O（1）带有GetMax和GetMin的JavaScript循环缓冲区
所以我一直在搜索网络，想找到一种方法来实现这一点，但我发现没有一种方法符合我们所寻找的确切解决方案 我有一个应用程序，它将浮点数存储在循环缓冲区中。循环缓冲区类可以在这里找到 在我的应用程序中，每隔几毫秒就会有新的数字出现，缓冲区可以容纳大约60K的值 为了解决这个问题，我创建了一个10的循环缓冲区，其中包含100个随机生成的数字流，以模拟传入的数据。这是生成模拟流的线：O（1）带有GetMax和GetMin的JavaScript循环缓冲区,javascript,time-complexity,max,min,circular-buffer,Javascript,Time Complexity,Max,Min,Circular Buffer,所以我一直在搜索网络，想找到一种方法来实现这一点，但我发现没有一种方法符合我们所寻找的确切解决方案 我有一个应用程序，它将浮点数存储在循环缓冲区中。循环缓冲区类可以在这里找到 在我的应用程序中，每隔几毫秒就会有新的数字出现，缓冲区可以容纳大约60K的值 为了解决这个问题，我创建了一个10的循环缓冲区，其中包含100个随机生成的数字流，以模拟传入的数据。这是生成模拟流的线： for (let i = 0; i < valuesToEnqueueForDemoPurposes.length;
for (let i = 0; i < valuesToEnqueueForDemoPurposes.length; i++) {
for（设i=0；istats = require("stats-lite");
var CircularBuffer = require("circular-buffer");
var circularBuffer10 = new CircularBuffer(10);
var valuesToEnqueueForDemoPurposes = Array.from(Array(100)).map(x=>Math.random() * 1000)
for (let i = 0; i < valuesToEnqueueForDemoPurposes.length; i++) {
var newValue = valuesToEnqueueForDemoPurposes[i];
circularBuffer10.enq(newValue);
let valuesArray = circularBuffer10.toarray();
var maxIndex = valuesArray.reduce((iMax, x, i, arr) => x > arr[iMax] ? i : iMax, 0);
var minIndex = valuesArray.reduce((iMin, x, i, arr) => x < arr[iMin] ? i : iMin, 0);
var max = valuesArray[maxIndex];
var min = valuesArray[minIndex];
var standardDeviation = stats.stdev(valuesArray);
console.log(maxIndex);
console.log(max);
console.log(minIndex);
console.log(min);
console.log(standardDeviation + "\n\n");
}
stats=require（“stats-lite”）；
var CircularBuffer=需要（“循环缓冲”）；
var CircularBuffer 10=新的CircularBuffer（10）；
var valuesToEnqueueForDemoPurposes=Array.from（Array（100））.map（x=>Math.random（）*1000）
for（设i=0；ix>arr[iMax]？i:iMax，0）；
var minIndex=值ray.reduce（（iMin，x，i，arr）=>x - N个项目的队列
- 用于跟踪最小/最大项的最小/最大堆
- 跟踪每个项目频率的哈希映射
也发现了这个C++解决方案，但它只适用于正常队列，最大值（不min），并且我不能在JavaScript中复制：
有人知道，对于这种类型的场景（有或没有循环缓冲区），使用任何数据结构组合，是否有可能在O（1）中找到最大值或最小值？多亏@thomas的建议，我能够改变我使用的循环缓冲区类别，以便在O（1）下平均计算总和、平均值、最大值、最小值和标准偏差，但在最差的O（N）下计算。对于我所需的性能来说，这是一种魅力 请注意，出于我的目的，我只修改了CBuffer循环缓冲区类的“unshift”方法。因此，其他方法无法正确更新最大、最小和标准偏差。以下是指向JSFIDLE的链接： 这是我的测试代码：
// A standard deviation object constructor. Running deviation (avoid growing arrays) which
// is round-off error resistant. Based on an algorithm found in a Knuth book.
class StandardDeviation {
constructor() {
this.v = 0;
this.w = 0;
this.S = 0;
this.count = 0;
}
// Add a measurement. Also calculates updates to stepwise parameters which are later used
// to determine sigma.
