【BZOJ1419】Red is good（期望DP）

Description

click me

Solution

用$f_{i,j}$表示还剩$i$张红牌、$j$张黑牌的期望值，考虑倒推。
转移：

$$f_{i,j}=\frac{i}{i+j}(f_{i-1,j}+1)+\frac{j}{i+j}(f_{i,j-1}-1)$$

Source

/**************************************
 * Au: Hany01
 * Date: Feb 8th, 2018
 * Prob: BZOJ1419 Red is good
 * Email: hany01@foxmail.com
**************************************/

#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<cstring>
#include<iostream>
#include<algorithm>

using namespace std;

typedef long long LL;
typedef pair<int, int> PII;
#define rep(i, j) for (register int i = 0, i##_end_ = (j); i < i##_end_; ++ i)
#define For(i, j, k) for (register int i = (j), i##_end_ = (k); i <= i##_end_; ++ i)
#define Fordown(i, j, k) for (register int i = (j), i##_end_ = (k); i >= i##_end_; -- i)
#define Set(a, b) memset(a, b, sizeof(a))
#define Cpy(a, b) memcpy(a, b, sizeof(a))
#define fir first
#define sec second
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
#define ALL(a) (a).begin(), (a).end()
#define SZ(a) ((int)(a).size())
#define INF (0x3f3f3f3f)
#define INF1 (2139062143)
#define Mod (1000000007)
#define debug(...) fprintf(stderr, __VA_ARGS__)

template <typename T> inline bool chkmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
template <typename T> inline bool chkmin(T &a, T b) { return b < a ? a = b, 1 : 0; }

inline int read()
{
    register int _, __; register char c_;
    for (_ = 0, __ = 1, c_ = getchar(); c_ < '0' || c_ > '9'; c_ = getchar()) if (c_ == '-') __ = -1;
    for ( ; c_ >= '0' && c_ <= '9'; c_ = getchar()) _ = (_ << 1) + (_ << 3) + (c_ ^ 48);
    return _ * __;
}

inline void File()
{
#ifdef hany01
    freopen("bzoj1419.in", "r", stdin);
    freopen("bzoj1419.out", "w", stdout);
#endif
}

const int maxn = 5005;

int r, b, t;
double f[2][maxn], Ans;

int main()
{
    File();
    r = read(), b = read();
    For(i, 1, r) {
        Set(f[t = i & 1], 0), f[t][0] = i;
        For(j, 1, b) chkmax(f[t][j], i * 1.0 / (i + j) * (f[t ^ 1][j] + 1) + j * 1.0 / (i + j) * (f[t][j - 1] - 1));
    }
    printf("%.6lf\n", (int)(f[t][b] * 1000000) / 1000000.0);
    return 0;
}
//殷勤花下同携手。更尽杯中酒。美人不用敛蛾眉。
//    -- 叶梦得《虞美人·雨后同干誉才卿置酒来禽花下作》