[从头学数学] 第74节 小数乘法

剧情提要：
[机器小伟]在[工程师阿伟]的陪同下进入练气期第九层功法的修炼，
这次要修炼的目标是[小数乘法]。

正剧开始：

经过坚持不懈的努力，[机器小伟]终于进入了练气期高手的境界，这不，他已经可以开始第九层功法的修炼了。

这是小伟刚从[人叫板老师]那里得到的练气期第九层功法修炼指南：

所以，小伟迫不及待的进入了对小数乘法的研究当中。

在开始乘法之前，小伟觉得需要能够更轻松地表示出小数，于是对数字类做了改进，这样，就可以产生以下的效果了：

但是，这样做的问题也是很大的，具体表现在竖式的不对位上，所以，最终，小伟选择了以下的方案：

这是小伟用来做测试的：

<span style="font-size:18px;">function myDraw() {     var config = new PlotConfiguration();      config.init();      config.setPreference(); //config.setSector(1,1,1,1);//config.axis2D(0, 0, 180);var vertExp = new VerticalExpression();var x = 300, y = 20, r = 20;vertExp.rightAlign(1.506, x, y, r);y += 30;vertExp.rightAlign(0.15060, x, y, r);y += 30;vertExp.rightAlign(10.150601, x, y, r);y += 30;vertExp.rightAlign(0.1506000008, x, y, r);y += 30;vertExp.rightAlign(-0.1506000008, x, y, r);y += 30;vertExp.leftAlign(0.15060, x, y, r);y += 30;vertExp.leftAlign(10.150601, x, y, r);y += 30;vertExp.leftAlign(0.1506000008, x, y, r);y += 30;vertExp.leftAlign(-0.1506000008, x, y, r);}</span>

好了，现在可以正式地开始修炼了。

上面这个两个水桶的问题，让[工程师阿伟]和[机器小伟]同时吃惊了，因为它的结果竟然是：

这两个桶可以盛出0-15kg范围内任意多的水来。

这是怎么回事呢？先看结果：

<span style="font-size:18px;">>>> -8次小桶, 3次大桶， 得到13次小桶, -1次大桶， 得到1-5次小桶, 2次大桶， 得到26次小桶, -2次大桶， 得到2-2次小桶, 1次大桶， 得到39次小桶, -3次大桶， 得到3-10次小桶, 4次大桶， 得到41次小桶, 0次大桶， 得到4-7次小桶, 3次大桶， 得到54次小桶, -1次大桶， 得到5-4次小桶, 2次大桶， 得到67次小桶, -2次大桶， 得到6-1次小桶, 1次大桶， 得到7-9次小桶, 4次大桶， 得到82次小桶, 0次大桶， 得到8-6次小桶, 3次大桶， 得到95次小桶, -1次大桶， 得到9-3次小桶, 2次大桶， 得到108次小桶, -2次大桶， 得到100次小桶, 1次大桶， 得到11-8次小桶, 4次大桶， 得到123次小桶, 0次大桶， 得到12-5次小桶, 3次大桶， 得到136次小桶, -1次大桶， 得到13-2次小桶, 2次大桶， 得到149次小桶, -2次大桶， 得到14-10次小桶, 5次大桶， 得到151次小桶, 1次大桶， 得到15def tmp():    a = 4;    b = 11;    for i in range(1, a+b+1):        for j in range(-10, 10):            for k in range(-10, 10):                if a*j + b*k == i:                    print('{0}次小桶, {1}次大桶， 得到{2}'.format(j, k, i));    return;</span>

