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Fixed titles, math rendering, and links on some pages
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# Backtracking
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---
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title: Backtracking
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showthedate: false
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---
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This algorithm tries to construct a solution to a problem one piece at a time. Whenever the algorithm needs to decide between multiple alternatives to the part of the solution it *recursively* evaluates every option and chooses the best one.
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Backtracking algorithms are used to make a *sequence of decisions*.
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When we design a new recursive backtracking algorithm, we must figure out in advance what information we will need about past decisions in the middle of the algorithm.
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When we design a new recursive backtracking algorithm, we must figure out in advance what information we will need about past decisions in the middle of the algorithm.
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# Dynamic Programming
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---
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title: Dynamic Programming
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---
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The book first goes into talking about the complexity of the Fibonacci algorithm
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@ -79,4 +81,4 @@ These algorithms are best developed in two distinct stages.
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## Greedy Algorithms
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If we're lucky we can just make decisions directly instead of solving any recursive subproblems. The problem is that greedly algorithms almost never work.
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If we're lucky we can just make decisions directly instead of solving any recursive subproblems. The problem is that greedly algorithms almost never work.
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# Greedy Algorithms
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---
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title: Greedy Algorithms
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showthedate: false
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---
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Greedy Algorithms are about making the best local choice and then blindly plowing ahead.
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The Gale-Shapley algorithm is a great greedy fit. It goes like this
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1. An arbitrary unmatched hospital A offers its position to the best doctor a who has not already rejected it.
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2. If a is unmatched, she tentatively accepts A's offer. If a already had a match but prefers A, she rejects her current match and tentatively accepts the new offer from A. Otherwise a rejects the new offer.
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2. If a is unmatched, she tentatively accepts A's offer. If a already had a match but prefers A, she rejects her current match and tentatively accepts the new offer from A. Otherwise a rejects the new offer.
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# Recursion
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---
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title: Recursion
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showthedate: false
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math: true
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---
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## Reductions
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