102 lines
2.7 KiB
Org Mode
102 lines
2.7 KiB
Org Mode
#+TITLE: Notes & Exercises: The Algorith Design Manual
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#+AUTHOR: Joseph Ferano
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#+OPTIONS: ^:{}
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* Chapter 1
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** Notes
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*** 1
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An /algorithm/ is a procedure that takes any of the possible input instances
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and transforms it to the desired output.
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The author provides an example of a sorting algorithm called
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~insertion_sort~. Here it is modified so it actually runs
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#+begin_src C :includes stdio.h
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void insertion_sort(int *nums, int len) {
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int i, j;
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for (i = 1; i < len; i++) {
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j = i;
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while (nums[j] < nums[j -1] && j > 0) {
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int temp = nums[j];
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nums[j] = nums[j - 1];
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nums[j - 1] = temp;
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j--;
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}
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}
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}
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int nums[8] = {1,4,5,2,8,3,7,9};
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insertion_sort(nums, 8);
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for (int i = 0; i < 8; i++) {
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printf("%d", nums[i]);
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}
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#+end_src
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#+RESULTS:
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: 12345789
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*** 1.1 Robots
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The Robot arm problem is presented where it is trying to solder contact points
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and visit all points in the shortest path possible.
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The first algorithm considered is ~NearestNeighbor~. However this is a naïve, and
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the arm hopscotches around
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Next we consider ~ClosestPair~, but that too misses in certain instances.
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Next is ~OptimalTSP~, which will always give the correct result because it
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enumerates all possible combinations and return the one with the shortest
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path. For 20 points however, the algorithm grows at a right of O(n!). TSP stands
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for Traveling Salesman Problem.
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**** TODO Implement NearestNeighbor
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**** TODO Implement ClosestPair
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**** TODO Implement OptimalTSP for N < 8
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*** 1.2 Right Jobs
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Here we are introduced to the Movie Scheduling Problem where we try to pick the
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largest amount of mutually non-overlapping movies an actor can pick to maximize
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their time. Algorithms considered are ~EarliestJobFirst~ to start as soon as
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possible, and then ~ShortestJobFirst~ to be done with it the quickest, but both
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fail to find optimal solutions.
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~ExhaustiveScheduling~ grows at a rate of O(2^{n}) which is much better than O(n!) as
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in the previous problem. Finally ~OptimalScheduling~ improves efficiency by first
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removing candidates that are overlapping such that it doesn't even compare them.
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*** 1.3 Correctness
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It's important to be clear about the steps in pseudocode when designing
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algorithms on paper. There are important things to consider about algorithm
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correctness;
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- Verifiability
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- Simplicity
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- Think small
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- Think exhaustively
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- Hunt for the weakness
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- Go for a tie
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- Seek extremes
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Other tecniques include *Induction*, *Recursion*, and *Summations*.
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*** 1.4 Modeling
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Most algorithms are designed to work on rigorously defined abstract
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structures. These fundamental structures include;
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- Permutations
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- Subsets
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- Trees
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- Graphs
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- Points
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- Polygons
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- Strings
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*** 1.5-1.6 War Story about Psychics
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* Chapter 2
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