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<!DOCTYPE HTML>
<html lang="zh-CN">
<head><meta name="generator" content="Hexo 3.9.0">
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<meta name="keywords" content="K-进制数, IT学习">
<meta name="description" content=" K-&#x8FDB;&#x">
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<body>
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<script>
window.requestAnimationFrame = (function(){
return window.requestAnimationFrame ||
window.webkitRequestAnimationFrame ||
window.mozRequestAnimationFrame ||
function( callback ){
window.setTimeout( callback, 1000/2 );
};
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var myCanvas = document.getElementById("canvas111");
var ctx = myCanvas.getContext("2d");//getContext 设置画笔
var num;
var w,h;
var duixiang = [];
var move = {};
function widthheight(){
w = myCanvas.width = window.innerWidth;
h = myCanvas.height = window.innerHeight;
num= Math.floor(w*h*0.0001);
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cX:Math.random()*0.6-0.3,
cY:Math.random()*0.6-0.3,
R:Math.floor(Math.random()*5)+2,
//CC:Math.floor(Math.random()*3)+2,
r: Math.floor(Math.random() * 254),
g: Math.floor(Math.random() * 254),
b:Math.floor(Math.random() * 254)
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// console.log(duixiang[i])
Cricle(duixiang[i].x,duixiang[i].y,duixiang[i].R,duixiang[i].r,duixiang[i].g,duixiang[i].b);
//Cricle(duixiang[i].x,duixiang[i].y,duixiang[i].R,duixiang[i].CC);
}
};widthheight();//获取浏览器的等宽度等高
function Cricle(x,y,R,r,g,b){
ctx.save();//保存路径
if(Math.random()>0.991) {ctx.globalAlpha= 0.9;}//ctx.fillStyle = "#CCC";}//填充的背景颜色
else { ctx.globalAlpha=0.47;}
ctx.fillStyle = "rgb("+ r +","+ g +","+ b +")";
ctx.beginPath();//开始绘画
ctx.arc(x,y,R,Math.PI*2,0);//绘画圆 x y 半径（大小） 角度 一个PI 是180 * 2 = 360 真假 0/1 true/false
ctx.closePath();//结束绘画
ctx.fill();//填充背景颜色
ctx.restore();//回复路径
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!function draw(){
ctx.clearRect(0,0,w,h)//先清除画布上的点
for(var i = 0;i < num;i++){
duixiang[i].x += duixiang[i].cX;
duixiang[i].y += duixiang[i].cY;
if(duixiang[i].x>w || duixiang[i].x<0){
duixiang[i].cX = -duixiang[i].cX;
}
if(duixiang[i].y>h || duixiang[i].y<0){
duixiang[i].cY = -duixiang[i].cY;
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Cricle(duixiang[i].x,duixiang[i].y,duixiang[i].R,duixiang[i].r,duixiang[i].g,duixiang[i].b);
//勾股定理判断两点是否连线
for(var j = i + 1;j < num;j++){
if( (duixiang[i].x-duixiang[j].x)*(duixiang[i].x-duixiang[j].x)+(duixiang[i].y-duixiang[j].y)*(duixiang[i].y-duixiang[j].y) <= 55*55 ){
line(duixiang[i].x,duixiang[i].y,duixiang[j].x,duixiang[j].y,0,i,j)
}
if(move.x){
if( (duixiang[i].x-move.x)*(duixiang[i].x-move.x)+(duixiang[i].y-move.y)*(duixiang[i].y-move.y) <= 100*100 ){
line(duixiang[i].x,duixiang[i].y,move.x,move.y,1,i,1)
}
}
}
}
window.requestAnimationFrame(draw)
}();
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ctx.globalAlpha=0.5;
color.addColorStop(0,"rgb("+ duixiang[i].r +","+ duixiang[i].g +","+ duixiang[i].b +")");
color.addColorStop(0.8,"#019ee5");
}
else
{
var color = ctx.createLinearGradient(x1,y1,x2,y2);
ctx.globalAlpha=0.9;
color.addColorStop(0,"rgb("+ duixiang[i].r +","+ duixiang[i].g +","+ duixiang[i].b +")");
color.addColorStop(1,"rgb("+ duixiang[j].r +","+ duixiang[j].g +","+ duixiang[j].b +")");
}
ctx.save();
ctx.strokeStyle = color;
ctx.lineWidth = 0.5;
ctx.beginPath();
ctx.moveTo(x1,y1);
