Minimum Path Sum in Grid in DSA C - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the first cell of the dp array with the grid's starting value.

DSA C

dp[0][0] = [1];

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Agrid[0][0]

B0

C1

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing dp[0][0] with 0 or 1 instead of grid[0][0].

Forgetting to initialize dp[0][0].

The minimum path sum starts at the top-left cell, so dp[0][0] must be initialized with grid[0][0].

2fill in blank

medium

Complete the code to fill the first row of the dp array by accumulating sums from the left.

DSA C

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

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A/

B-

C*

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction or multiplication instead of addition.

Using dp[0][j+1] instead of dp[0][j-1].

The minimum path sum for the first row is the sum of all previous cells plus the current grid value.

3fill in blank

hard

Fix the error in the code to correctly compute the minimum path sum for each cell.

DSA C

dp[i][j] = grid[i][j] + (dp[i-1][j] < dp[i][j-1] ? dp[i-1][j] : [1]);

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Adp[i][j]

Bdp[i-1][j-1]

Cdp[i][j-1]

Dgrid[i][j]

Attempts:

3 left

💡 Hint

Common Mistakes

Using dp[i-1][j-1] which is diagonal and not allowed.

Using dp[i][j] which is the current cell and causes wrong calculation.

We choose the smaller of the top or left cell's dp values to add to the current grid cell.

4fill in blank

hard

Fill both blanks to complete the nested loops that fill the dp array starting from row 1 and column 1.

DSA C

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

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A1

B0

C2

Dm

Attempts:

3 left

💡 Hint

Common Mistakes

Starting loops from 0 which overwrites initial values.

Starting from 2 which skips some cells.

We start filling dp from row 1 and column 1 because row 0 and column 0 are already initialized.

5fill in blank

hard

Fill all three blanks to complete the function that returns the minimum path sum from top-left to bottom-right.

DSA C

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

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A+

B-

Cn-1

Dm-1

Attempts:

3 left

💡 Hint

Common Mistakes

Using '-' instead of '+' in dp initialization.

Returning dp[m-1][m-1] instead of dp[m-1][n-1].

We add values when filling first column and row, and return dp[m-1][n-1] as the minimum path sum.