# OK to post homework
# Vikrant, Feb 27 2022, Assignment 10

# ================================================================================
# 0. Code that has been given.
# ================================================================================

read("C10.txt"):

# ================================================================================
# 1. Count instabilities.
# ================================================================================

CountInstabilities:=
    proc(M,W,pi)
        local i1,i2:
        add([seq(seq(`if`(IsStable1(M,W,pi,i1,i2),0,1),i1=1..nops(pi)),i2=1..nops(pi))]):
    end:

# ================================================================================
# 2. Stabilities generating function estimator.
# ================================================================================

GFStab:=
    proc(n,K,x)
        local i:
        add([seq(x^(CountInstabilities(RT(n),randperm(n))),i=1..K)]):
    end:

StabStat:=
    proc(n,K)
        local x:
        local d:= diff(GFStab(n,K,x),x)/K:
        evalf(subs(x=1,[d,diff(d,x)+d-d^2])):
    end:

(*

randomize(1305162298):
for n from 1 to 100 do
    for i from 1 to 5 do
        print(StabStat(n,1000)): 
    od:
    print():
od:

*)