"""CPLEX ILP solver."""


# Imports
from itertools import chain
from src.ilp.solution import Solution
import cplex
import math
import os


def _formulate_as_oct(G, mipgap=0, threads=1, timelimit=None, memlimit=None):
    """Construct an OCT problem with CPLEX.

    Paramters
    ---------
    G : Networkx Graph
        Graph to solve OCT on.
    mipgap : float
        Allowed tolerance.
    threads : int
        Number of threads to use.
    timelimit : float
        Time limit for computation, in seconds.
    memlimit : int
        Memory limit in Mb.
    """

    # Calculate number of nodes
    n = len(G.nodes())

    # Create a new cplex problem and set parameters
    prob = cplex.Cplex()
    prob.parameters.mip.tolerances.mipgap.set(mipgap)
    prob.parameters.emphasis.numerical.set(True)
    prob.parameters.parallel.set(
        prob.parameters.parallel.values.opportunistic
    )
    prob.parameters.threads.set(threads)
    if timelimit is not None:
        prob.parameters.timelimit.set(timelimit)
    if memlimit is not None:
        prob.parameters.workmem.set(memlimit)

    # Throw away default cplex output
    prob.set_results_stream(os.devnull)

    # Construct node variables
    node_vars = {
        node: ('c{}'.format(node), 's{}'.format(node))
        for node in G.nodes()
    }
    node_vars_flattened = list(chain.from_iterable(node_vars.values()))

    # Add vertices as variables to the LP
    prob.variables.add(
        names=node_vars_flattened,
        types=([prob.variables.type.integer] * len(node_vars_flattened))
    )

    # Add constraints for edges
    constraints = list(chain.from_iterable([
        (
            cplex.SparsePair(
                ind=(
                    node_vars[e[0]][1],
                    node_vars[e[1]][1],
                    node_vars[e[0]][0],
                    node_vars[e[1]][0]
                ),
                val=[1, 1, 1, 1]
            ),
            cplex.SparsePair(
                ind=(
                    node_vars[e[0]][1],
                    node_vars[e[1]][1],
                    node_vars[e[0]][0],
                    node_vars[e[1]][0]
                ),
                val=[1, 1, -1, -1]
            )
        )
        for e in G.edges()
    ]))

    num_edges = len(G.edges())
    prob.linear_constraints.add(
        lin_expr=constraints,
        senses=['G', 'L'] * num_edges,
        rhs=[1, 1] * num_edges
    )

    # Set LP objective
    prob.objective.set_sense(prob.objective.sense.minimize)
    prob.objective.set_linear(list(zip(
        [node_vars[node][0] for node in G.nodes()],
        [1] * n)
    ))

    # Return
    return prob, node_vars_flattened


def _formulate_as_vc(G, mipgap=0, threads=1, timelimit=None, memlimit=None):
    """Construct a Vertex Cover problem with CPLEX.

    Paramters
    ---------
    G : Networkx Graph
        Graph to solve Vertex Cover on.
    mipgap : float
        Allowed tolerance.
    threads : int
        Number of threads to use.
    timelimit : float
        Time limit for computation, in seconds.
    memlimit : int
        Memory limit in Mb.
    """

    # Calculate number of nodes
    n = len(G.nodes())

    # Create a new cplex problem and set parameters
    prob = cplex.Cplex()
    prob.parameters.mip.tolerances.mipgap.set(mipgap)
    prob.parameters.emphasis.numerical.set(True)
    prob.parameters.parallel.set(
        prob.parameters.parallel.values.opportunistic
    )
    prob.parameters.threads.set(threads)
    if timelimit is not None:
        prob.parameters.timelimit.set(timelimit)
    if memlimit is not None:
        prob.parameters.workmem.set(memlimit)

    # Throw away default cplex output
    prob.set_results_stream(os.devnull)

    # Construct node variables
    node_vars = {
        node: 'c{}'.format(node)
        for node in G.nodes()
    }
    node_vars_values = list(node_vars.values())

    # Add vertices as variables to the LP
    prob.variables.add(
        names=node_vars_values,
        types=([prob.variables.type.integer] * n)
    )

    # Add constraints for edges
    constraints = [
        cplex.SparsePair(
            ind=(node_vars[e[0]], node_vars[e[1]]),
            val=[1, 1]
        )
        for e in G.edges()
    ]
    num_constraints = len(constraints)
    prob.linear_constraints.add(
        lin_expr=constraints,
        senses=['G'] * num_constraints,
        rhs=[1] * num_constraints
    )

    # Set LP objective
    prob.objective.set_sense(prob.objective.sense.minimize)
    prob.objective.set_linear(list(zip(node_vars_values, [1] * n)))

    # Return
    return prob, node_vars_values


def solve_with_cplex(G, formulation='OCT', mipgap=0,
                     threads=1, timelimit=None, memlimit=None):
    """Solve an ILP problem instance with CPLEX.

