1. Running Time Exercises

2. k=1; for (i = 1; i < n; i++) k++;

3. if (x < 3) { k++; } else { k = 1; for (i = 1; i < n; i++) }

4. k = 1; for (i = 1; i < n; i++) for (j = 1; j < m; j++) k++;

5. for (i = 1; i < n * n; i++) k++;

6. k = 1; for (i = 1; i < n; i++) for (j = i + 1; j < n; j++) k++;

7. i = 0; while (i < n * n *n) i = i + (2 * n);

8. i = 1; while (i < n * n) i = i + (n / 4);

9. for (i = 1; i < n; i = 3 * i) { j = 1; while (j < n) j = j + 1; }

10. for (i = 1; i < n; i++) { j = 1; while (j < 10000) j = j + 1; }

11. int. arr = new int[n]; int. i,
int *arr = new int[n]; int *i,*j; for (i = arr; i < arr+n; i++) { j = i; while (j != arr) { *j = *i; j--; }

12. Compare Which one should be chosen? When? for (i = 0; i < n; i++) {
j = 0;
while (j < 10000)
j = j + 1; }
for (i = 0; i < n; i++) { j = 0; while (j < n) j = j + 1; }
Which one should be chosen? When?

13. Compare for (i = 0; i < n; i++) { j = 0; while (j < 10000)
j = j + 1; }
for (i = 0; i < n; i++) { j = 0; while (j < n) j = j + 1; } n
T1(n) - Θ(n)
T2(n) - Θ(n^2) 1
~ 10^4
~ 1
10^2
~ 10^6
~ 100*100=10^4
10^4
~ 10^8
~ 10^4*10^4=10^8
10^6
~ 10^10
~ 10^6*10^6=10^12
10^8
~ 10^12
~ 10^8*10^8=10^16

14. CS202 - Fundamentals of Computer Science II
More Problems
5/11/2019
CS202 - Fundamentals of Computer Science II

15. Recursive Algorithms

16. Factorial int factorial (int n) { if (n == 0) return 1;
return n * factorial(n-1); }
T(0) = Θ(1)
T(n) = T(n-1) + Θ(1)

17. Hanoi T(0) = Θ(1) T(n) = 2 T(n-1) + Θ(1)
void hanoi (int n, char source, char dest, char spare) {
if (n > 0) {
hanoi(n-1, source, spare, dest);
hanoi(n-1, spare, dest, source); }
T(0) = Θ(1)
T(n) = 2 T(n-1) + Θ(1)

18. Binary Search Best Case ? T(1) = Θ(1) T(n) = T(n/2) + Θ(1)
int binarySearch (int A[], int x, int low, int high) {
if (low > high)
return -1;
int mid = (low + high) / 2;
if (A[mid] == x) {
return mid;
if (A[mid] > x)
return binarySearch(A, x, low, mid-1);
return binarySearch(A, x, mid+1, high); }
Best Case ?
T(1) = Θ(1)
T(n) = T(n/2) + Θ(1)

19. Foo T(1) = Θ(1) T(n) = 2T(n/2) + Θ(1) void foo (int n) {
if (n > 1) {
foo(n/2); }
T(1) = Θ(1)
T(n) = 2T(n/2) + Θ(1)

20. Merge Sort
T(1) = Θ(1)
T(n) = 2T(n/2) + Θ(n)