import pulp

adj = {
    0: [5],
    1: [2,4,5],
    2: [1,3,4],
    3: [2,4,7,8,10],
    4: [1,2,3,5,6,7],
    5: [0,1,4,6,12],
    6: [4,5,7,11,12],
    7: [3,4,6,8,9,11],
    8: [3,7,9,10,11,13],
    9: [7,8,11],
    10: [3,8,13,14],
    11: [6,7,8,9,12,13],
    12: [5,6,11,13,15],
    13: [8,10,11,12,14,15],
    14: [10,13,15],
    15: [12,13,14]
}

n = 16
A = [[0 for _ in range(n)] for _ in range(n)]

# A[click][affected]
for click in range(n):
    A[click][click] = 2
    for affected in adj[click]:
        A[click][affected] = 1

prob = pulp.LpProblem("Map_Burning_Optimal", pulp.LpMinimize)

x = [pulp.LpVariable(f"x{i+1}", lowBound=0, cat="Integer") for i in range(n)]
b = [pulp.LpVariable(f"b{i+1}", cat="Binary") for i in range(n)]

prob += pulp.lpSum(x)

# Pole startuje od -1, a końcowo ma być 3 albo 4
# czyli suma wpływów ma dać 4 albo 5
for j in range(n):
    lhs = pulp.lpSum(A[k][j] * x[k] for k in range(n))
    prob += lhs == 4 + b[j]

prob.solve(pulp.PULP_CBC_CMD(msg=0))

status = pulp.LpStatus[prob.status]
objective = pulp.value(prob.objective)
solution_x = [int(pulp.value(var)) for var in x]
solution_v = [
    -1 + sum(A[k][j] * solution_x[k] for k in range(n))
    for j in range(n)
]

print(f"Status: {status}")
print(f"Minimal total clicks: {objective}")
print("Clicks per pole (x1 to x16):", solution_x)
print("Final burns per pole (v1 to v16):", solution_v)