Fixed titles, math rendering, and links on some pages

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Brandon Rozek 2021-07-26 09:13:20 -04:00
parent 9f096a8720
commit 330ace0de9
61 changed files with 303 additions and 115 deletions

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# Backtracking
---
title: Backtracking
showthedate: false
---
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*.
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.
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
---
title: Dynamic Programming
---
The book first goes into talking about the complexity of the Fibonacci algorithm
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## Greedy Algorithms
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.
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
---
title: Greedy Algorithms
showthedate: false
---
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
1. An arbitrary unmatched hospital A offers its position to the best doctor a who has not already rejected it.
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.
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
---
title: Recursion
showthedate: false
math: true
---
## Reductions