COSC 1P03 Data Structures and Abstraction 20.1
COSC 1P03 Data Structures and Abstraction 20.1
COSC 1P03 Data Structures and Abstraction 20.1
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<strong>COSC</strong> <strong>1P03</strong><br />
<strong>Data</strong> <strong>Structures</strong> <strong>and</strong> <strong>Abstraction</strong><br />
<strong>COSC</strong> <strong>1P03</strong><br />
Binary Search<br />
<br />
<br />
<br />
<br />
<br />
<br />
Large collections<br />
e.g. telephone book<br />
Requires - sorted by key<br />
Principle<br />
distribution of keys?<br />
probe at midpoint<br />
Algorithm<br />
probing<br />
bounds<br />
termination<br />
Analysis<br />
worst case<br />
each probe eliminates 1/2 remaining entries<br />
O(log n)<br />
E.g. view students<br />
<strong>Data</strong> <strong>Structures</strong> <strong>and</strong> <strong>Abstraction</strong> 20.7<br />
start with bounds being first <strong>and</strong> last items;<br />
while ( true ) {<br />
if ( bounds empty ) { not found; break; };<br />
access middle item between bounds<br />
if ( search key matches key on item ) { found; break; };<br />
if ( search key greater than key on item ) {<br />
set lower bound to next item<br />
}<br />
else {<br />
set upper bound to prior item<br />
};<br />
};<br />
Figure 20.4 Binary search algorithm<br />
lower<br />
bound<br />
new upper<br />
bound<br />
upper<br />
bound<br />
probe<br />
Figure 20.5 Probe in binary search<br />
20.3
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