cpp: 随机漫步者的位移与步数的关系模型实现

关于随机漫步的介绍参见：随机漫步理论

通过cpp实现随机漫步的关系模型。（计算移动目标位移需要随机漫步多少步）

~~通过实践才能知道自己的不足，仅仅是看书难免会感觉生疏。~~

下面是实现：
一共3个文件，分别是Vector.h–> 矢量类定义，Vector.cpp–>矢量类的具体实现，main.cpp–>随机漫步模型的具体实现。

//
// Created by cat on 2018/1/1.
//#ifndef CPP02_STEP_H
#define CPP02_STEP_H#include <iostream>
#include <cmath>
#include <math.h>#define Math_PI 3.1415927
/*** 矢量类*/
namespace VECTOR {class Vector {public:enum Mode {/*正坐标*/ RECT,/*极坐标*/ POL};private:Mode currentMode;double angle; // 角度 （0～360度）double length; // 步长��（1～3m)double xLen; // x 方向的位移double yLen; // y 方向的位移Vector set2RECT() const; // 转成正坐标Vector set2POL() const; // 转成级坐标double radian2Angle(double radian) const // 弧度转角度{return 1.0 * radian / Math_PI * 180;}double angle2Radian(double angle) const // 角度转弧度{return 1.0 * angle * Math_PI / 180;}public:Vector(double num1 = 0, double num2 = 0, Mode currentMode = POL);Vector(const Vector &data);double getLength() {return this->length;};virtual ~Vector();void reset(double num1 = 0, double num2 = 0, Mode currentMode = POL);// operatorVector operator*(double factor);Vector operator*=(double factor);Vector operator-();// friend operatorfriend std::ostream &operator<<(std::ostream &os, Vector &obj); // toStringfriend Vector operator+(const Vector &one, const Vector &another);friend Vector operator+=(Vector &one, const Vector &another);friend Vector operator-(const Vector &one, const Vector &another);friend Vector operator-=(Vector &one, const Vector &another);friend Vector operator*(double factor,  Vector &obj);friend Vector operator*=(double factor, Vector &obj);};}#endif //CPP02_STEP_H

//
// Created by cat on 2018/1/1.
//#include "Vector.h"
#include <cmath>namespace VECTOR {Vector::Vector(const Vector &data) {this->xLen = data.xLen;this->yLen = data.yLen;this->angle = data.angle;this->length = data.length;this->currentMode = data.currentMode;}Vector::Vector(double num1,double num2,Vector::Mode currentMode) {reset(num1, num2, currentMode);}void Vector::reset(double num1,double num2,Vector::Mode currentMode) {this->currentMode = currentMode;if (this->currentMode == POL) {this->angle = num1;this->length = num2;this->xLen = sin(radian2Angle(num1)) * num2;this->yLen = cos(radian2Angle(num1)) * num2;} else if (this->currentMode == RECT) {this->xLen = num1;this->yLen = num2;this->angle = radian2Angle(atan2(this->yLen, this->xLen));double len2 = pow(this->xLen, 2) + pow(this->yLen, 2);this->length = pow(len2, 0.5);} else {throw "error!";}}Vector::~Vector() {this->currentMode = POL;this->angle = 0;this->length = 0;this->xLen = 0;this->yLen = 0;}Vector Vector::set2RECT() const {Vector v = Vector(*this);if (this->currentMode == Vector::RECT) {return v;} else if (this->currentMode == Vector::POL) {v.currentMode = Vector::RECT;v.xLen = this->length * cos(this->angle2Radian(this->angle));v.yLen = this->length * sin(this->angle2Radian(this->angle));}return v;}Vector Vector::set2POL() const {Vector v = Vector(*this);if (this->currentMode == Vector::POL) {return v;} else {v.currentMode = Vector::POL;v.angle = radian2Angle(atan2(this->yLen, this->xLen));double len2 = pow(this->xLen, 2) + pow(this->yLen, 2);v.length = pow(len2, 0.5);}return v;}Vector operator+(const Vector &a, const Vector &b) {Vector obj;Vector one, another;one = a.set2RECT();another = b.set2RECT();obj = Vector(one.xLen + another.xLen, one.yLen + another.yLen, Vector::RECT);return obj;}Vector VECTOR::operator+=(Vector &one, const Vector &another) {one = operator+(one, another);return one;}Vector operator-(const Vector &a, const Vector &b) {Vector one, another;Vector::Mode mode = one.currentMode;one = a.set2RECT();another = b.set2RECT();Vector v = Vector(one.xLen - another.xLen, one.yLen - another.yLen, Vector::RECT);v.currentMode = mode;return v;}Vector operator-=(Vector &one, const Vector &another) {one = operator-(one, another);return one;}Vector Vector::operator*(double factor) {Vector obj;Vector::Mode mode = this->currentMode;this->set2RECT();obj = Vector(this->xLen * factor, this->yLen * factor, Vector::RECT);obj.currentMode = mode;return obj;}Vector Vector::operator*=(double factor) {return operator*(factor);}Vector operator*(double factor, Vector &obj) {return obj * factor;}Vector operator*=(double factor, Vector &obj) {return operator*(factor, obj);}Vector Vector::operator-() {Mode mode = this->currentMode;this->set2RECT();Vector v = Vector(-this->xLen, -this->yLen, Vector::RECT);v.currentMode = mode;return v;}std::ostream &operator<<(std::ostream &os, Vector &obj) {std::ios_base::fmtflags pref;std::streamsize preC;pref = os.setf(std::ios_base::fixed);  // store prevpreC = os.precision(1); // store prevos << "Vector:(" << obj.xLen << " , " << obj.yLen << ")|[RECT]\t";os.precision(2);os << "Vector:(" << obj.angle << " , " << obj.length << ")|[POL]\t";if (obj.currentMode == Vector::RECT) {os << "{RECT}\n";} else {os << "\t{POL}\n";}os.setf(pref);  // resetos.precision(preC); // resetreturn os;}}

