#!/bin/bash -
#===============================================================================
#
# FILE: Hanoi_tower.sh
#
# USAGE: ./Hanoi_tower.sh
#
# DESCRIPTION:
#
# OPTIONS: ---
# REQUIREMENTS: ---
# BUGS: ---
# NOTES: ---
# AUTHOR: Francis Drake K (), 772523354@qq.com
# ORGANIZATION: M33
# CREATED: 2018年08月16日 20:04
# REVISION: ---
#===============================================================================
tower_1=()
tower_2=()
tower_3=()
step=(0)
level_up=()
create_tower ()
{
for (( CNTR=0; CNTR<$1; CNTR+=1 )); do
tower_1=( ${tower_1[*]} `echo "$CNTR+1" |bc ` )
done
} # ---------- end of function create_tower ----------
#--- FUNCTION ----------------------------------------------------------------
# NAME: mv_to_tower3
# DESCRIPTION: 将标准塔移动到tower3
# PARAMETERS: tower_name()
# RETURNS:
#-------------------------------------------------------------------------------
mv_to_tower3 ()
{
if [ ${tower_3[*]} -ne 0 ] ; then
# 如果塔中有元素则更新目标塔
update_to_tower
fi
# 将参数数组（起始塔）的最上层元素（数组的下标0位置的数据）赋值给塔3的最上层元素
tower_3[0]= ${$1[0]}
# 删除参数数组（起始塔）的最上层元素
unset ${$1[0]}
# 更新起始塔(将数组中的全部元素全部下标-1)
update_from_tower $1
# 将元素，起始塔，目标塔当做参数传入count_step
count_step ${$1[0]} $1 tower_3
} # ---------- end of function mv_to_tower3 ----------
mv_to_tower2 ()
{
if [ ${tower_2[*]} -ne 0 ] ; then
# 如果塔中有元素则更新目标塔
update_to_tower
fi
# 将参数数组（起始塔）的最上层元素（数组的下标0位置的数据）赋值给塔3的最上层元素
tower_2[0]= ${$1[0]}
# 删除参数数组（起始塔）的最上层元素
unset ${$1[0]}
# 更新起始塔(将数组中的全部元素全部下标-1)
update_from_tower $1
# 将元素，起始塔，目标塔当做参数传入count_step
count_step ${$1[0]} $1 tower_2
} # ---------- end of function mv_to_tower2 ----------
mv_to_tower1 ()
{
if [ ${tower_1[*]} -ne 0 ] ; then
# 如果塔中有元素则更新目标塔
update_to_tower
fi
# 将参数数组（起始塔）的最上层元素（数组的下标0位置的数据）赋值给塔3的最上层元素
tower_1[0]= ${$1[0]}
# 删除参数数组（起始塔）的最上层元素
unset ${$1[0]}
# 更新起始塔(将数组中的全部元素全部下标-1)
update_from_tower $1
# 将元素，起始塔，目标塔当做参数传入count_step
count_step ${$1[0]} $1 tower_2
} # ---------- end of function mv_to_tower1 ----------
#--- FUNCTION ----------------------------------------------------------------
# NAME: update_tower
# DESCRIPTION: 更新起始塔（数组）
# PARAMETERS: tower_name
# RETURNS:
#-------------------------------------------------------------------------------
update_from_tower ()
{
for (( CNTR=1; CNTR<${$1[*]}; CNTR+=1 )); do
${$1[$CNTR-1]}= ${$1[$CNTR]}
done
} # ---------- end of function update_tower ----------
#--- FUNCTION ----------------------------------------------------------------
# NAME: update_to_tower
# DESCRIPTION: 更新目标塔（数组）
# PARAMETERS: tower——name
# RETURNS:
#-------------------------------------------------------------------------------
update_to_tower ()
{
for (( CNTR=0; CNTR<${$1[*]}; CNTR+=1 )); do
${$1[$CNTR+1]}= ${$1[$CNTR]}
unset ${$1[0]}
done
} # ---------- end of function update_to_tower ----------
#--- FUNCTION ----------------------------------------------------------------
# NAME: count_step
# DESCRIPTION: 记录起始塔，移动数，目标塔到step（）中
# PARAMETERS:
# RETURNS:
#-------------------------------------------------------------------------------
count_step ()
{
lev=`echo "L$1"`
tower_from=$2
tower_to=$3
step=(${step[*]} `echo "$lev $tower_from $tower_to"` )
} # ---------- end of function count_step ----------
#--- FUNCTION ----------------------------------------------------------------
