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. / * 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); // operator Vector operator*(double factor); Vector operator*=(double factor); Vector operator-(); // friend operator friend std::ostream &operator<<(std::ostream &os, Vector &obj); // toString friend 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 

讯享网// // 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 prev preC = os.precision(1); // store prev os << "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); // reset os.precision(preC); // reset return 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

讯享网

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：.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。~