用图示可以看得更清楚：

这样5kg水就量出来了。

<span style="font-size:18px;">//量水function myDraw() {     var config = new PlotConfiguration();      config.init();      config.setPreference(); //config.setSector(1,1,1,1);//config.axis2D(0, 0, 180);var y1 = 0, y2 = 0, h1= 110, h2=40, w = 30;plot.setStrokeStyle('orange');//config.setSector(4, 4, 1, 1);plot.setFillStyle('black').fillText('第 1 步', 0, -20, 50);plot.setFillStyle('blue').fillRect(0, h1-y1, w, y1).strokeRect(0,0,w,h1);plot.setFillStyle('green').fillRect(1.6*w, h1-y2, w, y2).strokeRect(1.6*w, h1-h2, w, h2);//y1 = 80, y2 = 40;config.setSector(4, 4, 1, 2);plot.setFillStyle('black').fillText('第 2 步', 0, -20, 50);plot.setFillStyle('blue').fillRect(0, h1-y1, w, y1).strokeRect(0,0,w,h1);plot.setFillStyle('green').fillRect(1.6*w, h1-y2, w, y2).strokeRect(1.6*w, h1-h2, w, h2);//y1 = 110, y2 = 10;config.setSector(4, 4, 1, 3);plot.setFillStyle('black').fillText('第 3 步', 0, -20, 50);plot.setFillStyle('blue').fillRect(0, h1-y1, w, y1).strokeRect(0,0,w,h1);plot.setFillStyle('green').fillRect(1.6*w, h1-y2, w, y2).strokeRect(1.6*w, h1-h2, w, h2);//y1 = 10, y2 = 40;config.setSector(4, 4, 3, 1);plot.setFillStyle('black').fillText('第 4 步', 0, -20, 50);plot.setFillStyle('blue').fillRect(0, h1-y1, w, y1).strokeRect(0,0,w,h1);plot.setFillStyle('green').fillRect(1.6*w, h1-y2, w, y2).strokeRect(1.6*w, h1-h2, w, h2);}</span>

下面是量取3kg水:

量取10kg水：

其它的也都可以量出来，太神奇了。

<span style="font-size:18px;">function myDraw() {     var config = new PlotConfiguration();      config.init();      config.setPreference(); //config.setSector(1,1,1,1);//config.axis2D(0, 0, 180);var x = 300, y = 20, r = 20;var vertExp = new VerticalExpression();vertExp.floatMul(0.049, 45,x , y, r);}</span>