add(measurement) {
this.count += 1;
this.w = this.v;
this.v = this.v + (measurement - this.v) / this.count;
this.S = this.S + (measurement - this.w) * (measurement - this.v);
}
// Performs the final step needed to get the standard deviation and returns it.
get() {
if (this.count < 2) {
// There are less measurements accumulated than necessary to perform computation
return 0.0;
} else {
return Math.sqrt(this.S / (this.count));
}
}
// Replaces the value x currently present in this sample with the
// new value y. In a sliding window, x is the value that
// drops out and y is the new value entering the window. The sample
// count remains constant with this operation.
replace(x, y) {
const deltaYX = y - x;
const deltaX = x - this.v;
const deltaY = y - this.v;
this.v = this.v + deltaYX / this.count;
const deltaYp = y - this.v;
const countMinus1 = this.count - 1;
this.S = this.S - this.count / countMinus1 * (deltaX * deltaX - deltaY * deltaYp) - deltaYX * deltaYp / countMinus1;
}
// Remove a measurement. Also calculates updates to stepwise parameters which are later used
// to determine sigma.
remove(x) {
this.w = (this.count * this.v - x) / (this.count - 1);
this.S -= (x - this.v) * (x - this.w);
this.v = this.w;
this.count -= 1;
}
}
function CBuffer() {
// handle cases where "new" keyword wasn't used
if (!(this instanceof CBuffer)) {
// multiple conditions need to be checked to properly emulate Array
if (arguments.length > 1 || typeof arguments[0] !== 'number') {
return CBuffer.apply(new CBuffer(arguments.length), arguments);
} else {
return new CBuffer(arguments[0]);
}
}
// if no arguments, then nothing needs to be set
if (arguments.length === 0)
throw new Error('Missing Argument: You must pass a valid buffer size');
// this is the same in either scenario
this.length = this.start = 0;
// set to callback fn if data is about to be overwritten
this.overflow = null;
// set to callback fn if data is about to be overwritten
this.maxIndex = null;
this.minIndex = null;
this.max = null;
this.min = null;
this.sum = null;
this.mean = null;
this.standardDeviation = new StandardDeviation();
// emulate Array based on passed arguments
if (arguments.length > 1 || typeof arguments[0] !== 'number') {
this.data = new Array(arguments.length);
this.end = (this.size = arguments.length) - 1;
this.push.apply(this, arguments);
} else {
this.data = new Array(arguments[0]);
this.end = (this.size = arguments[0]) - 1;
}
// need to `return this` so `return CBuffer.apply` works
return this;
}
function defaultComparitor(a, b) {
return a == b ? 0 : a > b ? 1 : -1;
}
function mod(n, m) {
return ((n % m) + m) % m;
}
CBuffer.prototype = {
// properly set constructor
constructor : CBuffer,
/* mutator methods */
// pop last item
pop : function () {
var item;
if (this.length === 0) return;
item = this.data[this.end];
// remove the reference to the object so it can be garbage collected
delete this.data[this.end];
this.end = (this.end - 1 + this.size) % this.size;
this.length--;
return item;
},
// push item to the end
push : function () {
var i = 0;
var returnOverflow = false;
// check if overflow is set, and if data is about to be overwritten
if (this.overflow && this.length + arguments.length > this.size) {
// call overflow function and send data that's about to be overwritten
for (; i < this.length + arguments.length - this.size; i++) {
returnOverflow = this.data[(this.end + i + 1) % this.size];
// this.overflow(this.data[(this.end + i + 1) % this.size], this);
}
}
// push items to the end, wrapping and erasing existing items
// using arguments variable directly to reduce gc footprint
for (i = 0; i < arguments.length; i++) {
