1. This is a divide and conquer problem, there are 1000 points in a plane, no three of them on the same line. Devise an algorithm to construct 100 decagons with their vertices at these points. The decagons need not be convex, but each of them has to be simple, is boundary should not cross itself, and no two decagons may have a common point. Create using python.
2. This is a greedy algorithm problem, write a program that determines the best route for a subway passenger to take from one designated station to another in a well-developed subway system like those in Washington, DC, or London, UK. Create using python.
3. The string edit distance problem, suppose that you want to transform the word ?algorithm? into the word ?alligator.? For each letter you can either copy the letter from one word to another at a cost of 5, you can delete a letter at cost of 20, or insert a letter at a cost of 20. The total cost to transform one word into another is used by spell check programs to provide suggestions for words that are close to one another. Use dynamic programming techniques to develop an algorithm that gives you the smallest edit distance between any two words. Create using python.
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