到现在为止，小伟的数字和竖式工具已经变成了：

<span style="font-size:18px;">/*** @usage   数字形状* @author  mw* @date    2015年12月01日  星期二  15:57:45 * @param* @return**/function Digit() {//8this.eight = function(x, y, r) {plot.save();var h = r * 0.4; //字半高var w = h / 2.2; //字半宽var w0 = r *0.1; //填充宽//填充shape.fillRect(x, y, h, w0); //中横shape.fillRect(x-w, y-w, w0, h); //上左竖shape.fillRect(x+w, y-w, w0, h); //上右竖shape.fillRect(x-w, y+w, w0, h); //下左竖shape.fillRect(x+w, y+w, w0, h); //下右竖shape.fillRect(x, y-h, h, w0); //上横shape.fillRect(x, y+h, h, w0); //下横plot.restore();}this.one = function(x, y, r) {plot.save();var h = r * 0.4; //字半高var w = h / 2.2; //字半宽var w0 = r *0.1; //填充宽//填充//shape.fillRect(x, y, h, w0); //中横//shape.fillRect(x-w, y-w, w0, h); //上左竖shape.fillRect(x+w, y-w, w0, h); //上右竖//shape.fillRect(x-w, y+w, w0, h); //下左竖shape.fillRect(x+w, y+w, w0, h); //下右竖//shape.fillRect(x, y-h, h, w0); //上横//shape.fillRect(x, y+h, h, w0); //下横plot.restore();}this.two = function(x, y, r) {plot.save();var h = r * 0.4; //字半高var w = h / 2.2; //字半宽var w0 = r *0.1; //填充宽//填充shape.fillRect(x, y, h, w0); //中横//shape.fillRect(x-w, y-w, w0, h); //上左竖shape.fillRect(x+w, y-w, w0, h); //上右竖shape.fillRect(x-w, y+w, w0, h); //下左竖//shape.fillRect(x+w, y+w, w0, h); //下右竖shape.fillRect(x, y-h, h, w0); //上横shape.fillRect(x, y+h, h, w0); //下横plot.restore();}this.three = function(x, y, r) {plot.save();var h = r * 0.4; //字半高var w = h / 2.2; //字半宽var w0 = r *0.1; //填充宽//填充shape.fillRect(x, y, h, w0); //中横//shape.fillRect(x-w, y-w, w0, h); //上左竖shape.fillRect(x+w, y-w, w0, h); //上右竖//shape.fillRect(x-w, y+w, w0, h); //下左竖shape.fillRect(x+w, y+w, w0, h); //下右竖shape.fillRect(x, y-h, h, w0); //上横shape.fillRect(x, y+h, h, w0); //下横plot.restore();}this.four = function(x, y, r) {plot.save();var h = r * 0.4; //字半高var w = h / 2.2; //字半宽var w0 = r *0.1; //填充宽//填充shape.fillRect(x, y, h, w0); //中横shape.fillRect(x-w, y-w, w0, h); //上左竖shape.fillRect(x+w, y-w, w0, h); //上右竖//shape.fillRect(x-w, y+w, w0, h); //下左竖shape.fillRect(x+w, y+w, w0, h); //下右竖//shape.fillRect(x, y-h, h, w0); //上横//shape.fillRect(x, y+h, h, w0); //下横plot.restore();}this.five = function(x, y, r) {plot.save();var h = r * 0.4; //字半高var w = h / 2.2; //字半宽var w0 = r *0.1; //填充宽//填充shape.fillRect(x, y, h, w0); //中横shape.fillRect(x-w, y-w, w0, h); //上左竖//shape.fillRect(x+w, y-w, w0, h); //上右竖//shape.fillRect(x-w, y+w, w0, h); //下左竖shape.fillRect(x+w, y+w, w0, h); //下右竖shape.fillRect(x, y-h, h, w0); //上横shape.fillRect(x, y+h, h, w0); //下横plot.restore();}this.six = function(x, y, r) {plot.save();var h = r * 0.4; //字半高var w = h / 2.2; //字半宽var w0 = r *0.1; //填充宽//填充shape.fillRect(x, y, h, w0); //中横shape.fillRect(x-w, y-w, w0, h); //上左竖//shape.fillRect(x+w, y-w, w0, h); //上右竖shape.fillRect(x-w, y+w, w0, h); //下左竖shape.fillRect(x+w, y+w, w0, h); //下右竖shape.fillRect(x, y-h, h, w0); //上横shape.fillRect(x, y+h, h, w0); //下横plot.restore();}this.seven = function(x, y, r) {plot.save();var h = r * 0.4; //字半高var w = h / 2.2; //字半宽var w0 = r *0.1; //填充宽//填充//shape.fillRect(x, y, h, w0); //中横//shape.fillRect(x-w, y-w, w0, h); //上左竖shape.fillRect(x+w, y-w, w0, h); //上右竖//shape.fillRect(x-w, y+w, w0, h); //下左竖shape.fillRect(x+w, y+w, w0, h); //下右竖shape.fillRect(x, y-h, h, w0); //上横//shape.fillRect(x, y+h, h, w0); //下横plot.restore();}this.nine = function(x, y, r) {plot.save();var h = r * 0.4; //字半高var w = h / 2.2; //字半宽var w0 = r *0.1; //填充宽//填充shape.fillRect(x, y, h, w0); //中横shape.fillRect(x-w, y-w, w0, h); //上左竖shape.fillRect(x+w, y-w, w0, h); //上右竖//shape.fillRect(x-w, y+w, w0, h); //下左竖shape.fillRect(x+w, y+w, w0, h); //下右竖shape.fillRect(x, y-h, h, w0); //上横shape.fillRect(x, y+h, h, w0); //下横plot.restore();}this.zero = function(x, y, r) {plot.save();var h = r * 0.4; //字半高var w = h / 2.2; //字半宽var w0 = r *0.1; //填充宽//填充//shape.fillRect(x, y, h, w0); //中横shape.fillRect(x-w, y-w, w0, h); //上左竖shape.fillRect(x+w, y-w, w0, h); //上右竖shape.fillRect(x-w, y+w, w0, h); //下左竖shape.fillRect(x+w, y+w, w0, h); //下右竖shape.fillRect(x, y-h, h, w0); //上横shape.fillRect(x, y+h, h, w0); //下横plot.restore();}/*** @usage   小数点* @author  mw* @date    2016年02月05日  星期五  09:21:38 * @param* @return**/this.dot = function(x, y, r) {plot.save();var h = r * 0.4; //字半高var w = h / 2.2; //字半宽var w0 = r *0.1; //填充宽//填充shape.fillRect(x, y+h, w0, w0); //下横plot.restore();}/*** @usage   负号* @author  mw* @date    2016年02月05日  星期五  09:21:38 * @param* @return**/this.minus = function(x, y, r) {plot.save();var h = r * 0.4; //字半高var w = h / 2.2; //字半宽var w0 = r *0.1; //填充宽//填充shape.fillRect(x, y, h, w0); //中横plot.restore();}/*** @usage   绘制数字* @author  mw* @date    2015年12月01日  星期二  16:50:23 * @param  n [0-9] 要绘制的数字 x, y, 中心点 r 外接圆尺寸* @return**/this.number = function(n, x, y, r) {switch (n) {case 0:case '0': this.zero(x, y, r); break;case 1:case '1': this.one(x, y, r); break;case 2:case '2': this.two(x,y,r); break;case 3:case '3': this.three(x, y, r); break;case 4:case '4': this.four(x,y,r);break;case 5:case '5': this.five(x,y,r);break;case 6:case '6': this.six(x,y,r); break;case 7:case '7': this.seven(x,y,r); break;case 8:case '8': this.eight(x,y,r); break;case 9:case '9': this.nine(x,y,r); break;case '.':this.dot(x,y,r); break;case '-':this.minus(x,y,r); break;default:break;}}}/*** @usage   四则运算竖式* @author  mw* @date    2016年01月07日  星期四  12:36:11 * @param* @return**/function VerticalExpression() {/*** @usage   把一个数字按照基准点右对齐绘制* @author  mw* @date    2016年01月01日  星期五  13:59:42 * @param* @return**/this.rightAlign = function(num, x, y, r) {var s = num.toString();var index = s.indexOf('.');var digitBit = s.length;var digit = new Digit();var xpos=x, ypos=y;var c = '';for (var i = digitBit-1; i > -1; i--) {c = s.charAt(i);if (c!='.') {digit.number(c, xpos, ypos, r);xpos -= r;}else {digit.number(c, xpos+0.5*r, ypos, r);}}}/*** @usage   把一个数字按照基准点左对齐绘制* @author  mw* @date    2016年01月21日  星期四  10:55:07 * @param* @return**/this.leftAlign = function(num, x, y, r) {var s = num.toString();var digitBit = s.length;var digit = new Digit();var xpos=x, ypos=y;var c = '';for (var i = 0; i < digitBit; i++) {c = s.charAt(i);if (c!='.') {digit.number(c, xpos, ypos, r);xpos += r;}else {digit.number(c, xpos-0.5*r, ypos, r);}}}/*** @usage   小数加法竖式* @author  mw* @date    2016年01月21日  星期四  10:49:56 * @param* @return**/this.floatAdd = function(augend, addend, precision, x, y, r) {var decimalPointPos = -1;plot.save().setFillStyle('black');var result = addend + augend;var xBeg = x ? x : 300, yBeg = y ? y :100, r = r ? r : 20;var maxBit = Math.max(addend, augend).toFixed(0).length;var decimalString = '';//整数和小数部分的分解augendDecimalPart = augend > 0 ? augend - Math.floor(augend) : Math.ceil(augend)- augend;addendDecimalPart = addend > 0 ? addend - Math.floor(addend) : Math.ceil(addend)-addend;resultDecimalPart = result > 0 ? result - Math.floor(result) : Math.ceil(result)-result;augend = augend > 0 ? Math.floor(augend) : Math.ceil(augend);addend = addend > 0 ? Math.floor(addend) : Math.ceil(addend);result = result > 0 ? Math.floor(result) : Math.ceil(result);x = xBeg, y = yBeg + r;var plusPos = x - (maxBit+2) * r;this.rightAlign(augend, x, y, r);decimalString = augendDecimalPart.toFixed(precision);decimalPointPos = decimalString.indexOf('.');if (decimalPointPos != -1) {decimalString = decimalString.substr(decimalPointPos+1, precision);augendDecimalPart = parseInt(decimalString);plot.fillText('.', x, y+0.4*r, r);this.leftAlign(augendDecimalPart, x + r, y , r);}y += 1.5 * r;this.rightAlign(addend, x, y, r);decimalString = addendDecimalPart.toFixed(precision);decimalPointPos = decimalString.indexOf('.');if (decimalPointPos != -1) {decimalString = decimalString.substr(decimalPointPos+1, precision);addendDecimalPart = parseInt(decimalString);plot.fillText('.', x, y+0.4*r, r);this.leftAlign(addendDecimalPart, x + r, y , r);}plot.setFont('normal normal normal '+r.toFixed(0)+'px'+ ' arial').fillText('+', plusPos, y+0.4*r, r);y += r;plot.beginPath().moveTo(plusPos - r, y).lineTo(x + (precision+ 2) *r, y).closePath().stroke();y += r;this.rightAlign(result, x, y, r);decimalString = resultDecimalPart.toFixed(precision);decimalPointPos = decimalString.indexOf('.');if (decimalPointPos != -1) {decimalString = decimalString.substr(decimalPointPos+1, precision);resultDecimalPart = parseInt(decimalString);plot.fillText('.', x, y+0.4*r, r);this.leftAlign(resultDecimalPart, x + r, y , r);}plot.restore();}/*** @usage   小数减法竖式* @author  mw* @date    2016年01月21日  星期四  10:49:56 * @param* @return**/this.floatSub = function(minuend, subtrahend, precision, x, y, r) {var decimalPointPos = -1;plot.save().setFillStyle('black');var result = minuend -subtrahend ;var xBeg = x ? x : 300, yBeg = y ? y :100, r = r ? r : 20;var maxBit = Math.max(subtrahend, minuend).toFixed(0).length;var decimalString = '';//整数和小数部分的分解minuendDecimalPart = minuend > 0 ? minuend - Math.floor(minuend) : Math.ceil(minuend)- minuend;subtrahendDecimalPart = subtrahend > 0 ? subtrahend - Math.floor(subtrahend) : Math.ceil(subtrahend)-subtrahend;resultDecimalPart = result > 0 ? result - Math.floor(result) : Math.ceil(result)-result;minuend = minuend > 0 ? Math.floor(minuend) : Math.ceil(minuend);subtrahend = subtrahend > 0 ? Math.floor(subtrahend) : Math.ceil(subtrahend);result = result > 0 ? Math.floor(result) : Math.ceil(result);x = xBeg, y = yBeg + r;var minusPos = x - (maxBit+2) * r;this.rightAlign(minuend, x, y, r);decimalString = minuendDecimalPart.toFixed(precision);decimalPointPos = decimalString.indexOf('.');if (decimalPointPos != -1) {decimalString = decimalString.substr(decimalPointPos+1, precision);minuendDecimalPart = parseInt(decimalString);plot.fillText('.', x, y+0.4*r, r);this.leftAlign(minuendDecimalPart, x + r, y , r);}y += 1.5 * r;this.rightAlign(subtrahend, x, y, r);decimalString = subtrahendDecimalPart.toFixed(precision);decimalPointPos = decimalString.indexOf('.');if (decimalPointPos != -1) {decimalString = decimalString.substr(decimalPointPos+1, precision);subtrahendDecimalPart = parseInt(decimalString);plot.fillText('.', x, y+0.4*r, r);this.leftAlign(subtrahendDecimalPart, x + r, y , r);}plot.setFont('normal normal normal '+r.toFixed(0)+'px'+ ' arial').fillText('-', minusPos, y+0.4*r, r);y += r;plot.beginPath().moveTo(minusPos - r, y).lineTo(x + (precision+ 2) *r, y).closePath().stroke();y += r;this.rightAlign(result, x, y, r);if (result < 0) {plot.fillText('-', minusPos, y+0.2*r, r);}decimalString = resultDecimalPart.toFixed(precision);decimalPointPos = decimalString.indexOf('.');if (decimalPointPos != -1) {decimalString = decimalString.substr(decimalPointPos+1, precision);resultDecimalPart = parseInt(decimalString);plot.fillText('.', x, y+0.4*r, r);this.leftAlign(resultDecimalPart, x + r, y , r);}plot.restore();}/*** @usage   加法竖式* @author  mw* @date    2016年01月01日  星期五  13:59:42 * @param* @return**//*算术竖式Vertical arithmetic加数addend被加数Augend加号Plus*/this.add = function(augend, addend, x, y, r) {plot.save().setFillStyle('black');var