[acm-icpc] binary search
TRANSCRIPT
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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