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recursion_fibonacci.html
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recursion_fibonacci.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="stylesheet" href="css/prism.css">
<style>
html,
body {
box-sizing: border-box;
margin: 0;
padding: 0;
height: 100%;
font-size: 12px;
}
body {
min-height: 500px;
}
section {
display: flex;
flex-wrap: wrap;
}
.code {
margin-top: 3px;
}
pre[class*=language-] {
margin: 0;
padding: 0;
}
main {
border-top: 2px solid #ccc;
width: 100%;
height: 65%;
min-height: 200px;
}
</style>
<title>斐波那契数列</title>
</head>
<body>
<section class="frames"></section>
<section style="display: none;">
<pre><code class="language-java">int factorial(int n) {
if (n == 1) {
return 1;
}
return n * factorial(n - 1);
}</code></pre>
</section>
<main></main>
<section>
<div style='background-color:#00FF99; margin: 2px 2px 0 0; padding: 4px 6px;'>进行中</div>
<div style='background-color:#ccc; margin: 2px 2px 0 0; padding: 4px 6px;'>已结束</div>
</section>
<div style='margin: 2px 2px 0 0; padding: 4px 6px;'>
<span>n </span><input type="text" id='n' class="saveable" value="5">
<span>动画速度(ms) </span><input type="number" step="100" value="300" id="animate_speed" class="saveable">
<input style='font-size:12px;' type="button" value="保存" onclick="onSave('fibonacci')">
<input style='font-size:12px;' type="button" value="显示重复" onclick="showDuplicate()">
<input type="checkbox" id="enable_cache" class="saveable bool"> 记忆化
</div>
<script src="js/p5.js"></script>
<script src="js/p5-svg.js"></script>
<script src="js/util.js"></script>
<script src="js/prism.js"></script>
<script>
/*
时间复杂度计算公式 ==> 2*f(n+1)-1
t(0) = 1
t(1) = 1
t(2) = t(0) + t(1) + 1 = 3 2*f(3)-1
t(3) = t(1) + t(2) + 1 = 5 2*f(4)-1
t(4) = t(2) + t(3) + 1 = 9 2*f(5)-1
t(5) = t(3) + t(4) + 1 = 15 2*f(6)-1
t(6) = t(4) + t(5) + 1 = 25 2*f(7)-1
...
通项公式计算
f(0) = (1.618^0 - 0.618^0) / 2.236 = 0
f(1) = (1.618^1 + 0.618^1) / 2.236 = 1
f(2) = (1.618^2 - 0.618^2) / 2.236 = 1
f(3) = (1.618^3 + 0.618^3) / 2.236 = 2
f(4) = (1.618^2 - 0.618^4) / 2.236 = 3
... 随着n增大, 后面0.618所在的项越来越不重要, 可以忽略
f(7) = (1.618^7 ...) / 2.236 = 13
*/
const colorMap = new Map()
const colorArray = ['#1abc9c', '#e67e22', '#3498db', '#f1c40f', '#9b59b6', '#e74c3c']
let colorIndex = 0
function showDuplicate() {
d.add({ cloned: clone(tree) }, ({ cloned }) => {
recursion(cloned, width / 2, DIAMETER, n - 1, 0, 0)
})
d.updateFrameButtons()
}
function recursion(node, x, y, deep, px, py) {
if (node) {
if (node.txt) {
if (px && py) {
stroke('white')
line(x, y, px, py)
noStroke()
}
}
recursion(node.left, x - Math.pow(2, deep) * DIAMETER / 4, y + Math.pow(2, n - deep) * DIAMETER / 4, deep - 1, x, y)
recursion(node.right, x + Math.pow(2, deep) * DIAMETER / 4, y + Math.pow(2, n - deep) * DIAMETER / 4, deep - 1, x, y)
if (node.txt) {
let c = colorMap.get(node.txt)
if (!c) {
colorMap.set(node.txt, colorArray[colorIndex++])
}
fill(colorMap.get(node.txt))
