The object of the game is to move all the disks onto a different pole. You can only move one disk at a time and you must follow size order -- a bigger disk can't go on a smaller disk.
Recursive Tower of Game to count bar-moving
#include<stdio.h>
int hanoi(int n){
if(n==0)
return 0;
else
return 2*hanoi(n-1)+1;
}
main(){printf("hanoi=%d",hanoi(3));}
Please copy script of Tower Hanoi in Java below:
#include<stdio.h>
int hanoi(int n){
if(n==0)
return 0;
else
return 2*hanoi(n-1)+1;
}
main(){printf("hanoi=%d",hanoi(3));}
Please copy script of Tower Hanoi in Java below:
<script language="JavaScript">
<!--
if (version == null)
document.write("Your browser doesn't have JavaScript 1.1 capabilities. "
+ "This program only works on Netscape 3+ and MSIE 4+.");
// -->
</script>
<SCRIPT LANGUAGE="JavaScript1.1">
<!-- hide from JavaScript challenged browsers
document.writeln("<BLOCKQUOTE>The object of the game is to move all the disks onto a different pole. You can only move one disk at a time and you must follow size order -- a bigger disk can't go on a smaller disk. [Hint: try it with 3 disks to start with.] Good luck!</BLOCKQUOTE><br>");
<!-- Original: Adam Stock (adam@digital-biz.com) -->
<!-- (c) Copyright 1998-99 Adam L. Stock. All Rights Reserved -->
imgdir = "images/";
function preload() {
this.length = preload.arguments.length;
for (var i = 0; i < this.length; i++) {
this[i] = new Image();
this[i].src = imgdir + preload.arguments[i];
}
}
var pics = new preload("disk1.gif","disk2.gif",
"disk3.gif","disk4.gif","disk5.gif","disk6.gif",
"disk7.gif","disk1h.gif","disk2h.gif",
"disk3h.gif","disk4h.gif","disk5h.gif","disk6h.gif",
"disk7h.gif","post.gif","posttop.gif");
var selectedr = null;
var selectedc = null;
var maxposts = 3;
var maxdisks = 7;
var all_posts = 3;
var startpost = 1;
var endpost = (startpost-1 < 0 ? maxposts-1 : startpost-1);
var disks = 7;
var imgwidth = 160;
var imgheight = 14;
var game_is_over = false;
var show_messages = false;
var board = new Array(maxposts);
board[0] = new Array(maxdisks + 1);
board[1] = new Array(maxdisks + 1);
board[2] = new Array(maxdisks + 1);
function initboard(startpost, disks) {
var len = board[0].length;
selectedc = null;
selectedr = null;
game_is_over = false;
endpost = (startpost-1 < 0 ? maxposts-1 : startpost-1);
for (i = 0; i < len; i++) {
board[0][i] = 0;
board[1][i] = 0;
board[2][i] = 0;
}
for (i = len-disks, j = 0; i < len; i++, j++) {
board[startpost][i] = len - j - 1;
}
}
function drawall() {
for (j=0; j<board.length; j++) {
for (i=0; i<board[j].length; i++) {
draw(j,i, getName( board[j][i]));
}
}
message("You may begin! Select a piece to move.");
}
function restart(start) {
startpost = start;
disks = document.forms[0].disc.options[document.forms[0].disc.selectedIndex].text;
initboard(startpost,disks);
drawall();
theAnim = new Animation();
}
initboard(startpost, disks);
function getName( num ) {
if (num == 0) return "post.gif";
return "disk" + num + ".gif";
}
function message(str, force) {
if (force || !game_is_over && !show_messages)
document.disp.message.value = str;
}
function messageadd(str) {
if (!game_is_over)
document.disp.message.value = document.disp.message.value + "\n" + str;
}
function isempty(num) {
for (i = 0; i < board[num].length; i++) {
if ( board[num][i] != 0) return false;
}
return true;
}
function topmost(num) {
for (i = 0; i < board[num].length; i++) {
if (board[num][i] != 0) return i;
}
return -1;
}
function ispost(i,j) {
return (board[j][i] == 0);
}
function istopdisk(i,j) {
return (board[j][i-1] == 0);
}
function drawboard() {
// document.writeln("<h2>The Towers of Hanoi</h2><p>");
document.writeln("<center><table cellspacing=0 cellpadding=0 border=0>");
document.write("<tr>");
for (j = 0; j < board.length; j++) {
document.write("<td>");
document.write("<a href='javascript:clicked("+0+","+j+")'><img src='" + imgdir + "posttop.gif' border=0></a><br>");
for (i=0; i< board[0].length; i++) {
document.write("<a href='javascript:clicked("+i+","+j+")'>");
document.write("<img src='" + imgdir + getName(board[j][i]) + "' name='pos"+ j + i + "' border=0><br>");
document.write("</a>");
}
document.writeln("</td>");
}
// document.write("</tr></table>");
document.write("</tr><tr><td colspan=3><img src='images/base.gif' border=0></td></tr></table>");
//
document.write("<form name='disp'><textarea name='message' wrap=virtual rows=2 cols=40></textarea><br>" +
"Disks: <select name=\"disc\" size=1><option>3<option>4<option>5<option>6<option selected>7</select><input "
+"type=button value=\"Start the Game Over\" onClick=\"restart(startpost);\"><input "
+"type=button value=\"Solve It!\" onClick=\"restart(startpost);setTimeout('hanoi(disks,startpost,endpost)',300)\"></form>");
}
function draw(x,y,name) {
document.images["pos"+x+""+y].src = imgdir + name;
}
function animate(x,y,name) {
theAnim.addFrame( "pos"+x+""+y, imgdir + name);
}
function clicked(i,j) {
document.forms[0].message.focus(); // get rid of annoying outline in MSIE
