Binary Search

陳鵬宇 (float)< float.tw @ gmail.com >

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Binary Search● Binary Search

– Search X, Given f(x) and f(X) = Y– f(x) must be Monotonic function (sorted)

● Basic Operation

– Find Value, Max or Min– "canbe" function– beg, mid, end

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0 1 2 3 4 5 6 7 8 9 10 11 12 13

Example● Find 33

6 13 14 25 33 43 51 65 66 76 78 81 98 99

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0 1 2 3 4 5 6 7 8 9 10 11 12 13

Example● Find 33

● f(0) = 6, f(1) = 13, f(2) = 14 …

6 13 14 25 33 43 51 65 66 76 78 81 98 99

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0 1 2 3 4 5 6 7 8 9 10 11 12 13

Example● Find 33

6 13 14 25 33 43 51 65 66 76 78 81 98 99

Beg End

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0 1 2 3 4 5 6 7 8 9 10 11 12 13

Example● Find 33

6 13 14 25 33 43 6551 66 76 78 81 98 99

Beg EndMid

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0 1 2 3 4 5 6 7 8 9 10 11 12 13

Example● Find 33

6 13 14 25 33 43 6551 66 76 78 81 98 99

Beg End

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0 1 2 3 4 5 6 7 8 9 10 11 12 13

Example● Find 33

6 13 3325 43 6551 66 76 78 81 98 99

Beg EndMid

14

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0 1 2 3 4 5 6 7 8 9 10 11 12 13

Example● Find 33

6 13 14 3325 43 6551 66 76 78 81 98 99

Beg End

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0 1 2 3 4 5 6 7 8 9 10 11 12 13

Example● Find 33

6 13 14 25 4333 6551 66 76 78 81 98 99

Beg EndMid

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C/C++ function● C: bsearch

void* bsearch (const void* key, const void* base,

size_t num, size_t size,

int (*compar)(const void*,const void*));

● C++: binary_search template <class ForwardIterator, class T, class Compare>

bool binary_search (ForwardIterator first, ForwardIterator last,

const T& val, Compare comp);

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maximize minimum valueminimize maximum value

Your job is to find out the minimal possible something which has maximal something.

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0 1 2 3 4 5 7 8 9 10 11 12 13

Example● Find Max < 60

6 13 14 25 33 43 65 66 76 78 81 98 99

Beg End

6

51

Mid

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0 1 2 3 4 5 7 8 9 10 11 12 13

Example● Find Max < 60

6 13 14 25 33 43 65 66 76 78 81 98 99

Beg End

6

51

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0 1 2 3 4 5 7 8 9 10 11 12 13

Example● Find Max < 60

6 13 14 25 33 43 65 66 78 81 98 99

Beg End

6

51

Mid

76

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0 1 2 3 4 5 7 8 9 10 11 12 13

Example● Find Max < 60

6 13 14 25 33 43 65 66 78 81 98 99

Beg End

6

51 76

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0 1 2 3 4 5 7 8 9 10 11 12 13

Example● Find Max < 60

6 13 14 25 33 43 66 78 81 98 99

Beg End

6

51 76

Mid

65

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0 1 2 3 4 5 7 8 9 10 11 12 13

Example● Find Max < 60

6 13 14 25 33 43 66 78 81 98 99

Beg

End

6

51 7665

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Practice

UVa - 11413

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Thank You for Your Listening.