Simple loop analysis - example 1
- What is the running time of
the following
program fragment:
for ( int i = 0; i < 10; i++ )
doPrimitive();
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Analysis:
The loop is executed 10 times for any input size
Running time = 10 doPrimitive() operations
Run time complexity = O(1) (constant time)
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Simple loop analysis - example 2
- What is the running time of
the following
program fragment:
n = input size (e.g.: # elements in an array)
for ( int i = 0; i < n; i++ )
doPrimitive();
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Analysis:
The loop is executed n times for input size n
Running time = n doPrimitive() operations
Run time complexity = O(n) (linear)
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Note:
n or
N
will
always denote the
input size in
algorithm analysis
Simple loop analysis - example 3
- What is the running time of
the following
program fragment:
int sum = 0;
for ( int i = 0; i < 5*n; i = i + 4 )
sum = sum + 1;
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Analysis:
The loop is executed (5/4)n times for input size n
Running time = (5/4)n primitive operations
Run time complexity = O(n) (linear)
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DEMO:
demo/13-analysis/Demo.java
Simple loop analysis - example 4
- What is the running time of
the following
program fragment:
int sum = 0;
for ( int i = n; i > 0; i = i - 4 )
sum = sum + 1;
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Analysis:
The loop is executed (1/4)n times for input size n
Running time = (1/4)n primitive operations
Run time complexity = O(n) (linear)
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