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24.html
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<!DOCTYPE HTML>
<html>
<head>
<meta charset="UTF-8" />
<title>Twenty-four Game</title>
<script type="text/javascript">
var nums;
var allNums, allOps;
var OPS = ['+', '-', '*', '/'];
var output;
// http://stackoverflow.com/questions/9960908/permutations-in-javascript
var permArr, usedChars;
function permute(input) {
var i, ch;
for (i = 0; i < input.length; i++) {
ch = input.splice(i, 1)[0];
usedChars.push(ch);
if (input.length == 0) {
permArr.push(usedChars.slice());
}
permute(input);
input.splice(i, 0, ch);
usedChars.pop();
}
return permArr;
};
var genOps = function(prefix) {
if (prefix.length == nums.length - 1) {
allOps.push(prefix.split(''));
return;
}
for (var op = 0; op < 4; op++) {
genOps(prefix.concat(op));
}
}
var init = function() {
// Initialize the numbers permutation
allNums = {};
var indices = [];
for (var i = 0; i < nums.length; i++) {
indices.push(i);
}
permArr = [];
usedChars = [];
permute(indices);
for (var i = 0; i < permArr.length; i++) {
var perm = permArr[i];
var num = [];
for (var j = 0; j < perm.length; j++) {
num.push(nums[perm[j]]);
}
allNums[num.join(" ")] = true;
}
allNums = Object.keys(allNums);
// document.getElementById("result").innerHTML = allNums.join(';');
// Initialize the operators permutation
allOps = [];
genOps("");
// document.getElementById("result").innerHTML = allOps.join(';');
};
var Node = function(v, op) {
this.v = v;
this.op = op;
this.left = null;
this.right = null;
};
Node.prototype.toString = function () {
if (this.left == null && this.right == null) return "" + this.v;
return "" + OPS[this.op];
}
var cloneNode = function (n) {
var nNode = new Node(n.v, n.op);
if (n.left != null) {
nNode.left = cloneNode(n.left);
}
if (n.right != null) {
nNode.right = cloneNode(n.right);
}
return nNode;
};
var printNode = function (n) {
if (n == null) return "#";
if (n.left == null && n.right == null) return n.toString();
return "(" + printNode(n.left) + " " + n.toString() + " " + printNode(n.right) + ")";
// return n.toString() + " (" + printNode(n.left) + " " + printNode(n.right) + ")";
};
var calculate = function (n) {
if (n.left == null && n.right == null) return Number(n.v);
var l = Number(calculate(n.left)), r = Number(calculate(n.right));
switch (n.op) {
case "0": return l + r;
case "1": return l - r;
case "2": return l * r;
case "3": return l / r;
default: return 0 / 0;
}
};
var createTrees = function() {
output = [];
var topologies = {};
topologies[1] = [new Node(0, 0)];
for (var i = 3; i <= nums.length * 2 - 1; i += 2) {
var list = [];
for (var j = 1; j < i; j += 2) {
var left = topologies[j], right = topologies[i - j - 1];
var comb = generateCombinations(left, right);
for (var k = 0; k < comb.length; k++) {
list.push(comb[k]);
}
}
topologies[i] = list;
}
var result = topologies[nums.length * 2 - 1];
// document.getElementById("result").innerHTML = result.join(" ");
for (var i = 0; i < result.length; i++) {
var tree = result[i];
for (var j = 0; j < allNums.length; j++) {
var ns = allNums[j].split(" ");
var nList = [];
for (var k = 0; k < ns.length; k++) {
nList.push(ns[k]);
}
assignNum(nList, tree, 0);
for (var k = 0; k < allOps.length; k++) {
var ops = allOps[k];
var nOps = [];
for (var l = 0; l < ops.length; l++) {
nOps.push(ops[l]);
}
assignOp(nOps, tree, 0);
var resultValue = calculate(tree);
if (resultValue == Number(document.getElementById("target").value)) {
output.push(printNode(tree));
return;
}
}
}
}
};
var assignNum = function (nList, nNode, pos) {
if (nNode == null) return;
assignNum(nList, nNode.right, pos + 1);
if (nNode.left == null && nNode.right == null) {
nNode.v = nList.shift();
}
assignNum(nList, nNode.left, pos + 1);
};
var assignOp = function (nOps, nNode, pos) {
if (nNode == null) return;
assignOp(nOps, nNode.right, pos + 1);
if (nNode.left != null || nNode.right != null) {
nNode.op = nOps.shift();
}
assignOp(nOps, nNode.left, pos + 1);
};
var generateCombinations = function (left, right) {
var list = [];
for (var i = 0; i < left.length; i++) {
for (var j = 0; j < right.length; j++) {
var nNode = new Node(0, 0);
nNode.left = cloneNode(left[i]);
nNode.right = cloneNode(right[j]);
list.push(nNode);
}
}
return list;
};
var solve = function() {
nums = document.getElementById("nums").value.toLowerCase().split(" ");
for (var i = 0; i < nums.length; i++) {
switch (nums[i]) {
case 't': nums[i] = 10; break;
case 'j': nums[i] = 11; break;
case 'q': nums[i] = 12; break;
case 'k': nums[i] = 13; break;
case 'a': nums[i] = 1; break;
default: nums[i] = Number(nums[i]);
}
}
init();
createTrees();
var t = output.join("<br/>");
if (output.length == 0) t = "No Answer!";
return t;
};
var displaySolve = function(t) {
document.getElementById("result").innerHTML = t;
};
// http://bost.ocks.org/mike/shuffle/
function shuffle(array) {
var m = array.length, t, i;
// While there remain elements to shuffle…
while (m) {
// Pick a remaining element…
i = Math.floor(Math.random() * m--);
// And swap it with the current element.
t = array[m];
array[m] = array[i];
array[i] = t;
}
return array;
}
var generate = function(n) {
var arr = [];
for (var i = 0; i < 52; i++) {
arr.push(i);
}
shuffle(arr);
result = [];
for (var i = 0; i < n; i++) {
result.push(arr[i] % 13 + 1);
}
document.getElementById("nums").value = result.join(" ");
};
var answer = "";
var stepSolve = function() {
var n = document.getElementById("result").innerHTML.length;
if (n == 0) answer = solve();
document.getElementById("result").innerHTML = answer.substring(0, n + 1);
};
</script>
</head>
<body>
<h1>Twenty-four Game</h1>
Note: Please use Chrome, not Firefox to ensure the speed.
<p>
Numbers (space-separated): <input type="text" id="nums" value="1 2 3 4 5 6" onchange=/> <input type="button" value="Random 6" onclick="generate(6);"/><br/>
Target (24, 219, etc.): <input type="text" id="target" value="219"/><br/>
<input type="button" value="Solve!" onclick="displaySolve(solve());"/> <input type="button" value="Step" onclick="stepSolve(0);"/> <input type="button" value="Clear" onclick="displaySolve('');"/>
</p>
<div id="result"></div>
<hr/>
Powered by CAQ, Oct 2015
</body>
</html>