ctx.lineTo(x2,y2);
ctx.stroke();
//ctx.restore();
}
//document.onmousemove = function(e){
// move.x = e.clientX;
// move.y = e.clientY;
//}
//console.log(move)
/*window.onresize = function(){
location.reload();
}*/
</script>
<style>
#canvas1 {
position: fixed;
pointer-events:none;//鼠标多层响应事件
// background: #ccc;
/*透明度*/
width: 100%;
height: 100%;
// opacity: 0;
overflow: auto;
z-index: 999;
}
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{ for (var i = 0; i < props.length; i++)
{var descriptor = props[i];descriptor.enumerable = descriptor.enumerable || false;descriptor.configurable = true;if ("value" in descriptor)
descriptor.writable = true;Object.defineProperty(target, descriptor.key, descriptor);}}
return function (Constructor, protoProps, staticProps)
{if (protoProps) defineProperties(Constructor.prototype, protoProps);
if (staticProps) defineProperties(Constructor, staticProps);
return Constructor;};}();function _classCallCheck(instance, Constructor)
{if (!(instance instanceof Constructor)) {throw new TypeError("Cannot call a class as a function");}}
var getRandom = function getRandom(min, max) {
return Math.random() * (max - min) + min;
};
var getRandomInt = function getRandomInt(min, max) {
return Math.floor(Math.random() * (max - min)) + min;
};
var getRandomColor = function getRandomColor() {
var colors = [
'rgba(231, 76, 60, 1)', // red
'rgba(241, 196, 15, 1)', // yellow
'rgba(46, 204, 113, 1)', // green
'rgba(52, 152, 219, 1)', // blue
'rgba(155, 89, 182, 1)' // purple
];
return colors[getRandomInt(0, colors.length)];
};
// Particle//粒子模块
var
Particle = function () {
function Particle(system, x, y) {_classCallCheck(this, Particle);
this.system = system;
this.universe = this.system.world.universe;
this.x = x;
this.y = y;
this.color = getRandomColor();
this.life = 1;
this.aging = getRandom(0.990, 0.999); // 0.99, 0.999 || 0.999, 0.9999
this.r = getRandomInt(12, 16);//初始粒子半径范围
this.speed = getRandom(18, 18.5);//粒子爆炸速度范围
this.velocity = [
getRandom(-this.speed, this.speed),
getRandom(-this.speed, this.speed)];
}_createClass(Particle, [{ key: 'update', value: function update(
dt) {
this.life *= this.aging;
if (
this.r < 0.1 ||
this.life === 0 ||
this.x + this.r < 0 ||
this.x - this.r > this.universe.width ||
this.y + this.r < 0 ||
this.y - this.r > this.universe.height)
{
this.system.removeObject(this);
}
this.r *= this.life;
this.x += this.velocity[0];
this.y += this.velocity[1];
} }, { key: 'render', value: function render(
ctx) {
// Main circle //亮圈模块
ctx.fillStyle = this.color;
ctx.beginPath();
ctx.arc(this.x, this.y, this.r*1.2, 0, 2 * Math.PI, false);
ctx.fill();
ctx.closePath();
var r = this.color.match(/([0-9]+)/g)[0];
var g = this.color.match(/([0-9]+)/g)[1];
var b = this.color.match(/([0-9]+)/g)[2];
// Gradient//梯度变化曲线
var spread = 1.5;
var gradient = ctx.createRadialGradient(
this.x, this.y, this.r,
this.x, this.y, this.r * spread);
gradient.addColorStop(0, 'rgba(' + r + ', ' + g + ', ' + b + ', 0.5)');
gradient.addColorStop(1, 'rgba(' + r + ', ' + g + ', ' + b + ', 0)');
ctx.globalCompositeOperation = 'lighter';
ctx.fillStyle = gradient;
ctx.beginPath();
ctx.arc(this.x, this.y, this.r * spread, 0, 2 * Math.PI, false);
ctx.fill();
ctx.closePath();
ctx.globalCompositeOperation = 'source-over';
// Aberration//偏差
var offset = this.r * 0.5;
var color = 'rgba(' + g + ', ' + b + ', ' + r + ', 0.5)';
ctx.globalCompositeOperation = 'lighter';
