一、算法
1、总算法
2、四阶幻方算法
3、奇数阶幻方算法
4、偶数阶幻方算法
二、代码
function createMagicSquare(factor,firstNum) {
var component = {};
//阶数
if(factor < 3){
alert("幻方阶数必须大于3");
return null;
}
component.factor = factor;
component.rows = new Array(); //
if(isNaN(firstNum))
firstNum = 1;
component.firstNum = firstNum;
//return;
(function () { //初始化自执行
for(var i = 0;i <component.factor;i++ ){
var numPerRow= new Array();
for(var j = 0;j <component.factor;j++){
numPerRow.push(0);
}
component.rows.push(numPerRow);
}
}());
//return;
//幻方平衡
component.balance = function () {
if(component.factor == 4){
_balance4(component);
}
else if(component.factor % 2 == 0){
_balanceEven(component);
}
else{
_balanceOdd(component);
}
};
//偶数阶幻方平衡
function _balanceEven(magicEvem){
var factor = magicEvem.factor;
var firstNum = magicEvem.firstNum;
if(factor%2 == 0){
//分区域算平衡
var sonFactor = factor/2;
var areaA = createMagicSquare(sonFactor,firstNum);
areaA.balance();
//areaA.show();
var areaB = createMagicSquare(sonFactor,firstNum + sonFactor * sonFactor);
areaB.balance();
//areaB.show();
var areaC = createMagicSquare(sonFactor,firstNum + 2*sonFactor * sonFactor);
areaC.balance();
//areaC.show();
var areaD = createMagicSquare(sonFactor,firstNum + 3*sonFactor * sonFactor);
areaD.balance();
//areaD.show();
//A,B,C,D 平衡算好后，交换数字
if(sonFactor%2 ==0){
//A <----> D相应位置交换，每行的交换方格数为subFactor/2
var exchangeNum = sonFactor/2;
for(var i = 0; i < sonFactor; i++){
for( j =0; j < exchangeNum;j++){
// A<---->D
var temp = areaA.rows[i][j];
areaA.rows[i][j] = areaD.rows[i][j];
areaD.rows[i][j] = temp;
// C<---->B
var temp = areaC.rows[i][j];
areaC.rows[i][j] = areaB.rows[i][j];
areaB.rows[i][j] = temp;
}
}
}
else{
var exchangeNum = (sonFactor - 1)/2;
for(var i = 0; i < sonFactor; i++){
for( j =0; j < exchangeNum;j++){
// A<---->D
var temp = areaA.rows[i][j];
areaA.rows[i][j] = areaD.rows[i][j];
areaD.rows[i][j] = temp;
if(j < exchangeNum - 1) {
// C<---->B
var temp = areaC.rows[i][j];
areaC.rows[i][j] = areaB.rows[i][j];
areaB.rows[i][j] = temp;
}
}
}
}
//交换完了，要把数字连成一片,连接A区
for(i = 0; i<sonFactor; i++){
var currentRow = magicEvem.rows[i];
for(j = 0; j<sonFactor; j++){
currentRow[j] = areaA.rows[i][j];
}
}
delete areaA.rows;
//连接C区
for(i = 0; i<sonFactor; i++){
var currentRow = magicEvem.rows[i];
for(j = 0; j<sonFactor; j++){
currentRow[sonFactor + j] = areaC.rows[i][j];
}
}
delete areaC.rows;
//连接D区
for(i = 0; i<sonFactor; i++){
var currentRow = magicEvem.rows[i + sonFactor];
for(j = 0; j<sonFactor; j++){
currentRow[j] = areaD.rows[i][j];
}
}
delete areaD.rows;
//连接B区
for(i = 0; i<sonFactor; i++){
var currentRow = magicEvem.rows[i + sonFactor];
for(j = 0; j<sonFactor; j++){
currentRow[sonFactor + j] = areaB.rows[i][j];
}
}
delete areaB.rows;
}
};
//奇数阶幻方平衡
function _balanceOdd (magicOdd){
if(magicOdd.factor%2 == 0)
{
alert("必须是奇数阶");
return;
}
var row = 0;
var col = (magicOdd.factor - 1)/2;
var currentNum = magicOdd.firstNum;
magicOdd.rows[row][col] = currentNum;
//document.write("<br/> factor: " + magicOdd.factor + " row:" + (row +1) + " col:" + (col +1) + " --- " + currentNum);
while(currentNum < magicOdd.firstNum + magicOdd.factor * magicOdd.factor - 1)
{
currentNum++;
row = row -1;
col = col + 1;
if(row < 0 )
{
if(col >= magicOdd.factor) { // 在本幻方外部的右上角
row = 1;
col = col - 1;
}
else
{
row = magicOdd.factor - 1;
}
}
else
{
if(col >= magicOdd.factor) { //仅仅超出右边界
col = 0;
}
else
{
//判断格子有没有被占
if(magicOdd.rows[row][col] != 0){
row = row +2;
col = col -1;
}
}
}
if(currentNum>=70)
debugger;
//document.write("<br/>row:" + (row +1) + " col:" + (col +1) + " --- " + currentNum);
magicOdd.rows[row][col] = currentNum;
}
};
//四阶幻方
//startx ==
function _balance4(magic4) {
if(magic4.factor != 4)
{
alert("必须是4阶");
}
for(var i = 0;i <4;i++ ){
var currentRow = component.rows[i];
for(var j = 0;j <4;j++){
currentRow[j] = component.firstNum + i * component.factor + j;
}
}
var temp = magic4.rows[3][3]; //本四阶里最后一行最后一个数字
magic4.rows[3][3] = magic4.rows[0][0];
magic4.rows[0][0] = temp;
temp = magic4.rows[3][0];
magic4.rows[3][0] = magic4.rows[0][3];
magic4.rows[0][3] = temp;
temp = magic4.rows[1][1];
magic4.rows[1][1] = magic4.rows[2][2];
magic4.rows[2][2] = temp;
temp = magic4.rows[1][2];
magic4.rows[1][2] = magic4.rows[2][1];
magic4.rows[2][1] = temp;
}
component.show = function () {
document.write("<table style='border-width: 1px'>")
for(var i = 0; i< component.factor;i++){
document.write("<tr>")
for(var j = 0; j< component.factor;j++){
document.write("<td>")
document.write(component.rows[i][j]);
document.write("</td>")
}
document.write("</tr>")
}
document.write("</table>")
}
return component;
}
