declare -r TRUE=0
declare -r FALSE=1

declare -r MAX_POLY=5
declare -r MAX_COEF=10

declare poly_A_coefs=()
declare poly_B_coefs=()
declare poly_C_coefs=()

#
# void init()
#
function init()
{
  local i=0
  while [ $i -lt $MAX_POLY ]
  do
    poly_A_coefs[$i]=0
    poly_B_coefs[$i]=0
    poly_C_coefs[$i]=0
    let i=$i+1
  done
  return 0
}

#
# int is_num(const char *str)
#
function is_num()
{
  local num=$1
  local len=${#num}
  local i=0
  local c
  while [ $i -lt $len ]
  do
    c=${num:$i:1}
    [ -n "${c/[0-9]/}" ] && return $FALSE
    let i=$i+1
  done
  return $TRUE
}

#
# int get_num(int min, int max)
#
function get_num()
{
  local min=$1
  local max=$2
  local num
  read num
  is_num $num || return $FALSE
  [ ${num} -lt ${min} -o ${num} -gt ${max} ] && return $FALSE
  echo $num
  return $TRUE
}

#
# int inputPolyNum(void)
#
function inputPolyNum()
{
  local num=-1
  while [ true ]
  do
    echo -n "Number of $1: "
    num=$(get_num 1 $MAX_POLY)
    [ $? -eq $TRUE ] && break
    echo "Out of range(1~$MAX_POLY). Retry!"
  done
  return $num
}

#
# put random number into random position of array
#
function makeRandomPoly()
{
  local poly=$1
  local nr=$2
  local pos
  local coef
  local sign
  local tmp
  local count=0
  while (($count < $nr))
  do
    let pos=$RANDOM%$MAX_POLY
    tmp="$poly[$pos]"
    [ ${!tmp} -ne 0 ] && continue
    let coef=($RANDOM%$MAX_COEF)+1
    let sign=$RANDOM%2
    [ $sign -eq 1 ] && eval $tmp=$coef || eval $tmp="-${coef}"
    ((count++))
  done
}

#
# add each paired entries for 2 arrays
#
function add_poly
{
  local poly1=$1
  local poly2=$2
  local res=$3
  local tmp1
  local tmp2
  local tmpr
  local pos
  local i=0
  while (($i < $MAX_POLY))
  do
    pos=$i
    ((i++))
    tmp1=$poly1[$pos]
    tmp2=$poly2[$pos]
    tmpr=$res[$pos]
    eval let ${tmpr}=${!tmp1}+${!tmp2}
  done
}

# 
# print out each entries except 0
#
function printPoly()
{
  local poly=$1
  local tmp
  local pos
  local exp
  local i=0
  while (($i < $MAX_POLY))
  do
    pos=$i
    ((i++))
    tmp=$poly[$pos]

    [ ${!tmp} -eq 0 ] && continue

    let exp=$MAX_POLY-$pos-1
    printf "%3dX^%-2d " "${!tmp}" "$exp"
  done
  echo ""
}

init

inputPolyNum "A"
declare -r poly_nr_A=$?

inputPolyNum "B"
declare -r poly_nr_B=$?

makeRandomPoly poly_A_coefs $poly_nr_A
makeRandomPoly poly_B_coefs $poly_nr_B
add_poly poly_A_coefs poly_B_coefs poly_C_coefs

echo -n "A      : "
printPoly poly_A_coefs

echo -n "B      : "
printPoly poly_B_coefs

echo -n "C=(A+B): "
printPoly poly_C_coefs