getProbabilitiy <- function(x, numbers){
  positions = match(numbers, x$numbers)
  probs = x$probs[positions]

  probs[is.na(probs)] = 0

  return(probs)
}


sumTwoDie <- function(x, y){
  range_z_min = min(x$numbers) + min(y$numbers)
  range_z_max = max(x$numbers) + max(y$numbers)

  z_numbers = c()
  probabilities = c()
  for(num in range_z_min:range_z_max){
    prob_num = sum(x$probs * getProbabilitiy(y, num - x$numbers))
    if(prob_num > 0){
      z_numbers = c(z_numbers, num)
      probabilities = c(probabilities, prob_num)
    }
  }

  z = makeDie(z_numbers, probabilities)
  return(z)
}

# comparerFun(x, y); which both x & y as Die, or one of them as numeric
compareDie <- function(x, y, comparerFun){
  if(class(x) == "Die" & class(y) == "Die"){
    jointProbs = expand.grid(x$probs, y$probs)
    jointProbs = jointProbs[,1]*jointProbs[,2]

    jointNumbers = expand.grid(x$numbers, y$numbers)
    matchResults = comparerFun(jointNumbers[,1], jointNumbers[,2])
    probTrue = sum(jointProbs[matchResults])

    z = makeDie(c(F,T), probs=c(1-probTrue, probTrue))
    return(z)
  }

  if(class(x) %in% c("numeric", "integer")){
    die = y
    constant = x

    xNumbers = constant
    yNumbers = die$numbers

  } else if(class(y) %in% c("numeric", "integer")){
    die = x
    constant = y

    xNumbers = die$numbers
    yNumbers = constant

  } else{
    stop("Can only compare two die or a die and a number")
  }

  if(length(constant) != 1){
    stop("Length of constant must be 1")
  }

  matchResults = comparerFun(xNumbers, yNumbers)
  probTrue = sum(die$probs[matchResults])

  z = makeDie(c(F,T), probs=c(1-probTrue, probTrue))
}