PALANTIR EDGE AI: META-CONSTELLATION DOWNSAMPLING

Difficulty: Easy Tags: Computer Vision, Max Pooling, Array Manipulation, Edge Inference

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Story

Palantir's MetaConstellation software integrates with satellite constellations to run object-detection micro-models on-orbit using Edge AI. High-resolution multispectral imagery is massive. To reduce the bandwidth needed to downlink it to tactical ground stations, the onboard micro-models downsample the imagery spatially, compressing the data while keeping the critical intelligence.

Your task is the forward pass of a 2D max pooling layer, the same operation as the Max Pooling question in the Vision track, written from scratch. You are given a single-channel feature map that holds radar or thermal signatures of ships or buildings. By keeping the maximum response in each local patch, you preserve the strongest signals (a hot engine, a metal hull) while shrinking the image dimensions.

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The Math: Max Pooling

Given an N x N input matrix X and a pooling window of size F, with a stride equal to F (the windows do not overlap), the output Y is an M x M matrix where M = N / F.

For every output position (i, j) with 0 <= i < M and 0 <= j < M, the value is the maximum of the matching F x F patch of the input:

Y[i][j] = max( X[i*F + a][j*F + b] )   over all 0 <= a < F and 0 <= b < F

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Input Format

N F
x_{0,0} x_{0,1} ... x_{0,N-1}
...
x_{N-1,0} x_{N-1,1} ... x_{N-1,N-1}

• N is the size of the square input grid. It is always divisible by F.
• F is the size of the pooling window, and also the stride.
• The next N lines each hold N space-separated floats: the feature map X.

Output Format

Print M lines, each holding M space-separated floats: the downsampled feature map Y.

Print every value with exactly 2 decimal places.

Judging: accepted if the output matches the reference solution exactly.

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Constraints

• 1 <= F <= N <= 1000
• N is divisible by F
• -10^6 <= x <= 10^6 for every value in X
• Time limit: 1.0 second. Memory limit: 64 MB.

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Example 1

Input

4 2
1.0 2.0 0.5 0.1
3.0 4.0 1.5 1.1
0.0 -1.0 5.0 2.0
2.0 1.0 3.0 4.0

Output

4.00 1.50
2.00 5.00

Explanation: The 4 x 4 input is split into four 2 x 2 patches.

• Top-left patch: max(1.0, 2.0, 3.0, 4.0) = 4.00
• Top-right patch: max(0.5, 0.1, 1.5, 1.1) = 1.50
• Bottom-left patch: max(0.0, -1.0, 2.0, 1.0) = 2.00
• Bottom-right patch: max(5.0, 2.0, 3.0, 4.0) = 5.00

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Example 2

Input

4 4
-3.5 -2.0 -7.25 -1.5
-9.0 -4.0 -6.0 -8.0
-2.5 -3.0 -1.25 -5.0
-7.0 -6.5 -4.5 -2.75

Output

-1.25

Explanation: The window covers the whole grid, so the output is a single value: the largest of the sixteen. Every value is negative, and the largest is -1.25, not 0.