A C++ program that implements these 3 algorithms and times them for various values of n.

Algorithm 1

sum=0

for i = 1 to n

sum= sum + i

Algorithm 2

sum=0

for i = 1 to n

{ for j = 1 to i sum= sum + 1 }

Algorithm 3

sum = n * (n+1)/2

you will need an implementation of the ADT bag whose method remove, removed all random entry instead of a specific one.