"""Lemma 22.4 (interleaving two chains): simulate the sequence of exchanges and check every hypothesis."""
import sys; import os; sys.path.insert(0,os.path.dirname(os.path.abspath(__file__)))
from exchange_checker import State
def run(r,d):
    b=r-d; N=r+b
    A=lambda i:i-1; B=lambda j:r+j-1
    def rt(a,c):
        v=[0]*N; v[a]=1; v[c]=-1; return tuple(v)
    is_root=lambda v: sorted(v)==[-1]+[0]*(N-2)+[1]
    S=set(); chi=set()
    for i in range(1,r+1):
        for k in range(i+1,r+1): S.add(rt(A(i),A(k)))
    for j in range(1,b+1):
        for k in range(j+1,b+1): S.add(rt(B(j),B(k)))
    for i in range(1,r):
        for j in range(1,b+1): S.add(rt(A(i),B(j)))
    for i in range(1,r): chi.add(rt(A(i),A(i+1)))
    for j in range(1,b): chi.add(rt(B(j),B(j+1)))
    st=State(S,chi,is_root)
    for i in range(r-1,0,-1):
        for j in range(1,i-d+1):
            if j>b: st.log.append('j out of range')
            st.exchange(rt(A(i),B(j)),rt(B(j),A(i+1)),f'({i},{j})')
    cross=set(v for v in st.S if any(v[A(i)] for i in range(1,r+1)) and any(v[B(j)] for j in range(1,b+1)))
    exp=set()
    for i in range(1,r):
        for j in range(1,b+1):
            if j>i-d: exp.add(rt(A(i),B(j)))
    for i in range(2,r+1):
        for j in range(1,b+1):
            if j<i-d: exp.add(rt(B(j),A(i)))
    print(f'r={r} d={d}: problems={len(st.log)} final cross roots as stated={cross==exp}', st.log[:3])
for r in range(2,8):
    for d in (-1,0,1):
        if r-d>=1: run(r,d)