Matrix Chain Multiplication?

Short answer: int MatrixChainOrder(int[] dims) { int n = dims.Length - 1; int[,] dp = new int[n, n]; for (int l = 2; l <= n; l++) { Follow on: for (int i = 0; i < n - l + 1; i++) { int j = i + l - 1; dp[i, j] = int.MaxValue; for (int k = i; k < j; k++) { int cost = dp[i, k] + dp[k + 1, j] + dims[i] * dims[k + 1] * dims[j + 1]; dp[i, j] = Math.Min(dp[i, j], cost); } } } return dp[0, n - 1]; } Explanation: DP calculates minimal…

Explain a bit more

cost to multiply chain of matrices by trying all partitions.

Example code

int MatrixChainOrder(int[] dims)
{
int n = dims.Length - 1;
int[,] dp = new int[n, n];
for (int l = 2; l <= n; l++)
{ Follow on: for (int i = 0; i < n - l + 1; i++)
{
int j = i + l - 1;
dp[i, j] = int.MaxValue;
for (int k = i; k < j; k++)
{
int cost = dp[i, k] + dp[k + 1, j] + dims[i] * dims[k + 1] * dims[j + 1]; dp[i, j] = Math.Min(dp[i, j], cost);
}
}
}
return dp[0, n - 1];
} Explanation: DP calculates minimal cost to multiply chain of matrices by trying all partitions.

Real-world example (ShopNest)

In coding rounds, state complexity aloud, write a clear ShopNest-flavored example (orders, carts), then handle edge cases (empty list, null, overflow).

Say this in the interview

1. Define — one clear sentence (the short answer above).
2. Example — relate it to a project like ShopNest or your real work.
3. Trade-off — when you would not use it.