Problem
Neural network layers, attention and most of machine learning boil down to matrix multiplication. For an n × k matrix A and a k × m matrix B, the product C = A × B is n × m, where each entry is the dot product of a row of A and a column of B:
C[i][j] = A[i][0] × B[0][j] + A[i][1] × B[1][j] + … + A[i][k-1] × B[k-1][j]
Implement matmul(a, b).
Input
a: An n × k matrix.
b: A k × m matrix (its number of rows equals the number of columns of a).
Output
Return the n × m product matrix.
Constraints
1 ≤ n, k, m ≤ 50
-100 ≤ each value ≤ 100
Examples
Input:
a = [
[1.0, 2.0],
[3.0, 4.0]
]
b = [
[5.0, 6.0],
[7.0, 8.0]
]
Expected output:
expected = [
[19.0, 22.0],
[43.0, 50.0]
]Input:
std::vector<std::vector<double>> a = {
{1.0, 2.0},
{3.0, 4.0}
};
std::vector<std::vector<double>> b = {
{5.0, 6.0},
{7.0, 8.0}
};
Expected output:
std::vector<std::vector<double>> expected = {
{19.0, 22.0},
{43.0, 50.0}
};Input:
double[][] a = new double[][] {
new double[] {1.0, 2.0},
new double[] {3.0, 4.0}
};
double[][] b = new double[][] {
new double[] {5.0, 6.0},
new double[] {7.0, 8.0}
};
Expected output:
double[][] expected = new double[][] {
new double[] {19.0, 22.0},
new double[] {43.0, 50.0}
};Explanation
C[0][0] = 1×5 + 2×7 = 19, C[0][1] = 1×6 + 2×8 = 22, C[1][0] = 3×5 + 4×7 = 43 and C[1][1] = 3×6 + 4×8 = 50.
Input:
a = [
[1.0, 0.0, 2.0]
]
b = [
[3.0],
[4.0],
[5.0]
]
Expected output:
expected = [
[13.0]
]Input:
std::vector<std::vector<double>> a = {
{1.0, 0.0, 2.0}
};
std::vector<std::vector<double>> b = {
{3.0},
{4.0},
{5.0}
};
Expected output:
std::vector<std::vector<double>> expected = {
{13.0}
};Input:
double[][] a = new double[][] {
new double[] {1.0, 0.0, 2.0}
};
double[][] b = new double[][] {
new double[] {3.0},
new double[] {4.0},
new double[] {5.0}
};
Expected output:
double[][] expected = new double[][] {
new double[] {13.0}
};Explanation
A 1 × 3 matrix times a 3 × 1 matrix gives a 1 × 1 matrix: 1×3 + 0×4 + 2×5 = 13.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
Each output cell comes from one row of the first matrix and one column of the second matrix.
Hint 2
Accumulate products across the shared inner dimension, then place the result in the matching output position.
Hint 3
Be careful with the shapes: the first matrix’s column count must match the second matrix’s row count.
Expected complexity
O(n k m) time, O(n m) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.