HDU 5236 Article (概率DP+贪心)

题意：要求输入一篇N个字符的文章，对所有非负整数i：每到第i+0.1秒时可以输入一个文章字符，每到第i+0.9秒时有P的概率崩溃（回到开头或者上一个存盘点）

每到第i秒有一次机会可以选择按下X个键存盘，或者不存，打印完整篇文章之后必须存盘一次才算完成输入多组N,P,X选择最佳策略使得输入完整篇文章时候按键的期望最小，

输出此期望

析：dp[i]表示打完前 i 个字符，概论是多少，dp[i] = dp[i-1] + p(1+dp[i]) + 1-p。然后解得dp[i] = (dp[i-1]+1) / (1-p)。

最后再枚举多少次保存。均匀分布是最优的。

代码如下：

#pragma comment(linker, "/STACK:1024000000,1024000000")

#include <cstdio>

#include <string>

#include <cstdlib>

#include <cmath>

#include <iostream>

#include <cstring>

#include <set>

#include <queue>

#include <algorithm>

#include <vector>

#include <map>

#include <cctype>

#include <cmath>

#include <stack>

#include <sstream>

#define debug() puts("++++");

#define gcd(a, b) __gcd(a, b)

#define lson l,m,rt<<1

#define rson m+1,r,rt<<1|1

#define freopenr freopen("in.txt", "r", stdin)

#define freopenw freopen("out.txt", "w", stdout)

using namespace std;

typedef long long LL;

typedef unsigned long long ULL;

typedef pair<int, int> P;

const int INF = 0x3f3f3f3f;

const LL LNF = 1e16;

const double inf = 0x3f3f3f3f3f3f;

const double PI = acos(-1.0);

const double eps = 1e-8;

const int maxn = 1e5 + 10;

const int mod = 1e9 + 7;

const int dr[] = {-1, 0, 1, 0};

const int dc[] = {0, 1, 0, -1};

const char *de[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"};

int n, m;

const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};

const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};

inline bool is_in(int r, int c){

  return r >= 0 && r < n && c >= 0 && c < m;

}

double dp[maxn];

int main(){

  int T;  cin >> T;

  for(int kase = 1; kase <= T; ++kase){

    double p;

    scanf("%d %lf %d", &n, &p, &m);

    dp[0] = 0;

    for(int i = 1; i <= n; ++i)  dp[i] = (dp[i-1]+1) / (1-p);

    double ans = inf;

    for(int i = 1; i <= n; ++i){

      int a = n / i;

      int b = n % i;

      ans = min(ans, dp[a+1] * b + dp[a] * (i-b) + (double)m*i);

    }

    printf("Case #%d: %f\n", kase, ans);

  }

  return 0;

}

巴特西

HDU 5236 Article (概率DP+贪心)

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