this.data[(this.end + i + 1) % this.size] = arguments[i];
}
// recalculate length
if (this.length < this.size) {
if (this.length + i > this.size) this.length = this.size;
else this.length += i;
}
// recalculate end
this.end = (this.end + i) % this.size;
// recalculate start
this.start = (this.size + this.end - this.length + 1) % this.size;
// return number current number of items in CBuffer
return returnOverflow;
},
// reverse order of the buffer
reverse : function () {
var i = 0,
tmp;
for (; i < ~~(this.length / 2); i++) {
tmp = this.data[(this.start + i) % this.size];
this.data[(this.start + i) % this.size] = this.data[(this.start + (this.length - i - 1)) % this.size];
this.data[(this.start + (this.length - i - 1)) % this.size] = tmp;
}
return this;
},
// rotate buffer to the left by cntr, or by 1
rotateLeft : function (cntr) {
if (typeof cntr === 'undefined') cntr = 1;
if (typeof cntr !== 'number') throw new Error("Argument must be a number");
while (--cntr >= 0) {
this.push(this.shift());
}
return this;
},
// rotate buffer to the right by cntr, or by 1
rotateRight : function (cntr) {
if (typeof cntr === 'undefined') cntr = 1;
if (typeof cntr !== 'number') throw new Error("Argument must be a number");
while (--cntr >= 0) {
this.unshift(this.pop());
}
return this;
},
// remove and return first item
shift : function () {
var item;
// check if there are any items in CBuff
if (this.length === 0) return;
// store first item for return
item = this.data[this.start];
// recalculate start of CBuffer
this.start = (this.start + 1) % this.size;
// decrement length
this.length--;
return item;
},
// sort items
sort : function (fn) {
this.data.sort(fn || defaultComparitor);
this.start = 0;
this.end = this.length - 1;
return this;
},
// add item to beginning of buffer
unshift : function () {
var i = 0;
var returnOverflow = false;
if (this.length == this.size) {
returnOverflow = this.last();
}
for (i = 0; i < arguments.length; i++) {
this.data[(this.size + this.start - (i % this.size) - 1) % this.size] = arguments[i];
}
if (this.size - this.length - i < 0) {
this.end += this.size - this.length - i;
if (this.end < 0) this.end = this.size + (this.end % this.size);
}
if (this.length < this.size) {
if (this.length + i > this.size) this.length = this.size;
else this.length += i;
}
this.start -= arguments.length;
if (this.start < 0) this.start = this.size + (this.start % this.size);
this.recalculateMaxMin(arguments[0], returnOverflow);
this.sum += arguments[0];
if (returnOverflow) {
this.sum -= returnOverflow;
this.standardDeviation.replace(returnOverflow, arguments[0])
}
else {
this.standardDeviation.add(arguments[0]);
}
this.mean = this.sum / this.length;
return returnOverflow;
},
/* accessor methods */
// return index of first matched element
indexOf : function (arg, idx) {
if (!idx) idx = 0;
for (; idx < this.length; idx++) {
if (this.data[(this.start + idx) % this.size] === arg) return idx;
}
return -1;
},
// return last index of the first match
lastIndexOf : function (arg, idx) {
if (!idx) idx = this.length - 1;
for (; idx >= 0; idx--) {
if (this.data[(this.start + idx) % this.size] === arg) return idx;
}
return -1;
},
// return the index an item would be inserted to if this
// is a sorted circular buffer
sortedIndex : function(value, comparitor, context) {
comparitor = comparitor || defaultComparitor;
var isFull = this.length === this.size,
low = this.start,
high = isFull ? this.length - 1 : this.length;
// Tricky part is finding if its before or after the pivot
// we can get this info by checking if the target is less than
// the last item. After that it's just a typical binary search.