result = addend + augend;var xBeg = x ? x : 300, yBeg = y ? y :100, r = r ? r : 20;var maxBit = Math.max(addend, augend).toFixed(0).length;x = xBeg, y = yBeg + r;var plusPos = x - (maxBit+2) * r;this.rightAlign(augend, x, y, r);y += 1.5 * r;this.rightAlign(addend, x, y, r);plot.setFont('normal normal normal '+r.toFixed(0)+'px'+ ' arial').fillText('+', plusPos, y+0.4*r, r);y += r;plot.beginPath().moveTo(plusPos - r, y).lineTo(x + r, y).closePath().stroke();y += r;this.rightAlign(result, x, y, r);plot.restore();}/*** @usage   连加竖式* @author  mw* @date    2016年01月07日  星期四  14:39:43 * @param* @return**/this.continuousAdd = function(taskArray, x, y, r) {plot.save().setFillStyle('black');var array = new Array();array = taskArray;var len = array.length;if (len < 2) return;var result = array[0] + array[1];var xBeg = x ? x : 300, yBeg = y ? y :100, large = r ? r : 20;var maxBit = Math.max(array[0], array[1]).toFixed(0).length;x = xBeg, y = yBeg + r;var plusPos = x - (maxBit+2) * r;this.rightAlign(array[0], x, y, r);y += 1.5 * r;this.rightAlign(array[1], x, y, r);plot.setFont('normal normal normal '+r.toFixed(0)+'px'+ ' arial').fillText('+', plusPos, y+0.4*r, r);y += 0.8 * r;plot.beginPath().moveTo(plusPos - r, y).lineTo(x + r, y).closePath().stroke();y += 1.0 * r;this.rightAlign(result, x, y, r);if (array.length > 2) {for (var i = 2; i < array.length; i++) {maxBit = Math.max(result, array[i]).toFixed(0).length;plusPos = x - (maxBit+2) * r;result += array[i];y += 1.2 * r;this.rightAlign(array[i], x, y, r);plot.fillText('+', plusPos, y+0.4*r, r);y += 0.8 * r;plot.beginPath().moveTo(plusPos - 1 * r, y).lineTo(x + 1 * r, y).closePath().stroke();y += 1.0 * r;this.rightAlign(result, x, y, r);}}}/*** @usage   减法竖式* @author  mw* @date    2016年01月01日  星期五  13:59:42 * @param* @return**//*被减数Minuend减数subtrahend减号Minus sign*/this.sub = function(minuend, subtrahend, x, y, r) {plot.save().setFillStyle('black');var result = minuend - subtrahend;var xBeg = x ? x : 300, yBeg = y ? y :100, large = r ? r : 20;var maxBit = Math.max(minuend, subtrahend).toFixed(0).length;var minusPos = x - (maxBit+2) * r;x = xBeg, y = yBeg+r;this.rightAlign(minuend, x, y, r);y += 1.5*r;this.rightAlign(subtrahend, x, y, r);plot.setFont('normal normal normal '+r.toFixed(0)+'px'+ ' arial').fillText('-', minusPos, y+0.2*r, r);y += 0.8*r;plot.beginPath().moveTo(minusPos -  r, y).lineTo(x + r, y).closePath().stroke();y += 1.0*r;this.rightAlign(result, x, y, r);if (result < 0) {plot.fillText('-', minusPos, y+0.2*r, r);}plot.restore();}/*** @usage   连减竖式* @author  mw* @date    2016年01月07日  星期四  14:39:43 * @param* @return**/this.continuousSub = function(taskArray, x, y, r) {plot.save().setFillStyle('black');var array = new Array();array = taskArray;var len = array.length;if (len < 2) return;var result = array[0] - array[1];var xBeg = x ? x : 300, yBeg = y ? y :100, large = r ? r : 20;var maxBit = Math.max(array[0], array[1]).toFixed(0).length;x = xBeg, y = yBeg + r;var minusPos = x - (maxBit+2) * r;this.rightAlign(array[0], x, y, r);y += 1.5 * r;this.rightAlign(array[1], x, y, r);plot.setFont('normal normal normal '+r.toFixed(0)+'px'+ ' arial').fillText('-', minusPos, y+0.2*r, r);y += 0.8 * r;plot.beginPath().moveTo(minusPos - r, y).lineTo(x + r, y).closePath().stroke();y += 1.0 * r;this.rightAlign(result, x, y, r);if (result < 0) {plot.fillText('-', minusPos, y+0.2*r, r);}if (array.length > 2) {for (var i = 2; i < array.length; i++) {maxBit = Math.max(result, array[i]).toFixed(0).length;minusPos = x - (maxBit+2) * r;result -= array[i];y += 1.0 * r;this.rightAlign(array[i], x, y, r);plot.fillText('-', minusPos, y+0.4*r, r);y += 0.8 * r;plot.beginPath().moveTo(minusPos - 1 * r, y).lineTo(x + 1 * r, y).closePath().stroke();y += 1.0 * r;this.rightAlign(result, x, y, r);if (result < 0) {plot.fillText('-', minusPos, y+0.2*r, r);}}}}/*** @usage   乘法竖式* @author  mw* @date    2016年01月14日  星期四  09:00:33 * @param* @return**//*multiplicand multiplier product*/this.mul = function(multiplicand, multiplier, x, y, r) {plot.save().setFillStyle('black');var result = multiplicand * multiplier;var xBeg = x ? x : 300, yBeg = y ? y :100, r = r ? r : 20;var maxBit = Math.max(multiplicand, multiplier).toFixed(0).length;x = xBeg, y = yBeg + r;var mulPos = x - (maxBit+2) * r;this.rightAlign(multiplicand, x, y, r);y += 1.5 * r;this.rightAlign(multiplier, x, y, r);plot.setFont('normal normal normal '+r.toFixed(0)+'px'+ ' arial').fillText('×', mulPos, y+0.4*r, r);var multiplierArray = new Array();var tmp1 = multiplier;var tmp2 = tmp1 % 10;//记录乘数中有多少位非零var noneZero = 0;while (true) {multiplierArray.push(tmp2);if (tmp2 > 0) noneZero++;tmp1 = (tmp1 - tmp2) / 10;if (tmp1 <= 0) break;tmp2 = tmp1 % 10;}var len = multiplierArray.length;var product = 0;if (noneZero <= 1) {//只有至多一位乘数非零}else {y += r;plot.beginPath().moveTo(mulPos - r, y).lineTo(xBeg + r, y).closePath().stroke();y += r;for (var i = 0; i < len; i++) {if (multiplierArray[i] == 0) {/*if (i == 0) {product = multiplierArray[i] * multiplicand;this.rightAlign(product, x, y, r);y += 1.5*r;}*/}else {product = multiplierArray[i] * multiplicand;this.rightAlign(product, x, y, r);if (i < len-1) {y += 1.5*r;}}x -= r;}}y += r;plot.beginPath().moveTo(mulPos - r, y).lineTo(xBeg + r, y).closePath().stroke();y += r;this.rightAlign(result, xBeg, y, r);plot.restore();}/*** @usage   小数乘法竖式* @author  mw* @date    2016年02月05日  星期五  10:00:29 * @param* @return**//*multiplicand multiplier product*/this.floatMul = function(multiplicand, multiplier, x, y, r) {plot.save().setFillStyle('black');var result = multiplicand * multiplier;var xBeg = x ? x : 300, yBeg = y ? y :100, r = r ? r : 20;var maxBit = Math.max(multiplicand.toString().length, multiplier.toString().length);x = xBeg, y = yBeg + r;var mulPos = x - (maxBit+2) * r;this.rightAlign(multiplicand, x, y, r);y += 1.5 * r;this.rightAlign(multiplier, x, y, r);plot.setFont('normal normal normal '+r.toFixed(0)+'px'+ ' arial').fillText('×', mulPos, y+0.4*r, r);//把被乘数和乘数都变成整数multiplicand = Math.abs(multiplicand);var s = multiplicand.toString();var index = s.indexOf('.');//len为字符串长度，prec1为小数部分位数，maxPrec为允许的最大精度//由于采用了把小数扩大10的精度倍数，做成整数的方法，所以maxPrec不能太大。var len = 0, prec1 = 0, prec2 = 0, maxPrec = 3;if (index > -1) {len = s.length;prec1 = len-1-index;if (prec1 < maxPrec) {multiplicand *= Math.pow(10, prec1);}else {prec1 = maxPrec;multiplicand *= Math.pow(10, prec1);}multiplicand = Math.floor(multiplicand);}//处理乘数multiplier = Math.abs(multiplier);s = multiplier.toString();index = s.indexOf('.');//有小数点if (index > -1) {len = s.length;prec2 = len-1-index;if (prec2 < maxPrec) {multiplier *= Math.pow(10, prec2);}else {prec2 = maxPrec;multiplier *= Math.pow(10, prec2);}//去尾multiplier = Math.floor(multiplier);}var multiplierArray = new Array();var tmp1 = multiplier;var tmp2 = tmp1 % 10;//记录乘数中有多少位非零var noneZero = 0;while (true) {multiplierArray.push(tmp2);if (tmp2 > 0) noneZero++;tmp1 = (tmp1 - tmp2) / 10;if (tmp1 <= 0) break;tmp2 = tmp1 % 10;}var len = multiplierArray.length;var product = 0;if (noneZero <= 1) {//只有至多一位乘数非零}else {y += r;plot.beginPath().moveTo(mulPos - r, y).lineTo(xBeg + r, y).closePath().stroke();y += r;for (var i = 0; i < len; i++) {if (multiplierArray[i] == 0) {/*if (i == 0) {product = multiplierArray[i] * multiplicand;this.rightAlign(product, x, y, r);y += 1.5*r;}*/}else {product = multiplierArray[i] * multiplicand;this.rightAlign(product, x, y, r);if (i < len-1) {y += 1.5*r;}}x -= r;}}y += r;plot.beginPath().moveTo(mulPos - r, y).lineTo(xBeg + r, y).closePath().stroke();y += r;this.rightAlign(result.toFixed(prec1+prec2), xBeg, y, r);plot.restore();}/*** @usage   除法竖式（简便写法）* @author  mw* @date    2016年01月06日  星期三  11:05:09 * @param* @return**/this.div = function(dividend, divisor, xOffset, yOffset, r) {plot.save();/*被除数 dividend除数 divisor商数 quotient余数 remainder*/var lenOfDividend =dividend.toFixed(0).length;var lenOfDivisor = divisor.toFixed(0).length;var quotient = Math.floor(dividend/divisor);var lenOfQuotient = quotient.toFixed(0).length;var remainder = dividend - quotient * divisor;a = [divisor, dividend, quotient, remainder];//除数位置var x0 = xOffset + lenOfDivisor * r, y0= yOffset + 2 * r;//被除数位置var x1 = x0 + r + lenOfDividend * r, y1 = y0;//商位置var x2 = x1, y2 = yOffset;plot.beginPath().bezierCurveTo(x0-r, y0+r, x0-0.5*r, y0+0.5*r, x0-0.2*r, y0-0.5*r, x0, y0-r)/*.moveTo(x0-r, y0+r).lineTo(x0, y0-1*r)*/.closePath().stroke();plot.beginPath().moveTo(x0, y0-1*r).lineTo(x2+r, y0-1*r).closePath().stroke();this.rightAlign(a[0], x0, y0, r);this.rightAlign(a[1], x1, y1, r);this.rightAlign(a[2], x2, y2, r);var tmp1, tmp2, tmp3, x, y;//x, y的初始位置x = x1 - (lenOfQuotient-1) *r, y = y1 + 1.5 * r;if (lenOfQuotient > 1) {for (var i = 0; i < lenOfQuotient; i++) {if (i == 0) {//待减tmp1 = (quotient.toFixed(0)[i] - '0')*divisor;//被减tmp2 = Math.floor(dividend / Math.pow(10, lenOfQuotient-i-2));//减得的差进入下一轮tmp3 = tmp2 - tmp1 * 10;this.rightAlign(tmp1, x, y, r);y += r;plot.beginPath().moveTo(x0, y).lineTo(x1 +r, y).closePath().stroke();y += r;if (tmp3 != 0 && quotient.toFixed(0)[i+1] - '0' > 0) {this.rightAlign(tmp3,x+r, y, r);y += 1.5 * r;}//位置递增x += r;} else if (i < lenOfQuotient-1 ) {//中间轮数tmp1 = (quotient.toFixed(0)[i] - '0')*divisor;tmp3 = tmp3*10 + (dividend.toFixed(0)[i+lenOfDividend-lenOfQuotient+1]-'0')-tmp1*10;if (tmp1 != 0) {this.rightAlign(tmp1, x, y, r);y += r;plot.beginPath().moveTo(x0, y).lineTo(x1 +r, y).closePath().stroke();y += 1.5 * r;}if (tmp3 != 0 && quotient.toFixed(0)[i+1] - '0' > 0) {this.rightAlign(tmp3,x+r, y, r);y += 1.5 * r;}x += r;}else {//最后一轮tmp1 = (quotient.toFixed(0)[i] - '0')*divisor;if (tmp1 != 0) {this.rightAlign(tmp1, x, y, r);y += r;plot.beginPath().moveTo(x0, y).lineTo(x1 +r, y).closePath().stroke();y += r;} else {y -= 0.5 * r;}this.rightAlign(a[3],x, y, r);}}}else {//最后一轮tmp1 = quotient*divisor;this.rightAlign(tmp1, x, y, r);plot.moveTo(x0, y+r).lineTo(x1 +r, y+r).stroke();plot.beginPath().moveTo(x0, y+r).lineTo(x1 +r, y+r).closePath().stroke();this.rightAlign(a[3],x, y+2*r, r);}}}</span>

<span style="font-size:18px;">def tmp():    import math;    d = 6.3;    price = 0;    if (d <= 3):        price = y;    else:        price = 7 + math.ceil(d-3)*1.5;    print(price);    return;</span>

<span style="font-size:18px;">def tmp():    import math;    d = 8+29/60;    price = 0;    if (d <= 3):        price = 0.22;    else:        price = 0.22 + math.ceil(d-3)*0.11;    print(price);    return;def tmp(d, local):    import math;    price = 0;    if local:               if (d <= 100):            price = math.ceil(d/20)*0.80;        else:            price = 100/20*0.80 + math.ceil((d-100)/100)*1.20;    else:        if (d <= 100):            price = math.ceil(d/20)*1.20;        else:            price = 100/20*1.20 + math.ceil((d-100)/100)*2.00;    print(price);    return;if __name__ == '__main__':    tmp(135, 1);    tmp(262, 0);</span>

本节到此结束，欲知后事如何，请看下回分解。