    Parameters
    ----------
    G : Networkx Graph
        Graph for which the problem will be computed
    formulation : string
        How the problem should be solved. Either OCT or VC.
    mipgap : float
        Allowed gap in tolerance
    threads : int
        Number of threads to use
    timelimit : float
        Time limit for computation, in seconds.
    memlimit : int
        Memory limit in Mb.
    """

    # Typecast numeric types for safety
    mipgap = float(mipgap)
    threads = int(threads)
    if timelimit is not None:
        timelimit = float(timelimit)
    if memlimit is not None:
        memlimit = int(memlimit)

    # Get problem formulation
    if formulation == 'OCT':
        problem, node_vars = _formulate_as_oct(
            G, mipgap=mipgap, threads=threads,
            timelimit=timelimit, memlimit=memlimit
        )
    elif formulation == 'VC':
        problem, node_vars = _formulate_as_vc(
            G, mipgap=mipgap, threads=threads,
            timelimit=timelimit, memlimit=memlimit
        )
    else:
        raise Exception('Unknown Formulation')

    # Optimize
    start = problem.get_time()
    problem.solve()
    end = problem.get_time()

    # Calculate total time
    time = round(end - start, 1)

    # Construct certificate from solution values
    solution = problem.solution.get_values(node_vars)
    certificate = [
        node_vars[i][1:]
        for i in range(len(solution))
        if math.isclose(solution[i], 1, abs_tol=1e-10)
        and node_vars[i][0] == 'c'
    ]

    # Record cuts
    cuts = [
        (
            problem.solution.MIP.cut_type[i],
            problem.solution.MIP.get_num_cuts(i)
        )
        for i in problem.solution.MIP.cut_type
    ]

    # Return solution
    return Solution(
        G=G,
        threads=threads,
        mipgap=mipgap,
        certificate=certificate,
        time=time,
        cuts=cuts
    )

"""CPLEX ILP solver."""


# Imports
from itertools import chain
from src.ilp.solution import Solution
import cplex
import math
import os


def _formulate_as_oct(G, mipgap=0, threads=1, timelimit=None, memlimit=None):
    """Construct an OCT problem with CPLEX.

    Paramters
    ---------
    G : Networkx Graph
        Graph to solve OCT on.
    mipgap : float
        Allowed tolerance.
    threads : int
        Number of threads to use.
    timelimit : float
        Time limit for computation, in seconds.
    memlimit : int
        Memory limit in Mb.
    """

    # Calculate number of nodes
    n = len(G.nodes())

    # Create a new cplex problem and set parameters
    prob = cplex.Cplex()
    prob.parameters.mip.tolerances.mipgap.set(mipgap)
    prob.parameters.emphasis.numerical.set(True)
    prob.parameters.parallel.set(
        prob.parameters.parallel.values.opportunistic
    )
    prob.parameters.threads.set(threads)
    if timelimit is not None:
        prob.parameters.timelimit.set(timelimit)
    if memlimit is not None:
        prob.parameters.workmem.set(memlimit)

    # Throw away default cplex output
    prob.set_results_stream(os.devnull)

    # Construct node variables
    node_vars = {
        node: ('c{}'.format(node), 's{}'.format(node))
        for node in G.nodes()
    }
    node_vars_flattened = list(chain.from_iterable(node_vars.values()))

    # Add vertices as variables to the LP
    prob.variables.add(
        names=node_vars_flattened,
        types=([prob.variables.type.integer] * len(node_vars_flattened))
    )

    # Add constraints for edges
    constraints = list(chain.from_iterable([
        (
            cplex.SparsePair(
                ind=(
                    node_vars[e[0]][1],
                    node_vars[e[1]][1],
                    node_vars[e[0]][0],
                    node_vars[e[1]][0]
                ),
                val=[1, 1, 1, 1]
            ),
            cplex.SparsePair(
                ind=(
                    node_vars[e[0]][1],
                    node_vars[e[1]][1],
                    node_vars[e[0]][0],
                    node_vars[e[1]][0]
                ),
                val=[1, 1, -1, -1]
            )
        )
        for e in G.edges()
    ]))

    num_edges = len(G.edges())
    prob.linear_constraints.add(
        lin_expr=constraints,
        senses=['G', 'L'] * num_edges,
        rhs=[1, 1] * num_edges
    )

    # Set LP objective
    prob.objective.set_sense(prob.objective.sense.minimize)
    prob.objective.set_linear(list(zip(
        [node_vars[node][0] for node in G.nodes()],
        [1] * n)
    ))

    # Return
    return prob, node_vars_flattened


def _formulate_as_vc(G, mipgap=0, threads=1, timelimit=None, memlimit=None):
    """Construct a Vertex Cover problem with CPLEX.

