Algorithmic Toolbox week4 Divide and Conquer --- Introduction

Def

1.Divide problem into sub problems that can be solved independently.
2.Sub problems have no overlap.
3.Sub problems's type are same as original problem.
  将一个矩形必须分解为若干个矩形，而不是三角形或者其他类型。

Divide

Conquer

Combine

In summary, the divide and conquer algorithm consists of one: breaking the problem into non-overlapping subproblems of the same type. Two: recursively solving those subproblems. And three: combining the results.

Divide and Conquer

Linear Search

Searching in an array

Linear Search

for low in (low, high+2)，也就是low将会从low增加到high+1，所以n=high-low+1.

Iterative version

Summary

Binary Search

Binary Search

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Binary Search Runtime

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The way to do that was an augmented set of arrays.