Unique Paths in Grid DP in DSA C - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the first row of the DP table with 1s.

DSA C

for (int j = 0; j < n; j++) {
    dp[0][j] = [1];
}

Drag options to blanks, or click blank then click option'

Aj

B0

C1

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Setting dp[0][j] to 0 instead of 1.

Using the loop variable j as the value.

The first row has only one way to reach each cell by moving right, so dp[0][j] should be set to 1.

2fill in blank

medium

Complete the code to initialize the first column of the DP table with 1s.

DSA C

for (int i = 0; i < m; i++) {
    dp[i][0] = [1];
}

Drag options to blanks, or click blank then click option'

Ai

Bm

C0

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Setting dp[i][0] to 0 instead of 1.

Using the loop variable i as the value.

The first column has only one way to reach each cell by moving down, so dp[i][0] should be set to 1.

3fill in blank

hard

Fix the error in the code to correctly compute the number of unique paths for each cell.

DSA C

for (int i = 1; i < m; i++) {
    for (int j = 1; j < n; j++) {
        dp[i][j] = dp[i - 1][j] [1] dp[i][j - 1];
    }
}

Drag options to blanks, or click blank then click option'

A+

B*

C/

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction or multiplication instead of addition.

Using division which is not meaningful here.

The number of unique paths to a cell is the sum of paths from the cell above and the cell to the left, so use '+'.

4fill in blank

hard

Fill both blanks to complete the nested loops iterating over the grid cells starting from (1,1).

DSA C

for (int [1] = 1; [2] < m; [1]++) {
    for (int j = 1; j < n; j++) {
        dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
    }
}

Drag options to blanks, or click blank then click option'

Ai

Bj

Ck

Dx

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variables in declaration and condition.

Using 'j' for the outer loop which is for columns.

The outer loop variable should be 'i' to iterate rows from 1 to m-1.

5fill in blank

hard

Fill all three blanks to return the total unique paths from top-left to bottom-right in the grid.

DSA C

int uniquePaths(int m, int n) {
    int dp[m][n];
    for (int i = 0; i < m; i++) dp[i][0] = 1;
    for (int j = 0; j < n; j++) dp[0][j] = 1;
    for (int i = 1; i < m; i++) {
        for (int j = 1; j < n; j++) {
            dp[i][j] = dp[i - 1][j] [1] dp[i][j - 1];
        }
    }
    return dp[[2]][[3]];
}

Drag options to blanks, or click blank then click option'

A+

B-

Cm - 1

Dn - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using '-' instead of '+' for summing paths.

Returning dp[m][n] which is out of bounds.

Use '+' to sum paths from top and left. Return dp[m-1][n-1] for bottom-right cell.