According to a recent episode of Radiolab (about “Falling”), a cat reaches terminal velocity by the 9th floor. After that, it relaxes and is less likely to be hurt. There are completely uninjured cats after a fall from above the 30th. The riskiest floors are 5th to 9th.
Divide and Conquer Divide and Conquer works by dividing the problem into sub-problems, conquer each sub-problem recursively and combine these solutions. Dynamic Programming Dynamic Programming is a technique for solving problems with overlapping subproblems. Each sub-problem is solved only once and the result of each sub-problem is stored in a table ( generally implemented as … Read more
OK, I will describe first the simplest solution which is O(N^2), where N is the size of the collection. There also exists a O(N log N) solution, which I will describe also. Look here for it at the section Efficient algorithms. I will assume the indices of the array are from 0 to N – … Read more
rev4: A very eloquent comment by user Sammaron has noted that, perhaps, this answer previously confused top-down and bottom-up. While originally this answer (rev3) and other answers said that “bottom-up is memoization” (“assume the subproblems”), it may be the inverse (that is, “top-down” may be “assume the subproblems” and “bottom-up” may be “compose the subproblems”). … Read more
Dynamic programming is when you use past knowledge to make solving a future problem easier. A good example is solving the Fibonacci sequence for n=1,000,002. This will be a very long process, but what if I give you the results for n=1,000,000 and n=1,000,001? Suddenly the problem just became more manageable. Dynamic programming is used … Read more
Relevant article on Programming.Guide: Dynamic programming vs memoization vs tabulation What is difference between memoization and dynamic programming? Memoization is a term describing an optimization technique where you cache previously computed results, and return the cached result when the same computation is needed again. Dynamic programming is a technique for solving problems of recursive nature, … Read more