    Paramters
    ---------
    G : Networkx Graph
        Graph to solve Vertex Cover on.
    mipgap : float
        Allowed tolerance.
    threads : int
        Number of threads to use.
    timelimit : float
        Time limit for computation, in seconds.
    memlimit : int
        Memory limit in Mb.
    """

    # Calculate number of nodes
    n = len(G.nodes())

    # Create a new cplex problem and set parameters
    prob = cplex.Cplex()
    prob.parameters.mip.tolerances.mipgap.set(mipgap)
    prob.parameters.emphasis.numerical.set(True)
    prob.parameters.parallel.set(
        prob.parameters.parallel.values.opportunistic
    )
    prob.parameters.threads.set(threads)
    if timelimit is not None:
        prob.parameters.timelimit.set(timelimit)
    if memlimit is not None:
        prob.parameters.workmem.set(memlimit)

    # Throw away default cplex output
    prob.set_results_stream(os.devnull)

    # Construct node variables
    node_vars = {
        node: 'c{}'.format(node)
        for node in G.nodes()
    }
    node_vars_values = list(node_vars.values())

    # Add vertices as variables to the LP
    prob.variables.add(
        names=node_vars_values,
        types=([prob.variables.type.integer] * n)
    )

    # Add constraints for edges
    constraints = [
        cplex.SparsePair(
            ind=(node_vars[e[0]], node_vars[e[1]]),
            val=[1, 1]
        )
        for e in G.edges()
    ]
    num_constraints = len(constraints)
    prob.linear_constraints.add(
        lin_expr=constraints,
        senses=['G'] * num_constraints,
        rhs=[1] * num_constraints
    )

    # Set LP objective
    prob.objective.set_sense(prob.objective.sense.minimize)
    prob.objective.set_linear(list(zip(node_vars_values, [1] * n)))

    # Return
    return prob, node_vars_values


def solve_with_cplex(G, formulation='OCT', mipgap=0,
                     threads=1, timelimit=None, memlimit=None):
    """Solve an ILP problem instance with CPLEX.

    Parameters
    ----------
    G : Networkx Graph
        Graph for which the problem will be computed
    formulation : string
        How the problem should be solved. Either OCT or VC.
    mipgap : float
        Allowed gap in tolerance
    threads : int
        Number of threads to use
    timelimit : float
        Time limit for computation, in seconds.
    memlimit : int
        Memory limit in Mb.
    """

    # Typecast numeric types for safety
    mipgap = float(mipgap)
    threads = int(threads)
    if timelimit is not None:
        timelimit = float(timelimit)
    if memlimit is not None:
        memlimit = int(memlimit)

    # Get problem formulation
    if formulation == 'OCT':
        problem, node_vars = _formulate_as_oct(
            G, mipgap=mipgap, threads=threads,
            timelimit=timelimit, memlimit=memlimit
        )
    elif formulation == 'VC':
        problem, node_vars = _formulate_as_vc(
            G, mipgap=mipgap, threads=threads,
            timelimit=timelimit, memlimit=memlimit
        )
    else:
        raise Exception('Unknown Formulation')

    # Optimize
    start = problem.get_time()
    problem.solve()
    end = problem.get_time()

    # Calculate total time
    time = round(end - start, 1)

    # Construct certificate from solution values
    solution = problem.solution.get_values(node_vars)
    certificate = [
        node_vars[i][1:]
        for i in range(len(solution))
        if math.isclose(solution[i], 1, abs_tol=1e-10)
        and node_vars[i][0] == 'c'
    ]

    # Record cuts
    cuts = [
        (
            problem.solution.MIP.cut_type[i],
            problem.solution.MIP.get_num_cuts(i)
        )
        for i in problem.solution.MIP.cut_type
    ]

    # Return solution
    return Solution(
        G=G,
        threads=threads,
        mipgap=mipgap,
        certificate=certificate,
        time=time,
        cuts=cuts
    )

CPLEX ILP solver. # Imports Construct an OCT problem with CPLEX.      Paramters     ---------     G : Networkx Graph         Graph to solve OCT on.     mipgap : float         Allowed tolerance.     threads : int         Number of threads to use.     timelimit : float         Time limit for computation, in seconds.     memlimit : int         Memory limit in Mb. # Calculate number of nodes # Create a new cplex problem and set parameters # Throw away default cplex output # Construct node variables # Add vertices as variables to the LP # Add constraints for edges # Set LP objective # Return Construct a Vertex Cover problem with CPLEX.      Paramters     ---------     G : Networkx Graph         Graph to solve Vertex Cover on.     mipgap : float         Allowed tolerance.     threads : int         Number of threads to use.     timelimit : float         Time limit for computation, in seconds.     memlimit : int         Memory limit in Mb. # Calculate number of nodes # Create a new cplex problem and set parameters # Throw away default cplex output # Construct node variables # Add vertices as variables to the LP # Add constraints for edges # Set LP objective # Return Solve an ILP problem instance with CPLEX.      Parameters     ----------     G : Networkx Graph         Graph for which the problem will be computed     formulation : string         How the problem should be solved. Either OCT or VC.     mipgap : float         Allowed gap in tolerance     threads : int         Number of threads to use     timelimit : float         Time limit for computation, in seconds.     memlimit : int         Memory limit in Mb. # Typecast numeric types for safety # Get problem formulation # Optimize # Calculate total time # Construct certificate from solution values # Record cuts # Return solution