#OK to post homework
#Nick Belov, March 30th 2025, Assignment 18
read "C18.txt":

AveLengthSP:=proc(G,a)
    local D,sm:
    D:=Dij(G,a):
    sm := add(D) / G[1]:
    return evalf(sm):
end:

#that picks a random weigted graph according to RWG(n,p,K)
#M times, finds for each AveLengthSP(G,a) and finds the average and variance for each run.
#going to assume a is fixed to be one here
AveLengthStat := proc(n,p,K,M)
    local i, G, x, s1, s2, mu, va:
    s1 := 0:
    s2 := 0:
    for i from 1 to M do
        G := RWG(n,p,K):
        x := AveLengthSP(G,1):
        s1 := s1 + x:
        s2 := s2 + x^2:
    od:
    mu := s1 / M:
    va := s2 / M - mu^2:
    return [evalf(mu), evalf(va)]
end:

#I toned down M to 100 instead of 10000 due to compute limits:
#[2.021400000, 0.014482040]
#[2.026000000, 0.014350000]
#[2.014200000, 0.015542360]
#[2.022500000, 0.013534750]
#[2.019000000, 0.012619000]