#!/usr/local/bin/maple
# -*- maplev -*-

# Nathaniel Shar
# HW 27
# Experimental Mathematics

# It is okay to link to this assignment on the course webpage.

#############
# Problem 1 #
#############

with(Optimization):

Waldorp := proc(J, R, DelayJ, u, S, Sspec) local y, A, H, i, j, r, s, solns:
    A := [seq([seq(`if`(incident(j,r), 1, 0), r=R)], j=J)]:
    H := [seq([seq(`if`(s[1]=r[1] and s[2]=r[-1], 1, 0), r=R)], s=S)]:
    print(nops(J)):
    solns :=  Minimize(add(int(DelayJ[j], u=0..y[j]), j=1..nops(J)),
                       {seq(add(H[i][j]*x[j], j=1..nops(R))=Sspec[i], i=1..nops(Sspec)),
                        seq(add(A[i][j]*x[j], j=1..nops(R))=y[i], i=1..nops(J)),
                        seq(x[j] >= 0, j=1..nops(R))}
                      ):
    return
    subs(solns[2], [seq(x[j], j=1..nops(R))]), #subs(solns[2], [seq(subs(u=y[j], DelayJ[j]), j=1..nops(J))]),
    subs(solns[2], [seq(add(A[j][i]*subs(u=y[j], DelayJ[j]), j=1..nops(J)), i=1..nops(R))]):
end:

incident := proc(j, r) local i:
    for i from 1 to nops(r)-1 do:
        if j[1] = r[i] and j[2] = r[i+1] then:
            return true:
        fi:
    od:
    return false:
end:

#############
# Problem 2 #
#############

# Waldorp([[1,2],[2,4],[1,3],[3,4]],
# [[1,2,4],[1,3,4]],[10*u,u+50,u+50,10*u],u,[[1,4]],[6]);

# gives [3,3], [83,83]


# and


# Waldorp([[1,2],[2,4],[1,3],[3,4],[2,3]],
# [[1,2,4],[1,3,4],[1,2,3,4]],[10*u,u+50,u+50,10*u,u+10],u,[[1,4]],[6]);


# gives [2,2,2], [92,92,92].

# This corresponds to the claims in the article.