Question

Calculate the complexities of the following pseudocodes and report your findings using Big- O notation (O(n)). Explain and show your work. Pseudocode I Method sum_pairs(list) for i from 0 to length(list)-2 for j from i+1 to length(list)-1 print list[i] + list[j] end end Pseudocode II Pseudocode III MERGE (A, p,q,r) 1 $n_1 = q - p + 1$ 2 $n_2 = r - q$ 3 let L[1..$n_1$ + 1] and R[1.. $n_2$ + 1] be new arrays 4 for i = 1 to $n_1$ 5 $L[i] = A[p + i - 1]$ 6 for j = 1 to $n_2$ 7 $R[j] = A[q + j]$ 8 $L[n_1 + 1] = \infty$ 9 $R[n_2 + 1] = \infty$ 10 i = 1 11 j = 1 12 for k = p to r 13 if $L[i] \le R[j]$ 14 $A[k] = L[i]$ 15 i = i + 1 16 else $A[k] = R[j]$ 17 j = j + 1 FOR iPass = 1 to Length(ArrayToSort) - 1 FOR i = 0 to Length(ArrayToSort) - 1 - iPass IF ArrayToSort(i) > ArrayToSort(i + 1) THEN Temp = ArrayToSort(i) ArrayToSort(i) = ArrayToSort(i + 1) ArrayToSort(i + 1) = Temp END IF NEXT i NEXT iPass

          Calculate the complexities of the following pseudocodes and report your findings using Big-
O notation (O(n)). Explain and show your work.
Pseudocode I
Method sum_pairs(list)
for i from 0 to length(list)-2
for j from i+1 to length(list)-1
print list[i] + list[j]
end
end
Pseudocode II
Pseudocode III
MERGE (A, p,q,r)
1 $n_1 = q - p + 1$
2 $n_2 = r - q$
3 let L[1..$n_1$ + 1] and R[1.. $n_2$ + 1] be new arrays
4
for i = 1 to $n_1$
5	$L[i] = A[p + i - 1]$
6 for j = 1 to $n_2$
7	$R[j] = A[q + j]$
8 $L[n_1 + 1] = \infty$
9 $R[n_2 + 1] = \infty$
10 i = 1
11 j = 1
12
for k = p to r
13	if $L[i] \le R[j]$
14		$A[k] = L[i]$
15		i = i + 1
16	else $A[k] = R[j]$
17		j = j + 1
FOR iPass = 1 to Length(ArrayToSort) - 1
FOR i = 0 to Length(ArrayToSort) - 1 - iPass
IF ArrayToSort(i) > ArrayToSort(i + 1) THEN
Temp = ArrayToSort(i)
ArrayToSort(i) = ArrayToSort(i + 1)
ArrayToSort(i + 1) = Temp
END IF
NEXT i
NEXT iPass

Calculate the complexities of the following pseudocodes and report your findings using Big-
O notation (O(n)). Explain and show your work.
Pseudocode I
Method sumpairs(list)
for i from 0 to length(list)-2
for j from i+1 to length(list)-1
print list[i] + list[j]
end
end
Pseudocode II
Pseudocode III
MERGE (A, p,q,r)
1 n1 = q - p + 1
2 n2 = r - q
3 let L[1..n1 + 1] and R[1.. n2 + 1] be new arrays
4
for i = 1 to n1
5 L[i] = A[p + i - 1]
6 for j = 1 to n2
7 R[j] = A[q + j]
8 L[n1 + 1] = ∞
9 R[n2 + 1] = ∞
10 i = 1
11 j = 1
12
for k = p to r
13 if L[i] ≤ R[j]
14 A[k] = L[i]
15 i = i + 1
16 else A[k] = R[j]
17 j = j + 1
FOR iPass = 1 to Length(ArrayToSort) - 1
FOR i = 0 to Length(ArrayToSort) - 1 - iPass
IF ArrayToSort(i) > ArrayToSort(i + 1) THEN
Temp = ArrayToSort(i)
ArrayToSort(i) = ArrayToSort(i + 1)
ArrayToSort(i + 1) = Temp
END IF
NEXT i
NEXT iPass

Added by Susana P.

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