dp求期望
区分 全局最优选择 和 当前最优选择。
本题是当前最优选择。
状态表示:
double dp[16][16][16][16][5][5];
bool vis[16][16][16][16][5][5];
状态下参数：
vector<int> up, vector<int> tmp。
so,记忆化搜索 + 回溯
//#pragma warning (disable: 4786)
//#pragma comment (linker, "/STACK:16777216")
//HEAD
#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <cstring>
#include <queue>
#include <string>
#include <set>
#include <stack>
#include <map>
#include <cmath>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
//LOOP
#define FE(i, a, b) for(int i = (a); i <= (b); ++i)
#define FD(i, b, a) for(int i = (b); i>= (a); --i)
#define REP(i, N) for(int i = 0; i < (N); ++i)
#define CLR(A,value) memset(A,value,sizeof(A))
#define CPY(a, b) memcpy(a, b, sizeof(a))
#define FC(it, c) for(__typeof((c).begin()) it = (c).begin(); it != (c).end(); it++)
//INPUT
#define RI(n) scanf("%d", &n)
#define RII(n, m) scanf("%d%d", &n, &m)
#define RIII(n, m, k) scanf("%d%d%d", &n, &m, &k)
#define RS(s) scanf("%s", s)
//OUTPUT
#define WI(n) printf("%d\n", n)
#define WS(s) printf("%s\n", s)
typedef long long LL;
const int INF = 1000000007;
const double eps = 1e-10;
const int MAXN = 1010;
vector<int> goal;
double dp[16][16][16][16][5][5];
bool vis[16][16][16][16][5][5];
inline bool check(vector<int> &tmp)
{
for (int i = 0; i < 4; i++)
if (goal[i] > tmp[i]) return false;
return true;
}
double dfs(vector<int> &tmp, vector<int> &up)
{
if (check(tmp)) return 0.0;
if (vis[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][tmp[5]])
return dp[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][tmp[5]];
vis[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][tmp[5]] = true;
double ret = 0;
int tot = 0;
REP(i, 4) tot += tmp[i]; tot = 54 - tot;
REP(i, 4)
{
if (up[i] > tmp[i])
{
tmp[i]++;
ret += (up[i] - tmp[i] + 1.0) / tot * dfs(tmp, up);
tmp[i]--;
}
}
if (up[4])
{
double retmin = 100;
REP(i, 4)
{
tmp[i]++; up[i]++; up[4]--; tmp[4] = i + 1;
retmin = min(retmin, 1.0 / tot * dfs(tmp, up));
tmp[i]--; up[i]--; up[4]++; tmp[4] = 0;
}
ret += retmin;
}
if (up[5])
{
double retmin = 100;
REP(i, 4)
{
tmp[i]++; up[i]++; up[5]--; tmp[5] = i + 1;
retmin = min(retmin, 1.0 / tot * dfs(tmp, up));
tmp[i]--; up[i]--; up[5]++; tmp[5] = 0;
}
ret += retmin;
}
dp[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][tmp[5]] = ++ret;
return ret;
}
int main ()
{
int T;
int ncase = 1;
RI(T);
while (T--)
{
int xx = 0, tot = 0;
goal.clear();
REP(i, 4)
{
int x; RI(x); goal.push_back(x);
if (x > 13) xx += x - 13;
tot += x;
}
double ans;
if (tot > 54 || xx > 2)
{
ans = -1.000;
}
else
{
memset(vis, 0, sizeof(vis));
vector<int> tmp, up;
REP(i, 6) tmp.push_back(0);
REP(i, 4) up.push_back(13); REP(i, 2) up.push_back(1);
ans = dfs(tmp, up);
if (ans < 0) ans = 0.000;
}
printf("Case %d: %.3lf\n", ncase++, ans);
}
return 0;
}
//#pragma warning (disable: 4786)
//#pragma comment (linker, "/STACK:16777216")
//HEAD
#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <cstring>
#include <queue>
#include <string>
#include <set>
#include <stack>
#include <map>
#include <cmath>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
//LOOP
#define FE(i, a, b) for(int i = (a); i <= (b); ++i)
#define FD(i, b, a) for(int i = (b); i>= (a); --i)
#define REP(i, N) for(int i = 0; i < (N); ++i)
#define CLR(A,value) memset(A,value,sizeof(A))
#define CPY(a, b) memcpy(a, b, sizeof(a))
#define FC(it, c) for(__typeof((c).begin()) it = (c).begin(); it != (c).end(); it++)
//INPUT
#define RI(n) scanf("%d", &n)
#define RII(n, m) scanf("%d%d", &n, &m)
#define RIII(n, m, k) scanf("%d%d%d", &n, &m, &k)
#define RS(s) scanf("%s", s)
//OUTPUT
#define WI(n) printf("%d\n", n)
#define WS(s) printf("%s\n", s)
typedef long long LL;
const int INF = 1000000007;
const double eps = 1e-10;
const int MAXN = 1010;
vector<int> goal;
double dp[14][14][14][14][5][5];
bool vis[14][14][14][14][5][5];
inline bool check(vector<int> &tmp)
{
int xx = tmp[4], yy = tmp[5];
if (xx) tmp[xx - 1]++; if (yy) tmp[yy - 1]++;
bool ret = true;
for (int i = 0; i < 4; i++)
if (goal[i] > tmp[i]) ret = false;
if (xx) tmp[xx - 1]--; if (yy) tmp[yy - 1]--;
return ret;
}
double dfs(vector<int> &tmp)
{
if (check(tmp)) return 0.0;
if (vis[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][tmp[5]])
return dp[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][tmp[5]];
vis[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][tmp[5]] = true;
double ret = 0;
int tot = 0;
REP(i, 4) tot += tmp[i];
int xx = tmp[4], yy = tmp[5];
if (xx) tot++; if (yy) tot++;
tot = 54 - tot;
REP(i, 4)
{
if (13 > tmp[i])
{
tmp[i]++;
ret += (13 - tmp[i] + 1.0) / tot * dfs(tmp);
tmp[i]--;
}
}
if (!xx)
{
double retmin = 100;
REP(i, 4)
{
tmp[4] = i + 1;
retmin = min(retmin, 1.0 / tot * dfs(tmp));
tmp[4] = 0;
}
ret += retmin;
}
if (!yy)
{
double retmin = 100;
REP(i, 4)
{
tmp[5] = i + 1;
retmin = min(retmin, 1.0 / tot * dfs(tmp));
tmp[5] = 0;
}
ret += retmin;
}
dp[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][tmp[5]] = ++ret;
return ret;
}
int main ()
{
int T;
int ncase = 1;
RI(T);
while (T--)
{
int xx = 0, tot = 0;
goal.clear();
REP(i, 4)
{
int x; RI(x); goal.push_back(x);
if (x > 13) xx += x - 13;
tot += x;
}
double ans;
if (tot > 54 || xx > 2)
{
ans = -1.000;
}
else
{
memset(vis, 0, sizeof(vis));
vector<int> tmp;
REP(i, 6) tmp.push_back(0);
ans = dfs(tmp);
if (ans < 0) ans = 0.000;
}
printf("Case %d: %.3lf\n", ncase++, ans);
}
return 0;
}
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原文地址：http://blog.csdn.net/guognib/article/details/38664747
