#!/usr/bin/env python3

import numpy as np
import random
from . import kSAT
import math

def generateRandomKSAT(numberOfClauses,
                       numberOfVariables,
                       numberOfVariablesPerClause):
    
    instance = kSAT.kSAT()
    
    clauses = [[] for i in range(numberOfClauses)]
    
    #make sure every variable is bound to at least one clause
    for varIndex in range(numberOfVariables):
        
        clauseIndex = random.choice(range(numberOfClauses))
        
        while (len(clauses[clauseIndex]) >= numberOfVariablesPerClause or
               varIndex + 1 in clauses[clauseIndex]):
            clauseIndex = random.choice(range(numberOfClauses))
        
        clauses[clauseIndex].append(varIndex + 1)
    
    #fill in the missing bindings
    for clauseIndex, clause in enumerate(clauses):
        tmpClause = []
        
        clauseIsUnique = False
        while not clauseIsUnique:
        
            tmpClause = clause.copy()
        
            numRemainingBindings = numberOfVariablesPerClause - len(tmpClause)
            variablesNotYetInClause = __getVariablesNotYetInClause(tmpClause,
                                                                   numberOfVariables)
        
            remainingBindings = random.sample(variablesNotYetInClause,
                                              numRemainingBindings)
        
            tmpClause += remainingBindings
        
            for i in range(len(tmpClause)):
                tmpClause[i] *= random.choice([-1, 1])
        
            tmpClause = list(np.sort(tmpClause))
            
            if tmpClause not in clauses:
                clauseIsUnique = True
                
        clauses[clauseIndex] = tmpClause
        
        instance.addClause(tmpClause)
                                        
    return instance


def __getVariablesNotYetInClause(clause, numberOfTotalVars):
    missingVariables = []
    
    prevVar = 1;
    for currVar in clause:
        missingVariables += list(range(prevVar, currVar))
        
        prevVar = currVar + 1
        
    missingVariables += list(range(prevVar, numberOfTotalVars + 1))
    
    return missingVariables

def number_of_possible_clauses(number_of_variables, variables_per_clause):    
    return int(__binom(number_of_variables, variables_per_clause)
                * __number_of_sign_placements(variables_per_clause))

def __binom(n, k):
    if n == k:
        return 1
    elif k == 1:
        return n
    else:
        return math.factorial(n) / (math.factorial(k) * math.factorial(n - k))
    
def __number_of_sign_placements(variables_per_clause):
    result = 0;
    
    for i in range(variables_per_clause + 1):
        result += __binom(variables_per_clause, i)
    
    return result