1. Pseudo-code 1 Running time of algorithm is O(n)
Algorithm1 arrayMax(A, n)
Input array A of n integers
Output maximum element of A
currentMax  A[0]
for i  1 to n  1 do
if A[i]  currentMax then
currentMax  A[i]
return currentMax
A pseudo code is more structured than English prose and less detailed than a program. Moreover, it hides program design issues.

2. Pseudo-code 2 Running time of algorithm is O(n2)
Algorithm2 prefixAverages(A, n)
Input array A of n integers
Output array X of n doubles
Let X be an array of n doubles
for i  1 to n  1 do
a  0
for j  0 to i  1 do
a  a + A[j]
X[i]  a / (i+1)
return X
A pseudo code is more structured than English prose and less detailed than a program. Moreover, it hides program design issues.

3. Pseudo-code 3 Running time of algorithm is O(2n) Algorithm3 m  1
result  0
for i  1 to n do
m  m * 2
for j  1 to m do
result  result + i*m*j
return result
A pseudo code is more structured than English prose and less detailed than a program. Moreover, it hides program design issues.

4. Recursive algorithm analysis: factorial
Factorial(n)
if(n==1)
return 1
else
return Factorial(n-1)*n
1st step: come up with a recurrence equation
T(n) = running time of Factorial(n)
=> T(n) = T(n-1) + 1
2nd step: identify a base case
That is, a termination condition (n=1)
T(1) = 1 step (i.e., a constant number of steps being executed)

5. Recursive algorithm analysis: factorial (cont’d)
3rd step: expand T(n)
4th step: see the pattern

6. Binary search recursion: pseudo-code
Boolean BS(A, key, start, end)
mid = (start+end)/2
if(A[mid] == key)
return true
else
if(end <= start)
return false
if (A[mid] > key)
return BS(A, key, start, mid-1)
return BS(A, key, mid+1, end)

7. Binary search recursion: running time analysis
1st step: find recurrence equation
T(n): running time of BS for input A of size n
T(n) = T(n/2) + 1
2nd step: look at termination condition
When the search pool is reduced to one
T(1) = 1

8. Binary search recursion: running time analysis (cont’d)
3rd step: expand T(n)
4th step: pattern matching