unique Paths DP?

AAll zeros

BDecreasing sequence

CIncreasing sequence

DAll ones

Which moves are allowed in Unique Paths problem?

ADown and right

BUp and right

CUp and left

DDown and left

How do obstacles affect the DP table in Unique Paths with obstacles?

AThey double the paths

BThey set paths to zero for that cell

CThey have no effect

DThey add one extra path

What is the time complexity of Unique Paths DP solution?

AO(m*n)

BO(m+n)

CO(m^2*n^2)

DO(1)

Explain how to build the DP table for Unique Paths problem step-by-step.

Describe how obstacles change the Unique Paths DP approach.