Python Program for Mathematical Solutions

A real estate owner in California, Lida, inherits a piece of land. The land is modeled as a rectangular patch of variable size. The patch of land is represented with an image (list of lists). To make some money out of it, she can decide to lease the land to other people. To do that, she may decide to divide the land into four other patches. In case she decides to not lease the land, no further sub-patches are created. On the contrary, in case the land is divided into four sub-patches, some colored marks (straight lines) on the land are drawn with a thickness of one pixel to mark the private properties that are created. There is no prior knowledge of how and where the lines will be drawn, nor which colors will be used (there is no regular pattern). The only knowledge is that the lines are axis-aligned. The four lessees that receive the sub-patches of land may take the same decision that Lida took before them. They may decide to sublease once again their small patch to others or, else, to keep the land all for themselves. The decision for each lessee is independent of each other. For example, lessee #1 may decide to sublease again, while lessee #2 may keep the land for himself, etc, whereas lessee #3 and #4 may subdivide. If they sublease and divide, they follow the same policy of dividing in four parts and setting their boundaries with line drawing but obviously with a different splitting position of their land. For sure, they will be using a color that is different from the colors used by Lida yet they will be using the same color among them, at the same level of splitting. NOTE: An important note is that the color of the background (bg) of the land is not given (i.e. we do not know if the bg is black, or white or blue etc) but we do know that the background land color is NOT used by any of the lessees ever to mark their boundaries. The subdivision process could continue until when all the lessees in all patches stop subdividing their land. This process described here leads us to the image that is taken as input to a program. NOTE: You can assume that the smallest possible rectangular patch has the shortest side of two pixels in length. Think well about the problem and once you are sure of a solution, design on the paper (this "design" needs be then described into the pseudo code part) and then implement a program ex1(input_file, output_file) which: - reads the file indicated by the parameter 'input_file' using the 'images' library - preprocesses the image--if needed--and implements a *recursive* function to solve the requirements below. - counts all the patches of lands that are in the image and returns the number of patches. It should return the number of rectangles with the color of the background that is present in the image. Regarding the simplified case below: # +++++++++++++++++++ # +-1-|-2-|---------+ # ++++a+++|----5----+ # +-3-|-4-|---------+ # ++++++++b++++++++++ # +-------|--7-|-8--+ # +---6---|++++c+++++ # +-------|-10-|-9--+ # +++++++++++++++++++ the approach should return 10 as the total number of patches. (The numbers in the simplified case above are just added for the sake of clarity. The image data does not contain those numbers, obviously). - finally, given that the real estate registry needs to book-keep all the boundaries created, the program shall build an output image of the size of 1x(N+1). The image encodes as the first pixel the color of the background. Then it should encode "the color hierarchy" of all the N colors used to subdivide the patches of land. The hierarchy is defined by "visiting" first in depth the upper left patch, then upper right patch, then lower left, and lower right. The colors should be stored in reverse order with respect to the "visit" made. With reference to the previous semplified case, assuming a boundary color is described with a letter, the output image should contain: out_colors = bg b c a Another case a bit more complex: +++++++++++++++++++++++++++++++++++++ +-1-|-2-|---------|--------|--------+ ++++a+++|----5----|---6----|----7---+ +-3-|-4-|---------|--------|--------+ ++++++++b+++++++++|++++++++c+++++++++ +-------|--9-|-10-|--------|--------+ +--8----|++++d++++|---13---|---14---+ +-------|-11-|-12-|--------|--------+ ++++++++++++++++++e++++++++++++++++++ +-15|-16|---------|--------|-21|-22-+ ++++f+++|---19----|---20---|+++g+++++ +-17|-18|---------|--------|-23|--24+ ++++++++h+++++++++|++++++++l+++++++++ +-------|-26-|-27-|--------|-31-|-32+ +--25---|++++m++++|---30---|+++n+++++ +-------|-29-|-28-|--------|-33-|-34+ +++++++++++++++++++++++++++++++++++++ n_rect is: 34 the color hierarchy is: bg e l n g h m f c b d a NOTE: it is forbidden to import/use other libraries or open files except the one indicated NOTE: The test system recognizes recursion ONLY if the recursive function/method is defined in the outermost level. DO NOT define the recursive function within another function/method otherwise, you will fail all the tests. """ import images def ex1(input_file, output_file): # write your code here pass if __name__ == '__main__': # write your tests here pass