# cogirth-packing gap of projections of graphic matroids

from sage.all import *
from sage.matroids.all import *
from sage.graphs.all import *
import gurobipy as gp
from gurobipy import GRB

env = gp.Env(empty=True)
env.setParam("OutputFlag",0)
env.start()


def cogirthip(bases, integral=true):
    model = gp.Model("mip1",env=env)
    # model.Params.LogToConsole = 0
    groundset=frozenset()
    for B in bases: groundset=groundset|frozenset(B)
    x = dict()
    if integral:
        for e in groundset: x[e]=model.addVar(vtype=GRB.BINARY)
    else:
        for e in groundset: x[e]=model.addVar(vtype=GRB.CONTINUOUS,lb=0)
    model.setObjective(gp.quicksum([x[e] for e in groundset]), GRB.MINIMIZE)
    for B in bases:
        model.addConstr(gp.quicksum([x[e] for e in B])>=1)
    model.optimize()
    return model.ObjVal


cnt=0   # actual number of instances tested
f = lambda g: g.is_connected()
for n in range(4,20):
    for g in filter(f, graphs(n)):
        A=g.incidence_matrix()
        n,m = A.dimensions()
        # enumerate all vectors in F_2^n with even number of 1s
        V = VectorSpace(GF(2), n)
        for v in filter(lambda v: v.hamming_weight() % 2 == 0 and v!=0, V):
            v_col=matrix(v).transpose()
            A_t=A.augment(v_col)
            # print(A_t)
            M=Matroid(matrix=A_t,field=GF(2))/m     #contract the last element
            # print(M)
            bases=M.bases()
            strength=cogirthip(bases,integral=false)
            cogirth =cogirthip(bases,integral=true)
            gap = cogirth/strength
            if gap > 2.01:
                print(f"bad example! gap={gap}")
                with open("projection.out", "a") as f:
                    f.write(str(gap)+"\n"+str(A_t)+"\n")
            else:
                print(f"n={n},m={m},gap={gap}")