document.forms[0].message.blur();
if (game_is_over) restart(startpost = endpost);
if (!isselection() && ispost(i,j)) { message("Select a piece to move."); return; }
if (!ispost(i,j)) { toggle(j); return; };
if (ispost(i,j) && selectedc == j) { message("Move the piece to a different post."); return; }
if (!legalmove(j)) { message("That is not a legal move. Try again."); return; }
move(j); return;
}
function legalmove(j) {
if (isempty(j)) return true;
return (board[j][topmost(j)] < board[selectedc][selectedr]);
}
function isselection() {
return selectedc != null;
}
function toggle( num ) {
var toppos = topmost(num);
if (selectedc == num && selectedr == toppos) {
selectedc = null; selectedr = null;
animate(num,toppos,"disk" + board[num][toppos] + ".gif");
message("Select a piece to move.");
return;
}
if (isselection()) {
animate(selectedc,selectedr,"disk" + board[selectedc][selectedr] + ".gif");
}
selectedc = num; selectedr = toppos;
animate(num,toppos,"disk" + board[num][toppos] + "h.gif");
message("Click on the post to which you want to move the disk.");
}
function move( num ) {
var toppos = (!isempty(num) ? topmost(num) : board[num].length);
board[num][toppos-1] = board[selectedc][selectedr];
board[selectedc][selectedr] = 0;
animate(selectedc,selectedr,"post.gif");
animate(num,toppos-1,"disk" + board[num][toppos-1] + ".gif");
selectedc = null; selectedr = null;
message("Select a piece to move.");
game_over();
}
function hanoi(no_of_disks, start_post, goal_post) {
if (no_of_disks > 0) {
var free_post = all_posts - start_post - goal_post;
hanoi (no_of_disks - 1, start_post, free_post);
show_messages = true;
toggle(start_post);
move(goal_post);
show_messages = false;
hanoi (no_of_disks - 1 , free_post, goal_post);
game_over(true);
}
}
function game_over(forceMsg) {
var filledpost = null;
var val = 0;
for (k = 0; k < board.length; k++) {
val += ( isempty(k) ? 1 : 0 );
if (!isempty(k)) filledpost = k;
}
if (val == 2 && isempty(startpost)) {
message("You won!", forceMsg);
game_is_over = true;
endpost = filledpost;
}
return game_is_over;
}
//
// Animation functions
//
function Animation() {
this.imageNum = new Array(); // Array of indicies document.images to be changed
this.imageSrc = new Array(); // Array of new srcs for imageNum array
this.frameIndex = 0; // the frame to play next
this.alreadyPlaying = false; // semaphore to ensure we play smoothly
this.getFrameCount = getframecount; // the total number of frame so far
this.moreFrames = moreframes; // tells us if there are more frames to play
this.addFrame = addframe; // add a frame to the animation
this.drawNextFrame = drawnextframe; // draws the next frame
this.startAnimation = startanimation; // start the animation if necessary
}
function getframecount() { return this.imageNum.length; }
function moreframes() { return this.frameIndex < this.getFrameCount(); }
function startanimation() {
if (!this.alreadyPlaying) {
theAnim.alreadyPlaying = true;
setTimeout('theAnim.drawNextFrame()',5);
}
}
function addframe(num, src) {
var theIndex = theAnim.imageNum.length;
theAnim.imageSrc[theIndex] = src;
theAnim.imageNum[theIndex] = num;
theAnim.startAnimation();
}
function drawnextframe() {
if (theAnim.moreFrames()) {
document.images[ theAnim.imageNum[theAnim.frameIndex] ].src = theAnim.imageSrc[theAnim.frameIndex];
theAnim.frameIndex++;
setTimeout('theAnim.drawNextFrame()', 30);
} else {
theAnim.alreadyPlaying = false;
}
}
drawboard();
var theAnim = new Animation();
message("You may begin! Select a piece to move.");
document.disp.message.value = "";
// End -->
</script>
---------------------------------------------
History
The Towers of Hanoi puzzle was published in 1883 by French mathematician Edouard Lucas, under the pen-name, N. Lucas de Siam.
The "legend" which accompanied the game stated that in Benares, during the reign of the Emperor Fo Hi, there was a temple with a dome which marked the center of the world. Within the dome, priests moved golden disks between diamond needlepoints, a cubit high and as thick as the body of a bee. God placed 64 gold disks on one needle at the time of creation. It was said that when they completed their task, the universe would come to an end.
(Since it would take at least 264 -1 moves to complete the task, we're safe for now. Assuming one move per second, and no wrong moves, it would take almost 585,000,000,000 years to complete (see it below).)
How many years?
How many years would it take, at one move per second, to make 264 -1 moves?
First, convert 264 to seconds:
264 seconds = 1.844674 x 1019 seconds
Then calculate the number of seconds in a year:
60 seconds in a minute
x 60 minutes in an hour
x 24 hours in a day
x 365 days in a year (we'll ignore the extra 1/4 day from leap-years)
31,536,000 seconds per year
Then, divide the total number of seconds, by the number of seconds in one year: 18.44674 x 1018 seconds
3.1536 x 107 seconds per year => 5.849424 x 1011, or 584,942,400,000 years !