circle(x, y, DIAMETER)
fill('black')
text(node.txt, x, y + 3)
}
}
}
const options = loadOptionsFromStorage('fibonacci')
const DIAMETER = 25 // 直径 diameter
const RECT_WIDTH = 30 // 矩形宽度、圆直径
const RECT_HEIGHT = 20 // 值矩形高度
const SPACING = 1 // 间隙
const INDEX_RECT_HEIGHT = 20 // 索引矩形高度
const n = options.n
const d = new Draw(options.animate_speed)
const enable_cache = options.enable_cache
function preload() {
// const font = loadFont('JetBrainsMono-Regular.ttf')
}
function setup() {
const WIN_WIDTH = document.querySelector('main').clientWidth
const WIN_HEIGHT = document.querySelector('main').clientHeight
const FONT_SIZE = 10
createCanvas(WIN_WIDTH, WIN_HEIGHT, SVG)
textSize(FONT_SIZE)
textAlign(CENTER)
d.add({}, frame)
fibonacci(n, tree)
d.updateFrameButtons()
noStroke()
}
function draw() {
d.draw(() => background('#2d2d2d'))
}
function frame({ cloned, array: cache }) {
drawTree(cloned, width / 2, DIAMETER, n - 1, 0, 0)
if (enable_cache) {
const LEFT = (width - cache.length * (RECT_WIDTH + SPACING)) / 2
for (let i = 0; i < cache.length; i++) {
// 注：矩形以左下角 x, y 作为起点坐标
let x = LEFT + i * (RECT_WIDTH + SPACING)
let y = height - (SPACING + INDEX_RECT_HEIGHT)
stroke(255)
noStroke()
fill('#67cdcc')
rect(x, y, RECT_WIDTH, -RECT_HEIGHT)
fill('#ffffff')
text(cache[i], x + RECT_WIDTH / 2, y - 6)
fill('#cc99cd')
rect(x, height, RECT_WIDTH, -INDEX_RECT_HEIGHT)
fill('#ffffff')
text(`f(${i})`, x + RECT_WIDTH / 2, height - 6)
}
}
}
function drawTree(node, x, y, deep, px, py) {
if (node) {
if (node.txt) {
if (px && py) {
stroke('white')
line(x, y, px, py)
noStroke()
}
}
drawTree(node.left, x - Math.pow(2, deep) * DIAMETER / 4, y + Math.pow(2, n - deep) * DIAMETER / 4, deep - 1, x, y)
drawTree(node.right, x + Math.pow(2, deep) * DIAMETER / 4, y + Math.pow(2, n - deep) * DIAMETER / 4, deep - 1, x, y)
if (node.txt) {
if (node.done) {
fill('#ccc')
} else {
fill('#00FF99')
}
circle(x, y, DIAMETER)
fill('black')
text(node.txt, x, y + 3)
}
}
}
const tree = { done: false }
const cache = []
cache[0] = 0
cache[1] = 1
function fibonacci(n, t) {
t.txt = `f(${n})`
// console.log('去', clone(tree))
d.add({ cloned: clone(tree), array: cache }, frame)
if (enable_cache && cache[n] !== undefined) {
t.done = true
d.add({ cloned: clone(tree), array: cache }, frame)
return cache[n]
}
if (n == 0) {
t.done = true
// console.log('回', n, clone(tree))
d.add({ cloned: clone(tree), array: cache }, frame)
return 0
}
if (n == 1) {
t.done = true
// console.log('回', n, clone(tree))
d.add({ cloned: clone(tree), array: cache }, frame)
return 1
}
t.left = { done: false }
t.right = { done: false }
const l = fibonacci(n - 1, t.left)
const r = fibonacci(n - 2, t.right)
const m = l + r
t.done = true
// d.add({ cloned: clone(tree), array:cache }, frame)
if (enable_cache) {
cache[n] = m
}
d.add({ cloned: clone(tree), array: cache }, frame)
// console.log('回', n, clone(tree))
return m
}
function clone(tree) {
return JSON.parse(JSON.stringify(tree))
}
</script>
</body>
</html>