Asymptotic Complexity

• How many iterations does binary search take?

N+1 1 2 4 8 16 32 ...

#iterations 0 1 2 3 4 5 ... log2(N+1)

• In contrast, how many iterations does sequential search take in the worst case?

/* Given A[0..N] sorted in non-decreasing order, return the subscript of an occurrence of val in A (if val occurs in A) or N+1 otherwise. */

int find(int[] A, int N, int val)

{

int k = 0;

while (k <= N && val != A[k]) k++;

return k;

}

N+1 1 2 4 8 16 32 ...

#iterations 1 2 4 8 16 32 ... N+1

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