题目传送门：http://www.lydsy.com/JudgeOnline/problem.php?id=2318
网上绝大部分证明完全没有说清楚好吗？ (╯‵□′)╯︵┻━┻
只有这一份题解才稍微正常一点：http://codeplay0314.coding.me/2015/07/10/BZOJ2318/
本地备份：http://oi.cyo.ng/wp-content/uploads/2016/08/12345687856456754.png
不过这一题的推式子还是很神的，有一定参考价值。
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cstdio>
#include<cmath>
#include<bitset>
#define LL long long
#define abs(x) ((x)>0?(x):-(x))
using namespace std;
const int N = 1000+9;
const int LIM = 1000;
int n;
double f[N],g[N],p,q;
inline int read(){
char c=getchar(); int ret=0,f=1;
while (c<'0'||c>'9') {if(c=='-')f=-1;c=getchar();}
while (c<='9'&&c>='0') ret=ret*10+c-'0',c=getchar();
return ret*f;
}
int main(){
int T=read(); while (T--) {
n = min(read(), LIM); scanf("%lf%lf",&p,&q);
f[0] = 0; g[0] = 1;
for (int i=1;i<=n;i++) {
if (f[i-1] > g[i-1]) p = 1 - p, q = 1 - q;
f[i] = (p*g[i-1] + (1-p)*q*f[i-1]) / (1 - (1-p)*(1-q));
g[i] = (q*f[i-1] + (1-q)*p*g[i-1]) / (1 - (1-p)*(1-q));
if (f[i-1] > g[i-1]) p = 1 - p, q = 1 - q;
}
printf("%.6lf\n",f[n]);
}
return 0;
}
值得一提的是，我最开始定义的g[i]为胜i个石子时，Bob先走，Bob的胜算是多少
这样写出来的方程是： \(\begin{array}{l}
{a_i} = \left\{ \begin{array}{l}
p(1 – {b_i}) + (1 – p)(1 – {b_{i – 1}}),{b_i} < {b_{i - 1}}\\
p(1 - {b_{i - 1}}) + (1 - p)(1 - {b_i}),{b_i} > {b_{i – 1}}
\end{array} \right.\\
{b_i} = \left\{ \begin{array}{l}
q(1 – {a_i}) + (1 – q)(1 – {a_{i – 1}}),{a_i} < {a_{i - 1}}\\
q(1 - {a_{i - 1}}) + (1 - q)(1 - {a_i}),{a_i} > {a_{i – 1}}
\end{array} \right.
\end{array}\)
但你会发现，这么推，推不出来QAQ
仔细想一想为什么，我觉得是f[i]与(1-f[i])混用了吧？
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