how to traverse an n-dimensional array with stride

Traversing an n-dimensional array with stride involves using nested loops to iterate over each element of the array efficiently, taking into account the strides or step sizes for each dimension. Strides are the number of elements to skip in each dimension to move to the next element along that dimension.

Let's consider a 3-dimensional array for simplicity, but the same approach can be extended to higher dimensions. Here's a general algorithm to traverse an n-dimensional array with stride:

1. Determine the dimensions of your n-dimensional array, and store them in variables (e.g., dim1, dim2, dim3 for a 3D array).

2. Determine the strides for each dimension (e.g., stride1, stride2, stride3).

3. Use nested loops to iterate over each element of the array. The loops should run from 0 to the dimension size minus one, and in each iteration, you should access the element using the appropriate strides.

Here's a code example for a 3-dimensional array in Python:

pythonCopy code
# Example 3D array dimensions
dim1 = 3
dim2 = 4
dim3 = 5

# Example strides for each dimension
stride1 = dim2 * dim3
stride2 = dim3
stride3 = 1

# Example 3D array
data = [[[i*100 + j*10 + k for k in range(dim3)] for j in range(dim2)] for i in range(dim1)]

# Traversing the 3D array with strides
for i in range(dim1):
    for j in range(dim2):
        for k in range(dim3):
            # Access the element using the strides
            element = data[i*stride1 + j*stride2 + k*stride3]
            print(f"Element at ({i}, {j}, {k}): {element}")

In this example, the strides define the steps required to move between elements along each dimension. We use these strides to access the correct element in the 3D array while iterating through the nested loops.

You can extend this approach to higher-dimensional arrays by adding more nested loops and corresponding strides for each dimension. However, keep in mind that as the dimensionality increases, the number of nested loops will increase, and the code can become more complex and harder to maintain. In such cases, consider using NumPy, a powerful library for numerical computing in Python, which provides convenient functions for working with n-dimensional arrays and strides.