ctx.fillStyle = color;
ctx.beginPath();
ctx.arc(this.x + offset, this.y + offset, this.r, 0, 2 * Math.PI, false);
ctx.fill();
ctx.closePath();
ctx.globalCompositeOperation = 'source-over';
} }]);return Particle;}();
// Crown //水波纹圈模块
var
Crown = function () {
function Crown(system, x, y) {_classCallCheck(this, Crown);
this.system = system;
this.x = x;
this.y = y;
this.r = getRandomInt(5, 15); // 5, 20 水波纹圈半径范围
this.mod = 1.1;
this.life = 0.5; //水波纹线
this.aging = getRandom(0.830, 0.899);
this.speed = getRandom(8, 9);
this.color = {
r: getRandomInt(236, 242),
g: getRandomInt(70, 80),
b: getRandomInt(50, 70) };
this.angle1 = Math.PI * getRandom(0, 2);
this.angle2 = this.angle1 + Math.PI * getRandom(0.3, 0.4);//水波纹圈完整度
}_createClass(Crown, [{ key: 'update', value: function update(
dt) {
this.life *= this.aging;
if (this.life <= 0.0001) this.system.removeObject(this);
this.r += Math.abs(1 - this.life) * this.speed;
this.x1 = this.x + this.r * Math.cos(this.angle1);
this.y1 = this.y + this.r * Math.sin(this.angle1);
this.angle3 = this.angle1 + (this.angle2 - this.angle1) / 2;
this.x2 = this.x + this.r * this.mod * Math.cos(this.angle3);
this.y2 = this.y + this.r * this.mod * Math.sin(this.angle3);
} }, { key: 'render', value: function render(
ctx) {
var gradient = ctx.createRadialGradient(
this.x, this.y, this.r * 0.9,
this.x, this.y, this.r);
gradient.addColorStop(0, 'rgba(' + this.color.r + ', ' + this.color.g + ', ' + this.color.b + ', ' + this.life + ')');
gradient.addColorStop(1, 'rgba(' + this.color.r + ', ' + this.color.g + ', ' + this.color.b + ', ' + this.life * 0.5 + ')');
ctx.fillStyle = gradient;
ctx.beginPath();
ctx.arc(this.x, this.y, this.r, this.angle1, this.angle2, false);
ctx.quadraticCurveTo(this.x2, this.y2, this.x1, this.y1);
ctx.fill();
ctx.closePath();
} }]);return Crown;}();
// Explosion //爆炸模块
var
Explosion = function () {
function Explosion(world, x, y) {_classCallCheck(this, Explosion);
this.world = world;
this.x = x;
this.y = y;
this.objects = [];
var particles = getRandomInt(10, 30); // 10, 30 amount of particles//爆炸 粒子数量
var crowns = particles * getRandom(0.4, 0.5);
while (crowns-- > 0) {this.addCrown();}
while (particles-- > 0) {this.addParticle();}
}_createClass(Explosion, [{ key: 'update', value: function update(
dt) {
this.objects.forEach(function (obj) {
if (obj) obj.update(dt);
});
if (this.objects.length <= 0) {
this.world.clearExplosion(this);
}
} }, { key: 'render', value: function render(
ctx) {
this.objects.forEach(function (obj) {
if (obj) obj.render(ctx);
});
} }, { key: 'addCrown', value: function addCrown()
{
this.objects.push(new Crown(this, this.x, this.y));
} }, { key: 'addParticle', value: function addParticle()
{
this.objects.push(new Particle(this, this.x, this.y));
} }, { key: 'removeObject', value: function removeObject(
obj) {
var index = this.objects.indexOf(obj);
if (index !== -1) {
this.objects.splice(index, 1);
}
} }]);return Explosion;}();
// World
var
ConfettiWorld = function () {function ConfettiWorld()
{_classCallCheck(this, ConfettiWorld);}_createClass(ConfettiWorld, [{ key: 'init', value: function init()
{
this.objects = [];
window.addEventListener('click', this.explode.bind(this));
// Initial explosion //初始爆炸
var counter = 0;
while (counter-- > 0) {
this.explode({
clientX: window.event.clientX, //getRandomInt(10, this.universe.width) , //this.universe.width / 2,
clientY: window.event.clientY //getRandomInt(10, 50) //this.universe.height / 2