# NAME: 3_level_tower_to
# DESCRIPTION: 初始化level_up（）将三阶汉诺塔从塔1移动到塔3的方法存入
# PARAMETERS:
# RETURNS:
#-------------------------------------------------------------------------------
3_level_tower_to ()
{
level_up=(${level_up[*]} echo 'mv_to_tower3 tower_1')
# L1从塔1移动到塔3
level_up=(${level_up[*]} echo 'mv_to_tower2 tower_1')
# L2从塔1移动到塔2
level_up=(${level_up[*]} echo ' mv_to_tower2 tower_3')
# L1从塔1移动到塔2
level_up=(${level_up[*]} echo 'mv_to_tower3 tower_3')
# L3从塔1移动到塔3
level_up=(${level_up[*]} echo 'mv_to_tower1 tower_2')
# L1从塔1移动到塔1
level_up=(${level_up[*]} echo 'mv_to_tower3 tower_2')
# L2从塔1移动到塔3
level_up=(${level_up[*]} echo 'mv_to_tower3 tower_1')
# L1从塔1移动到塔3
}# ---------- end of function 3_level_tower_to ----------
#--- FUNCTION ----------------------------------------------------------------
# NAME: 3_level_tower_back
# DESCRIPTION: 三阶汉诺塔从塔3移动到塔1
# PARAMETERS:
# RETURNS:
#-------------------------------------------------------------------------------
# 3_level_tower_back ()
# {
# mv_to_tower1 tower_3
# L1从塔3移动到塔1
# mv_to_tower2 tower_3
# L2从塔3移动到塔2
# mv_to_tower2 tower_1
# L1从塔1移动到塔2
# mv_to_tower1 tower_3
# L3从塔3移动到塔1
# mv_to_tower3 tower_2
# L1从塔2移动到塔3
# mv_to_tower1 tower_2
# L2从塔2移动到塔1
# mv_to_tower1 tower_3
# L1从塔3移动到塔1
# } # ---------- end of function 3_level_tower_back ----------
#--- FUNCTION ----------------------------------------------------------------
# NAME: change_num
# DESCRIPTION: 对换角标,例:参数 mv_to_tower1 tower3 可返回结果mv_to_tower3 tower1
# PARAMETERS:
# RETURNS:
#-------------------------------------------------------------------------------
change_num ()
{
way_num_tmp=` echo $1 |rev |cut -c1 `
change_from=` echo $2 |rev |cut -c1 `
way_output= ` echo "mv_to_tower"$change_from `
from_output=` echo "tower"$way_num_tmp
level_up=(${level_up[*]} `echo "$way_output $from_output"` )
} # ---------- end of function change_num ----------
#--- FUNCTION ----------------------------------------------------------------
# NAME: tower_level_up
# DESCRIPTION: 塔的移动方法随阶数的增长自动升级，并将其存入level_up（）
# PARAMETERS:
# RETURNS:
#-------------------------------------------------------------------------------
tower_level_up ()
{
#-------------------------------------------------------------------------------
# 核心算法 汉诺塔学习升级
# 如果要求n阶汉诺塔:应先求3阶汉诺塔
# 通过三阶汉诺塔为基础进行变换
# 例：4阶汉诺塔的移动方法
# 3阶汉诺塔正向移动 + 第四阶移动到塔2
# +3阶汉诺塔反向移动 + 第四阶移动到塔3
# +3阶汉诺塔正向移动
# 由此可知若已有4阶汉诺塔的移动方法可求5阶移动方法
# 所以已知3阶汉诺塔可求n阶汉诺塔
# 但由于时间复杂度的提升和数据的溢出
# 不可求过高阶的汉诺塔
#
#-------------------------------------------------------------------------------
# 因为数组中存入了3阶汉诺塔的正向移动方法所以无需改变
for (( CNTR=3; CNTR<$1; CNTR+=1 )); do
# 添加步骤 将高1阶的塔从塔1移动到塔2
level_up=(${level_up[*]} echo "mv_to_tower2 tower_1"
# 防止计算错错误锁定低阶汉诺塔的正向移动方法的数组位置
arry_end=echo "`echo ${#level_up[@]}-2 |bc`"
for (( i=0; i<$arry_end; i+=1 )); do
# 生成反向移动，并存入数组
change_num ${level_up[$i]}
done
# 添加步骤 将高一阶的塔从塔2移动到塔3
level_up=(${level_up[*]} echo"mv_to_tower3 tower_2"
# 再次使用低阶正向移动方法
for (( j=0; j<$arry_end; CNTR+=1 )); do
level_up=(${level_up[*]} `echo ${level_up[j]}`)
done
done
} # ---------- end of function tower_level_up ----------
main ()
{:
# 输入一个要完成的阶数
# 生成数组
# create_tower
# 传入tower_level_up
# 得出目标方法
# 运行目标方法
# 输出countstep内容
# 即可获得移动步骤和最终塔
} # ---------- end of function main ----------