机器小伟在工程师阿伟的指导下，深入研究小数乘法，通过改进数字表示方式，实现任意小数范围内的精确计算。通过实例展示了小桶装水问题的解决方法，揭示了看似简单的数学原理背后的巧妙应用。
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]。
用图示可以看得更清楚：
本节到此结束，欲知后事如何，请看下回分解。
[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>
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1
3次小桶, -1次大桶， 得到1
-5次小桶, 2次大桶， 得到2
6次小桶, -2次大桶， 得到2
-2次小桶, 1次大桶， 得到3
9次小桶, -3次大桶， 得到3
-10次小桶, 4次大桶， 得到4
1次小桶, 0次大桶， 得到4
-7次小桶, 3次大桶， 得到5
4次小桶, -1次大桶， 得到5
-4次小桶, 2次大桶， 得到6
7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8
2次小桶, 0次大桶， 得到8
-6次小桶, 3次大桶， 得到9
5次小桶, -1次大桶， 得到9
-3次小桶, 2次大桶， 得到10
8次小桶, -2次大桶， 得到10
0次小桶, 1次大桶， 得到11
-8次小桶, 4次大桶， 得到12
3次小桶, 0次大桶， 得到12
-5次小桶, 3次大桶， 得到13
6次小桶, -1次大桶， 得到13
-2次小桶, 2次大桶， 得到14
9次小桶, -2次大桶， 得到14
-10次小桶, 5次大桶， 得到15
1次小桶, 1次大桶， 得到15
def 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() {
//8
this.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。
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