});
}
} }, { key: 'update', value: function update(
dt) {
this.objects.forEach(function (obj) {
if (obj) obj.update(dt);
});
var amount = this.objects.reduce(function (sum, explosion) {
return sum += explosion.objects.length;
}, 0);
} }, { key: 'render', value: function render(
ctx) {
this.objects.forEach(function (obj) {
if (obj) obj.render(ctx);
});
} }, { key: 'explode', value: function explode(
event) {
var x = event.clientX;
var y = event.clientY;
this.objects.push(new Explosion(this, x, y));
} }, { key: 'clearExplosion', value: function clearExplosion(
explosion) {
var index = this.objects.indexOf(explosion);
if (index !== -1) {
this.objects.splice(index, 1);
}
} }]);return ConfettiWorld;}();
// Time
var
Time = function () {
function Time() {_classCallCheck(this, Time);
this.now = 0; // current tick time
this.prev = 0; // prev tick time
this.elapsed = 0; // elapsed time from last tick
this.delta = 0; // time from last update
this.fps = 60; // desired fps
this.step = 1 / 60; // step duration
}_createClass(Time, [{ key: 'update', value: function update(
time) {
this.now = time;
this.elapsed = (this.now - this.prev) / 1000;
this.prev = this.now;
this.delta += this.elapsed;
} }, { key: 'raf', value: function raf(
func) {
window.requestAnimationFrame(func);
} }, { key: 'hasFrames', value: function hasFrames()
{
return this.delta >= this.step;
} }, { key: 'processFrame', value: function processFrame()
{
this.delta -= this.step;
} }]);return Time;}();
// Canvas
var
Universe = function () {
function Universe(element) {_classCallCheck(this, Universe);
this.el = element;
this.ctx = this.el.getContext('2d');
this.pixelRatio = window.devicePixelRatio;
this.time = new Time();
this.worlds = {};
this.world = null; // current state
this.updateSize();
window.addEventListener('resize', this.updateSize.bind(this));
this.addWorld('confetti', ConfettiWorld);
this.setWorld('confetti');
this.start();
}_createClass(Universe, [{ key: 'start', value: function start()
{
this.time.raf(this.tick.bind(this));
} }, { key: 'tick', value: function tick(
time) {
this.time.update(time);
if (this.time.hasFrames()) {
this.update();
this.time.processFrame();
}
this.render();
this.time.raf(this.tick.bind(this));
} }, { key: 'update', value: function update()
{
this.world.update(this.time.step);
} }, { key: 'render', value: function render()
{
var gradient = this.ctx.createLinearGradient(0, 0, this.width, this.height);
// gradient.addColorStop(0, '#34495e');
//gradient.addColorStop(1, '#2c3e50');
this.ctx.clearRect(0, 0, this.width, this.height);
// this.ctx.fillStyle = '#2c3e50'
// //this.ctx.fillStyle = gradient;
// // this.ctx.fillRect(0, 0, this.width, this.height);
this.world.render(this.ctx);
}
// Helpers 库
}, { key: 'updateSize', value: function updateSize()
{
this.width = window.innerWidth;
this.height = window.innerHeight;
this.el.width = this.width * this.pixelRatio;
this.el.height = this.height * this.pixelRatio;
this.el.style.width = window.innerWidth + 'px';
this.el.style.height = window.innerHeight + 'px';
this.ctx.scale(this.pixelRatio, this.pixelRatio);
} }, { key: 'addWorld', value: function addWorld(
worldName, World) {
this.worlds[worldName] = new World();
this.worlds[worldName].universe = this;
this.worlds[worldName].init();
} }, { key: 'setWorld', value: function setWorld(
worldName) {
this.world = this.worlds[worldName];
} }]);return Universe;}();
// Main
