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2次元ランダムウォーク (Nested Flatten)
まずはシンプルなところで。
   1   0  -1
   2   0   0
   3   0   1
   4  -1   1
   5  -2   1
   6  -1   1
   7   0   1
   8  -1   1
   9  -1   0
  10  -1   1
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#include <cstdlib>
#include <complex>
#include <iostream>
#include <iomanip>

int main(int args, char* argv[])
{
    std::complex<int> d[] =
    {
        std::complex<int>( 1,  0),
        std::complex<int>( 0,  1),
        std::complex<int>(-1,  0),
        std::complex<int>( 0, -1)
    };

    std::complex<int> p(0, 0);

    for(int i = 1; i <= 10; ++i)
    {
        p += d[std::rand() % 4];
        std::cout << std::setw(4) << i
                  << std::setw(4) << p.real()
                  << std::setw(4) << p.imag()
                  << std::endl;
    }

    return 0;
}

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