if (low && comparitor.call(context, value, this.data[high]) > 0) {
low = 0, high = this.end;
}
while (low < high) {
var mid = (low + high) >>> 1;
if (comparitor.call(context, value, this.data[mid]) > 0) low = mid + 1;
else high = mid;
}
return !isFull ? low :
// http://stackoverflow.com/a/18618273/1517919
(((low - this.start) % this.length) + this.length) % this.length;
},
/* iteration methods */
// check every item in the array against a test
every : function (callback, context) {
var i = 0;
for (; i < this.length; i++) {
if (!callback.call(context, this.data[(this.start + i) % this.size], i, this))
return false;
}
return true;
},
// loop through each item in buffer
// TODO: figure out how to emulate Array use better
forEach : function (callback, context) {
var i = 0;
for (; i < this.length; i++) {
callback.call(context, this.data[(this.start + i) % this.size], i, this);
}
},
// construct new CBuffer of same length, apply map function, and return new CBuffer
map : function (callback, context) {
var outCBuffer = new CBuffer(this.size);
for (var i = 0; i < this.length; i++) {
var n = (this.start + i) % this.size;
outCBuffer.push(callback.call(context, this.data[n], i, this));
}
return outCBuffer;
},
// check items agains test until one returns true
// TODO: figure out how to emulate Array use better
some : function (callback, context) {
var i = 0;
for (; i < this.length; i++) {
if (callback.call(context, this.data[(this.start + i) % this.size], i, this))
return true;
}
return false;
},
// calculate the average value of a circular buffer
avg : function () {
return this.length == 0 ? 0 : (this.sum() / this.length);
},
// loop through each item in buffer and calculate sum
sum : function () {
var index = this.length;
var s = 0;
while (index--) s += this.data[index];
return s;
},
// loop through each item in buffer and calculate sum
getMaxPosition : function () {
// return 0
return (this.start + this.start + this.maxIndex) % this.size;
},
// loop through each item in buffer and calculate sum
getStandardDeviation : function () {
// return 0
return this.standardDeviation.get();
},
// loop through each item in buffer and calculate sum
getMinPosition : function () {
// return 0
return (this.start + this.start + this.minIndex) % this.size;
},
recalculateMaxMin : function (newValue, returnOverflow) {
if (this.length == 1) {
this.max = newValue;
this.maxIndex = this.start;
this.min = newValue;
this.minIndex = this.start;
return;
}
// Max / Mins
if (newValue > this.max) {
this.max = newValue;
this.maxIndex = this.start;
}
if (newValue < this.min) {
this.min = newValue;
this.minIndex = this.start;
}
// If overflow max or min recalculate
if (
returnOverflow && (returnOverflow >= this.max || returnOverflow <= this.min)
) {
this.maxIndex = 0;
this.minIndex = 0;
this.max = this.data[0];
this.min = this.data[0];
for (let i = 0; i < this.length; i++) {
if (this.data[i] > this.max) {
this.maxIndex = i;
this.max = this.data[i];
}
if (this.data[i] < this.min) {
this.minIndex = i;
this.min = this.data[i];
}
}
}
},
// loop through each item in buffer and calculate median
median : function () {
if (this.length === 0)
return 0;
var values = this.slice().sort(defaultComparitor);
var half = Math.floor(values.length / 2);
if(values.length % 2)
return values[half];
else
return (values[half-1] + values[half]) / 2.0;
},
/* utility methods */
// reset pointers to buffer with zero items
// note: this will not remove values in cbuffer, so if for security values
// need to be overwritten, run `.fill(null).empty()`
empty : function () {
var i = 0;
this.length = this.start = 0;
this.end = this.size - 1;
return this;
},
// fill all places with passed value or function
fill : function (arg) {
var i = 0;
if (typeof arg === 'function') {
while(this.data[i] = arg(), ++i < this.size);
} else {
while(this.data[i] = arg, ++i < this.size);
}
// reposition start/end
this.start = 0;
this.end = this.size - 1;