console.clear();
var element = document.querySelector('#canvas1');
window.Canvas= new Universe(element);</script>
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K-进制数
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<p> </p> <blockquote> <h1 style="margin-left: 0.0px;"><span style="color: rgb(51,51,51);"><strong><span style="color: rgb(51,51,51);"> K-进制数</span></strong></span></h1> <h3><span style="color: rgb(51,51,51);"><strong><span style="color: rgb(102,102,102);">题目描述</span></strong></span></h3> <h3 style="margin-left: 0.0px;"><span style="color: rgb(51,51,51);">考虑包含N位数字的K-进制数. 定义一个数有效, 如果其K-进制表示不包含两连续的0.</span></h3> <h3 style="margin-left: 0.0px;"><span style="color: rgb(51,51,51);">考虑包含N位数字的K-进制数. 定义一个数有效, 如果其K-进制表示不包含两连续的0. <br><br> 例: <br> 1010230 是有效的7位数 <br> 1000198 无效 <br> 0001235 不是7位数, 而是4位数. <br><br> 给定两个数N和K, 要求计算包含N位数字的有效K-进制数的总数. <br><br> 假设2 <= K <= 10; 2 <= N; 4 <= N+K <= 18.</span></h3> <h3><span style="color: rgb(51,51,51);"><strong><span style="color: rgb(102,102,102);">输入</span></strong></span></h3> <h3 style="margin-left: 0.0px;"><span style="color: rgb(51,51,51);">两个十进制整数N和K</span></h3> <h3 style="margin-left: 0.0px;"><span style="color: rgb(51,51,51);"> 2</span></h3> <h3 style="margin-left: 0.0px;"><span style="color: rgb(51,51,51);">10</span></h3> <h3><span style="color: rgb(51,51,51);"><strong><span style="color: rgb(102,102,102);">输出</span></strong></span></h3> <h3 style="margin-left: 0.0px;"><span style="color: rgb(51,51,51);">十进制表示的结果</span></h3> <h3 style="margin-left: 0.0px;"><span style="color: rgb(51,51,51);"> 90</span></h3> <h3><span style="color: rgb(51,51,51);"><strong><span style="color: rgb(102,102,102);">样例输入</span></strong></span></h3> <h3><span style="color: rgb(51,51,51);"><strong><span style="color: rgb(102,102,102);">样例输出</span></strong></span></h3> </blockquote> <p> </p> <p> </p> <p>根据题意，要知道 N 位K 进制并且 不能有连续两个0出现 还有首位不能为0 的限制条件。</p> <p> 本着<span style="color: rgb(243,59,69);">由简到难</span>的思想 ：</p> <p> 假设是让你求 1位 K 进制的满足条件的数，那么满足条件的数则有 1，2，3…..K-1 一共K-1个数对吧，</p> <p>我们记作 <span style="color: rgb(51,153,234);">res_1=K-1,</span>那么不满足条件的数 只有 0 ，一共1个数 ，我们记作<span style="color: rgb(51,153,234);">res_0=1。</span></p> <p> </p> <p> 假设是让你求 2位 K 进制的满足条件的数，那么先考虑首位（也就是第2位），可以填的数为除去0的其他数，</p> <p>有 1，2，3…..K-1 一共K-1个数对吧，而这第二位可以填的数 可以和第一位的所有数搭配，</p> <p>以1为例，有 11，12，13,…..1(K-1),还有在第一位不满足条件的 0 搭配 10，也是满足条件的数，</p> <p>所以2位K进制满足条件的数res_1=（K-1）<em>(K-1+1),即<span style="color: rgb(51,153,234);"> res_1=(K-1)</span></em>（res_1+res_0）,对吧，</p> <p>再来看不满足条件的数 即 首位为0的 有 01，02，03…..0（K-1）,一共有K-1个也就是res_0=K-1,即 <span style="color: rgb(51,153,234);">res_0=res_1</span>(上一个)。</p> <p><span style="color: rgb(243,59,69);">第一位满足条件的数res_1对吧,因为不能连0 ，虽然00也是不满足，但是 00这种情况是绝对不满足，</span></p> <p><span style="color: rgb(243,59,69);">而首位不满足的情况是相对不满足，绝对和相对 懂吧。</span></p> <p> </p> <p> 那么继续，假设是让你求 3位 K 进制的满足条件的数，同样先考虑首位（也就是第3位），</p> <p>可以填的数为除去0的其他数，有 1，2，3…..K-1 一共K-1个数对吧，而这第3位可以填的数 </p> <p>可以和2位K进制满足条件和（相对）不满足条件的数搭配，即<span> res_1=（K-1）<em>[(K-1)</em>(K-1+1)+(K-1)],</span></p> <p>即<span style="color: rgb(51,153,234);"> res_1=(K-1)<em>(res_1+res_0),</em></span>不满足条件的数则是可以和2位K进制满足条件的数搭配，</p> <p>res_0=（k-1）(K-1+1),即<span style="color: rgb(51,153,234);">res_0=res_1。</span></p> <p> 后面的位数就以此类推，再看看图解。</p> <p><img src="logo-loading1.png" data-original="https://uploadfiles.nowcoder.com/images/20190720/683055227_1563577305845_5A2F10B571AD4B7A6665FFBD7D0E0A19"></p> <p> </p> <p>AC代码：</p>