Problems

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Max Pooling Forward

Neural Networks

Medium

Max pooling is a downsampling operation commonly used in convolutional neural networks to reduce spatial dimensions while retaining the most prominent features. It slides a window over the input and takes the maximum value in each window position.

Given a 2D input matrix X (height H, width W), a pool size p, and a stride s, compute the max pooling output.

Algorithm

Compute the output dimensions:

H_{out} = \lfloor \frac{H - p}{s} \rfloor + 1, \quad W_{out} = \lfloor \frac{W - p}{s} \rfloor + 1

For each output position (i, j), extract the p x p window and take the maximum:

\text{out}[i][j] = \max_{0 \le a < p,\; 0 \le b < p} X[i \cdot s + a][j \cdot s + b]

Loading visualization...

Examples

Input:

X = [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]], pool_size = 2, stride = 2

Output:

[[6, 8], [14, 16]]

The 4x4 input is divided into four non-overlapping 2x2 windows. The max of each window: top-left max(1,2,5,6)=6, top-right max(3,4,7,8)=8, bottom-left max(9,10,13,14)=14, bottom-right max(11,12,15,16)=16.

Input:

X = [[1,5,3],[4,2,6],[7,8,0]], pool_size = 2, stride = 1

Output:

[[5, 6], [8, 8]]

With stride 1, the 2x2 window slides by 1 each step, producing overlapping windows. Top-left max(1,5,4,2)=5, top-right max(5,3,2,6)=6, bottom-left max(4,2,7,8)=8, bottom-right max(2,6,8,0)=8.

Hint 1

Compute output dimensions first: out_h = (H - pool_size) // stride + 1. Then use four nested loops: two for output positions (i, j) and two for positions within the pooling window (a, b). Track the maximum in each window.

Hint 2

The input element for output position (i, j) and window offset (a, b) is at X[i * stride + a][j * stride + b]. Initialize max_val to negative infinity for each window.

Requirements

Apply 2D max pooling with the given pool size and stride
Each output element is the maximum value in its pooling window
Handle both overlapping (stride < pool_size) and non-overlapping (stride = pool_size) cases
Return the pooled output as a list of lists of floats or ints

Constraints

X has at least pool_size rows and pool_size columns
pool_size >= 1, stride >= 1
Return a list of lists
Time limit: 300 ms

Try Similar Problems

Max Pooling 2d Average Pooling 2d Global Avg Pooling Simple Cnn Layer Conv2d Image Filtering

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Max Pooling Forward

Neural Networks

Medium

Given a 2D input matrix X (height H, width W), a pool size p, and a stride s, compute the max pooling output.

Algorithm

Compute the output dimensions:

H_{out} = \lfloor \frac{H - p}{s} \rfloor + 1, \quad W_{out} = \lfloor \frac{W - p}{s} \rfloor + 1

For each output position (i, j), extract the p x p window and take the maximum:

\text{out}[i][j] = \max_{0 \le a < p,\; 0 \le b < p} X[i \cdot s + a][j \cdot s + b]

Loading visualization...

Examples

Input:

X = [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]], pool_size = 2, stride = 2

Output:

[[6, 8], [14, 16]]

Input:

X = [[1,5,3],[4,2,6],[7,8,0]], pool_size = 2, stride = 1

Output:

[[5, 6], [8, 8]]

With stride 1, the 2x2 window slides by 1 each step, producing overlapping windows. Top-left max(1,5,4,2)=5, top-right max(5,3,2,6)=6, bottom-left max(4,2,7,8)=8, bottom-right max(2,6,8,0)=8.

Hint 1

Hint 2

The input element for output position (i, j) and window offset (a, b) is at X[i * stride + a][j * stride + b]. Initialize max_val to negative infinity for each window.

Requirements

Apply 2D max pooling with the given pool size and stride
Each output element is the maximum value in its pooling window
Handle both overlapping (stride < pool_size) and non-overlapping (stride = pool_size) cases
Return the pooled output as a list of lists of floats or ints

Constraints

X has at least pool_size rows and pool_size columns
pool_size >= 1, stride >= 1
Return a list of lists
Time limit: 300 ms

Try Similar Problems

Max Pooling 2d Average Pooling 2d Global Avg Pooling Simple Cnn Layer Conv2d Image Filtering

Case 1

Case 2

X =

Accepts: array

pool_size =

Accepts: number

stride =

Accepts: number