Matrix Chain Multiplication in DSA Typescript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the dp table with zeros.

DSA Typescript

const n = dims.length - 1;
const dp: number[][] = Array(n).fill(0).map(() => Array(n).fill([1]));

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

A1

B0

CInfinity

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing dp with 1 instead of 0

Using Infinity which is used for initial max cost, not for dp initialization

The dp table should be initialized with zeros because initially, the cost of multiplying one matrix is zero.

2fill in blank

medium

Complete the code to set the chain length for the outer loop.

DSA Typescript

for (let length = 2; length <= n; length[1]) {

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

A++

B*=

C+=

D--

Attempts:

3 left

💡 Hint

Common Mistakes

Using -- which decreases the length

Using *= which multiplies length

The chain length increases by 1 in each iteration, so we use ++ to increment length.

3fill in blank

hard

Fix the error in the cost calculation inside the nested loops.

DSA Typescript

const cost = dp[i][k] + dp[k + 1][j] + dims[i] * dims[k + 1] * dims[[1] + 1];

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

Ai

Bk

Cj

Dk - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using dims[k] instead of dims[j + 1]

Using dims[i] twice

The cost of multiplying matrices from i to j includes dims[i] * dims[k+1] * dims[j + 1].

4fill in blank

hard

Fill both blanks to correctly update the dp table and loop indices.

DSA Typescript

for (let i = 0; i <= n - [1]; i++) {
  let j = i + [2] - 1;

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

Alength

Cn

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using n instead of length

Incorrect calculation of j

The loop runs while i <= n - length, and j is calculated as i + length - 1 to cover the chain segment.

5fill in blank

hard

Fill all three blanks to complete the minimum cost update inside the innermost loop.

DSA Typescript

if (cost < dp[i][j]) {
  dp[i][j] = [1];
  split[i][j] = [2];
}

// Return the minimum cost
return dp[3];

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

Acost

Bk

C[0][n - 1]

Ddp[i][j]

Attempts:

3 left

💡 Hint

Common Mistakes

Assigning dp[i][j] to dp[i][j] instead of cost

Returning dp[i][j] instead of dp[0][n-1]

We update dp[i][j] with cost, record split point k, and finally return dp[0][n-1] for full chain cost.