幻方算法

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- 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;
}