# OK to post homework
# James Betti, 2 Mar 2025, Assignment 10

SimulateNAND := proc(n,k,K) local total,_,P;
    total := 0;
    for _ to K do
        P := RSLP(n,k);
        total := total + nops(EvalSP(P,n));
    od;
    total/K;
end:

SimulateNAND(10,5,1000);                # 696.576
SimulateNAND(10,10,1000);               # 661.712
SimulateNAND(10,20,1000);               # 645.716
SimulateNAND(10,50,1000);               # 635.187

Monotone := proc(n,k,p) local ra,P,i,i1,j1,gate;
    ra := rand(1..denom(p));
    P := [seq(i,i=1..n)];
    for i from n+1 to k+n do
        i1 := rand(1..nops(P)-1)();
        j1 := rand(i1+1..nops(P))();
        gate := OR;
        if ra() <= numer(p) then
            gate := AND;
        fi;
        P := [op(P),[i1,j1,gate]];
    od;
    P;
end:

# Redefine `EvalSP1` to use OR/AND as needed for `SimulateMonotone`.
EvalSP1 := proc(P,IN) local P1,n,i,i1,j1;
    P1 := IN;
    n := nops(IN);
    for i from n+1 to nops(P) do
        i1 := P[i][1];
        j1 := P[i][2];
        P1 := [op(P1),P[i][3](P1[i1],P1[j1])];
    od;
    P1[-1];
end:

SimulateMonotone := proc(n,k,p,K) local total,_,P;
    total := 0;
    for _ to K do
        P := Monotone(n,k,p);
        total := total + nops(EvalSP(P,n));
    od;
    total/K;
end:

for k in {5,10,20,50} do
    for p in {1/2,3/4,1} do
        printf("SimulateMonotone(10,%d,%d/%d,1000):",k,numer(p),denom(p));
        print(evalf(SimulateMonotone(10,k,p,1000)));
    od;
od;

# ====================RESULTS====================
# SimulateMonotone(10, 5,1/1,1000):    166.0800000
# SimulateMonotone(10, 5,1/2,1000):    506.8160000
# SimulateMonotone(10, 5,3/4,1000):    342.6240000
# SimulateMonotone(10,10,1/1,1000):    114.5720000
# SimulateMonotone(10,10,1/2,1000):    513.8160000
# SimulateMonotone(10,10,3/4,1000):    288.5680000
# SimulateMonotone(10,20,1/1,1000):    67.59000000
# SimulateMonotone(10,20,1/2,1000):    517.2260000
# SimulateMonotone(10,20,3/4,1000):    246.7590000
# SimulateMonotone(10,50,1/1,1000):    24.75800000
# SimulateMonotone(10,50,1/2,1000):    497.4980000
# SimulateMonotone(10,50,3/4,1000):    173.2520000