2020/round2/elimination.cpp

// Elimination
// Solution by Jacob Plachta

#include <algorithm>
#include <functional>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <complex>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <cassert>
#include <string>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <sstream>
using namespace std;

#define LL long long
#define LD long double
#define PR pair<int,int>

#define Fox(i,n) for (i=0; i<n; i++)
#define Fox1(i,n) for (i=1; i<=n; i++)
#define FoxI(i,a,b) for (i=a; i<=b; i++)
#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
#define FoxR1(i,n) for (i=n; i>0; i--)
#define FoxRI(i,a,b) for (i=b; i>=a; i--)
#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
#define Min(a,b) a=min(a,b)
#define Max(a,b) a=max(a,b)
#define Sz(s) int((s).size())
#define All(s) (s).begin(),(s).end()
#define Fill(s,v) memset(s,v,sizeof(s))
#define pb push_back
#define mp make_pair
#define x first
#define y second

template<typename T> T Abs(T x) { return(x < 0 ? -x : x); }
template<typename T> T Sqr(T x) { return(x * x); }
string plural(string s) { return(Sz(s) && s[Sz(s) - 1] == 'x' ? s + "en" : s + "s"); }

const int INF = (int)1e9;
const LD EPS = 1e-12;
const LD PI = acos(-1.0);

#define GETCHAR getchar_unlocked

#define LIM 8001

// dyn[b][w] = expected number of remaining rounds
//             when there are b better and w worse players than you
LD dyn[LIM][LIM];

int NumPairs(int c)
{
  return(c * (c - 1) / 2);
}

// inv indicates that b/w have been swapped to capture worse players winning
LD Comp(int b, int w, bool inv)
{
  LD p = (LD)1 / NumPairs(b + w + 1), d = 0;
  // elimination of better player than you
  if (b > 0)
    d += NumPairs(b) * p * (inv ? dyn[w][b - 1] : dyn[b - 1][w]);
  // elimination of worse player than you
  if (w > 0)
    d += (w * (b + 1) + NumPairs(w)) * p * (inv ? dyn[w - 1][b] : dyn[b][w - 1]);
  return(d);
}

void ProcessCase()
{
  int N, i, b, w;
  LD P;
  // input
  scanf("%d%Lf", &N, &P);
  // DP
  Fill(dyn, 0);
  Fox(b, N)
  {
    Fox(w, N - b)
    {
      if (b + w)
      {
        dyn[b][w] = 1 +
          Comp(b, w, false) * P + // better players winning
          Comp(w, b, true) * (1 - P); // worse players winning
      }
    }
  }
  // output
  Fox(i, N)
    printf("%.8Lf\n", dyn[N - i - 1][i]);
}

int main()
{
  int T, t;
  scanf("%d\n", &T);
  Fox1(t, T)
  {
    printf("Case #%d:\n", t);
    ProcessCase();
  }
  return(0);
}