Question

Analyze Runtime (15 points) Formally derive the run time of the each algorithm below as a function of n and determine its Big-O upper bound. You must show the derivation of the end result; if all you do is state the Big-O bound, you'll receive zero points. (a) r = 0; for i in the range [1, n] { for j in the range [i, n] for k in the range [1, j-i] r++; print (r); } (b) x = Math.pow(2, n) for (i = 1; i <=x; i = i*2) for j in range [1, i] Constant Number of Operations (c) i = n while i >= 1 for j in range [1, i] Constant Number of Operations i = i / 2

          Analyze Runtime (15 points) Formally derive the run time of the each algorithm below as
a function of n and determine its Big-O upper bound. You must show the derivation of the
end result; if all you do is state the Big-O bound, you'll receive zero points.
(a) r = 0;
for i in the range [1, n] {
for j in the range [i, n]
for k in the range [1, j-i]
r++;
print (r);
}
(b) x = Math.pow(2, n)
for (i = 1; i <=x; i = i*2)
for j in range [1, i]
Constant Number of Operations
(c)
i = n
while i >= 1
for j in range [1, i]
Constant Number of Operations
i = i / 2

Analyze Runtime (15 points) Formally derive the run time of the each algorithm below as
a function of n and determine its Big-O upper bound. You must show the derivation of the
end result; if all you do is state the Big-O bound, you'll receive zero points.
(a) r = 0;
for i in the range [1, n]
for j in the range [i, n]
for k in the range [1, j-i]
r++;
print (r);

(b) x = Math.pow(2, n)
for (i = 1; i <=x; i = i*2)
for j in range [1, i]
Constant Number of Operations
(c)
i = n
while i >= 1
for j in range [1, i]
Constant Number of Operations
i = i / 2

Added by Michelle F.

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