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COP 4530 Homework 2

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COP 4530 Homework 2
Worksheet Questions
1. If I prove that an algorithm takes O(n
2
) worst-case time, is it possible that it takes O(n) on some inputs?
2. If I prove that an algorithm takes O(n
2
) worst-case time, is it possible that it takes O(n) on all inputs?
Exercises 10.4
For the code segments in Exercises 7-12, determine which of the orders of magnitude given in this section is the
best O to use to express the worst-case computing time as a function of n.
8. // Matrix addition
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
c[i][j] = a[i][j] + b[i][j]
10. // Bubble sort
for (int i = 0; i < n – 1; i++)
{
for (int j = 0; j < n – 1; j++)
if (x[j] > x[j + 1])
{
temp = x[j];
x[j] = x[j+1];
x[j+1] = temp;
}
}
11. while (n >= 1)
n /= 2;
12. x = 1;
for (int i = 1; i <= n; i++)
{
for (int j = 1; j <= x; j++)
cout << j << endl;
x *= 2
}
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