#include <iostream>
#include <sstream>
#include <random>
#include <stdlib.h>
#include "Vector.h"void end();void resetCin();void executeFromUser();void execute(double length, double step);void executeTimes(unsigned int times);const unsigned int MAX_FREE = 10;bool USER_INPUT = false; // 是否每次都让用户输入static int usedTimes = 0;static int currentSteps = 0;int main() {using namespace std;using VECTOR::Vector;Vector v1 = Vector(20, 30, Vector::RECT);Vector v2 = Vector(40, 50, Vector::RECT);v1 += v2;cout << v1 << endl;//    executeFromUser();executeTimes(100);return 0;
}void executeTimes(unsigned int times) {using namespace std;using VECTOR::Vector;cout << "随机漫步模拟.\n";double avg = 0;double length; // 总位移double eachLen;// 单步长度string input;stringstream ostr;cout << "请输入总位移长度（退出请按q）：";getline(cin, input);ostr << input;while (1) {if (ostr >> length) {cout << "length==" << length;ostr.clear();cout << "请输入单步位移长度（退出请按q）：";getline(cin, input);ostr << input;if (ostr >> eachLen) {cout << "todo: SUCCESS\n";for (int pos = 0; pos < times; ++pos) {execute(length, eachLen);avg += currentSteps;}goto fuck;} else {cout << "输入不合法, 请重新输入！\n";}} else {cout << "输入不合法, 请重新输入！\n";}}fuck:;avg = avg / times;streamsize precision = cout.precision(2);cout << "随机漫步目标位移为" << length << "时的平均步数为：" << avg << "\n";cout.precision(precision);
}void execute(double length, double step) {using namespace std;using VECTOR::Vector;Vector init{};
//    cout << "init.Length=" << init.getLength() << " , length=" << length << endl;while (init.getLength() < length) {currentSteps++;double angle = random() % 360;double el = step;Vector each = Vector(angle, el);
//                    cout << "........each:" << each;init += each;}streamsize precision = cout.precision(2);cout << "RESULT:" << init;cout << "这一次走完目标距离(" << length << ")一共用了[" << currentSteps << "]步，";cout << "目前距离长度为：" << init.getLength() << " > 目标长度：" << length << endl;usedTimes++;cout << "还有(" << (MAX_FREE - usedTimes) << ")次机会\n";cout.precision(precision);
}void executeFromUser() {using namespace std;using VECTOR::Vector;cout << "随机漫步模拟.\n";double length; // 总位移double eachLen;// 单步长度string input;stringstream ostr;while (usedTimes <= MAX_FREE) {cout << "请输入总位移长度（退出请按q）：";getline(cin, input);ostr << input;if (ostr >> length) {cout << "length==" << length;ostr.clear();cout << "请输入单步位移长度（退出请按q）：";getline(cin, input);ostr << input;if (ostr >> eachLen) {cout << "todo: SUCCESS\n";execute(length, eachLen);if (!USER_INPUT) {goto fuck;}} else {cout << "输入不合法, 请重新输入！\n";}} else {cout << "输入不合法, 请重新输入！\n";}}if (usedTimes > MAX_FREE) {cout << "体验机会已经用光，继续体验请充值~^_^\n";}end();fuck:;
}void end() {resetCin();std::cout << "Bye.\n";
}void resetCin() {std::cin.clear();while (std::cin.get() != '\n')continue;
}

完整的项目可以参见：随机漫步关系模型cpp实现

当然，这个代码写得不好，没有去优化内存。

可以看一下输出效果：

随机漫步模拟.
请输入总位移长度（退出请按q）：100
请输入单步位移长度（退出请按q）：1
随机漫步目标位移为100.00时的平均步数为：497246.73

从输出结果可以看到，通过1000次的模拟，得出的平均数是49万步，才能前进100米。（假设步长是固定的，为1米）。

ps: 这个结果也不一定正确，说不定程序逻辑有问题。~

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cpp: 随机漫步者的位移与步数的关系模型实现

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