RobotSimulate

#include <bits/stdc++.h>
// tiom4eg's precompiler options
// POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS
// IO settings
#define fastIO ios_base::sync_with_stdio(false); cin.tie(0)
// Quick types
#define ll long long
#define ld double
#define ull unsigned long long
#define pii pair <int, int>
#define pll pair <ll, ll>
#define vi vector <int>
#define mi vector <vector <int> >
// Quick functions
#define endl "\n"
#define F first
#define S second
#define all(a) a.begin(), a.end()
#define sz(a) a.size()
#define pb push_back
#define mp make_pair
#define min(a, b) ((a < b) ? (a) : (b))
#define max(a, b) ((a > b) ? (a) : (b))
// Quick fors
#define FOR(i, a, b) for (int i = a; i < b; ++i)
#define RFOR(i, a, b) for (int i = a; i >= b; --i)
// Pragmas
#pragma GCC optimize("O3,unroll-loops") // let the chaos begin!
#pragma GCC target("avx,avx2,bmi,bmi2,popcnt,lzcnt,tune=native")
#pragma GCC comment(linker, "/stack:200000000")
// PBDS
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ordered_set tree <int, null_type, less <int>, rb_tree_tag, tree_order_statistics_node_update>
#define ook order_of_key
#define fbo find_by_order
// POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS
using namespace std;
using namespace __gnu_pbds;
mt19937 rd(std::chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now().time_since_epoch()).count());

int rng(int n) { return rd() % n + 1; } // [1; n]

// Simulation settings
const int ITER = 66666, GEN = 1000;
const int U = 25, D = 25, L = 25, R = 25; // 25%
// Statistics
double dist = 0.0;

void sim() {
    int x = 0, y = 0;
    FOR(i, 0, ITER) {
        int cv = rng(U + D + L + R);
        if (cv <= U) y += 1;
        else if (cv <= U + D) y -= 1;
        else if (cv <= U + D + L) x -= 1;
        else x += 1;
    }
    dist += sqrt(x * x + y * y);
}

int main() {
    cout << fixed << setprecision(6);
    cout << "simulating " << GEN << " generations with " << ITER << " iterations each" << endl;
    FOR(i, 0, GEN) sim();
    cout << "done" << endl;
    cout << "avg dist: " << dist / (double)GEN;
}