this.length = this.size;
return this;
},
// return first item in buffer
first : function () {
return this.data[this.start];
},
// return last item in buffer
last : function () {
return this.data[this.end];
},
// return specific index in buffer
get : function (arg) {
return this.data[mod(this.start + arg, this.size)];
},
isFull : function (arg) {
return this.size === this.length;
},
// set value at specified index
set : function (idx, arg) {
return this.data[(this.start + idx) % this.size] = arg;
},
// return clean array of values
toArray : function () {
return this.slice();
},
// return a string based on the array
join : function(separator) {
if (!separator) separator = ',';
var outString = new String(this.data[0]);
for (var i = 1; i < this.length; i++) {
var n = (this.start + i) % this.size;
outString = outString.concat(separator, this.data[i]);
}
return outString;
},
// slice the buffer to an arraay
slice : function (start, end) {
var size = this.length;
start = +start || 0;
if (start < 0) {
if (start >= end)
return [];
start = (-start > size) ? 0 : size + start;
}
if (end == null || end > size)
end = size;
else if (end < 0)
end += size;
else
end = +end || 0;
size = start < end ? end - start : 0;
var result = Array(size);
for (var index = 0; index < size; index++) {
result[index] = this.data[(this.start + start + index) % this.size];
}
return result;
}
};
var bufferLength = 3;
var numbersToGenerate = 10;
var circularBufferN = new CBuffer(bufferLength);
var valuesToEnqueueForDemoPurposes = Array.from(Array(numbersToGenerate)).map(x=>Math.random() * 1000)
for (let i = 0; i < valuesToEnqueueForDemoPurposes.length; i++) {
var newValue = valuesToEnqueueForDemoPurposes[i];
console.log("\n\nNEW VALUE****************************************************************:");
console.log(newValue);
console.log("STARTING UNSHIFT:");
console.log(circularBufferN.unshift(newValue));
let valuesArray = circularBufferN.data;
var maxIndex = circularBufferN.maxIndex;
var minIndex = circularBufferN.minIndex;
var max = valuesArray[maxIndex];
var min = valuesArray[minIndex];
console.log("Max Index");
console.log(maxIndex);
console.log("Max:");
console.log(max);
console.log("Min Index:");
console.log(minIndex);
console.log("Min:");
console.log(min);
console.log("Start:");
console.log(circularBufferN.start);
console.log("ORDERED ARRAY:");
console.log(circularBufferN.toArray());
console.log("Max Position:");
console.log(circularBufferN.getMaxPosition());
console.log("Min Position:");
console.log(circularBufferN.getMinPosition());
console.log('Sum:');
console.log(circularBufferN.sum);
console.log("mean:");
console.log(circularBufferN.mean);
console.log("Derived Standard Deviation");
console.log(circularBufferN.getStandardDeviation());
}
//一个标准偏差对象构造函数。运行偏差（避免数组增长）可以
//基于Knuth书中的一个算法。
类标准差{
构造函数（）{
这个。v=0；
这是w=0；
这个。S=0；
此值为0.count；
}
//添加测量值。还计算后续使用的逐步参数的更新
//确定西格玛。
添加（测量）{
这是1.count+=1；
此.w=此.v；
this.v=this.v+（测量-this.v）/this.count；
this.S=this.S+（测量-this.w）*（测量-this.v）；
}
//执行获取标准偏差所需的最后一步并返回它。
得到（）{
如果（该计数小于2）{
//累积的测量值少于执行计算所需的测量值
返回0.0；
}否则{
返回Math.sqrt（this.S/（this.count））；
}
}
//将此示例中当前存在的值x替换为
//新值y。在滑动窗口中，x是
//退出，y是进入窗口的新值。示例
//计数在此操作中保持不变。
更换（x，y）{
常数deltaYX=y-x；
const deltaX=x-这一点v；
const deltaY=y——这一点；v；
this.v=this.v+deltaYX/this.count；
常数deltaYp=y-这个.v；
const countMinus1=this.count-1；
this.S=this.S-this.count/countMinus1*（deltaX*deltaX-deltaY*deltaYp）-deltaYX*deltaYp/countMinus1；
}
//删除测量值。还计算后续使用的逐步参数更新
//确定西格玛。
删除（x）{
this.w=（this.count*this.v-x）/（this.count-1）；
this.S-=（x-this.v）*（x-this.w）；
这个.v=这个.w；
这是1.count-=1；
}
}
函数CBuffer（）{
//处理未使用“new”关键字的情况
如果（！（此CBuffer实例））{
//需要检查多个条件才能正确模拟阵列
if（arguments.length>1 | |参数类型[0]！=='number'）{
返回CBuffer.apply（新的CBuffer（arguments.length），arguments）；
}否则{
返回新的CBuffer（参数[0]）；
}
}
//如果没有参数，则不需要设置任何内容
if（arguments.length==0）
抛出新错误（'缺少参数：必须传递有效的缓冲区大小'）；
//这两种情况都是一样的
this.length=this.start=0；
//如果数据即将被覆盖，则设置为回调fn
this.overflow=null；
//设置为回调fn，如果da