Vectorize and minimize Python loops; Load the CIFAR$-10$ dataset, which provides a collection of small images to use as tiles for the mosaic.

Load the target input image, resizing it to $512$x$512$ pixels, ensuring it$$s an RGB image. This image will be transformed into a mosaic using the CIFAR$-10$ tiles.tiles $=$ tiles$\_$dataset.load$\_$data$()[0][0]$ Calculate Mean Colors: For each CIFAR$-10$ tile, compute the mean RGB color and store this as a $3-$dimensional vector. This mean color will represent each tile and allow for easier comparison with individual pixels in the input image.

Build KD$-$Tree: Construct a KD$-$tree using the mean colors of the tiles. KD$-$trees allow efficient searches for nearest neighbors in low$-$dimensional spaces $($like our $3$D RGB vectors$).$

Query KD$-$Tree: Generate $10$ random colors and, for each one, query the KD$-$tree to find the closest mean color. Display each random color, its nearest match in the KD$-$tree, and the tile image that corresponds to that mean color.

Validation: Check that the nearest mean color and corresponding tile closely match the random color generated, keeping in mind that average colors may differ slightly due to color blending in the tiles.Using the KD$-$tree, replace each pixel in the $512$x$512$ input image with a $32$x$32$ tile image that has a similar color.

Efficiently Place Tiles: Create a large numpy array to hold the final mosaic image and $$paste$$ each tile into its corresponding position using slice notation. Attempt a more complex numpy approach by using np$.$transpose and np$.$reshape to assemble the mosaic without Python loops, achieving an efficient and compact solution.Display a sample of your mosaic, specifically the top$-$left $8$x$8$ tiles, to visually check the result.