水概率....SGU里难得的水题.... 495. Kids and Prizes Time limit per test: 0.5 second(s)Memory limit: 262144 kilobytes input: standardoutput: standard ICPC (International Cardboard Producing Company) is in the business of producing cardboard boxes. Recently the…

题目链接 495. Kids and Prizes Time limit per test: 0.25 second(s)Memory limit: 262144 kilobytes input: standardoutput: standard ICPC (International Cardboard Producing Company) is in the business of producing cardboard boxes. Recently the company organiz…

http://acm.sgu.ru/problem.php?contest=0&problem=495 学习:当一条路走不通,换一种对象考虑,还有考虑对立面. 495. Kids and Prizes Time limit per test: 0.25 second(s)Memory limit: 262144 kilobytes input: standardoutput: standard ICPC (International Cardboard Producing Company) is…

题意: N个礼品箱, 每个礼品箱内的礼品只有第一个抽到的人能拿到. M个小孩每个人依次随机抽取一个,  求送出礼品数量的期望值. 1 ≤ N, M ≤ 100, 000 挺水的说..设f(x)表示前x个人都选择完成后礼品剩下数的期望值( f(0) = N ), 那么f(x) = f(x - 1) - f(x - 1) / N = f(x - 1) * (N - 1) / N (显然). 那么答案就是等于 N - N * [(N - 1) / N]^M. 后面部分可以用快速幂优化.时间复杂度O(l…

http://acm.sgu.ru/problem.php?contest=0&problem=495 题意:N个箱子M个人,初始N个箱子都有一个礼物,M个人依次等概率取一个箱子,如果有礼物则拿出礼物放回盒子,如果没有礼物则不操作.问M个人拿出礼物个数的期望.(N,M<=100000) #include <cstdio> using namespace std; double mpow(double a, int n) { double r=1; while(n) { if(n&…

题目链接:http://acm.sgu.ru/problem.php?contest=0&problem=495 题意: 有n个礼物盒,m个人. 最开始每个礼物盒中都有一个礼物. m个人依次随机选一个盒子,如果有礼物就拿走,然后放回空盒子. 问你所有人得到总礼物数的期望. 题解: 三种做法:期望dp,概率dp,推公式 一.期望dp 表示状态: dp[i] = 该第i个人拿箱子时的总礼物的期望 找出答案: ans = dp[m] 如何转移: 对于第i个人,拿到礼物或没拿到. (1)φ(没拿到) =…

495. Kids and Prizes Time limit per test: 0.25 second(s)Memory limit: 262144 kilobytes input: standardoutput: standard ICPC (International Cardboard Producing Company) is in the business of producing cardboard boxes. Recently the company organized a…

题目链接:http://acm.sgu.ru/problem.php?contest=0&problem=495 题目大意:有N个盒子,里面都放着礼物,M个人依次去选择盒子,每人仅能选一次,如果里面有礼物则将礼物取出来,把空盒子放回原位,若没有礼物,则把空盒子放回原位.求礼物被拿走的个数的数学期望. 令 x[i] 代表第i个人拿到的礼物的个数,即值为0或1. 那么,N个人拿到的礼物的个数为 X = Sigma(X[i]). 因此 E[X] = E[Sigma(X[i])] = Sigma(E[X…

题目链接:http://acm.sgu.ru/problem.php?contest=0&problem=495 题意:有n个盒子,每个盒子里面放了一个奖品,m个人轮流去选择盒子,如果盒子里面有奖品,就把奖品拿走,盒子留下,否则直接走人.求最后被抽走的奖品数期望... 如果直接考虑用期望来建立DP,复杂度都很高,而且题目精度过高.换一个角度思考,考虑每个奖品不被拿走的概率(1/n)^m,那么不被拿走的期望就是n*(1/n)^m,则拿走的期望n-n*(1/n)^m,复杂度O(1).还可以考虑f[i…

495. Kids and Prizes Time limit per test: 0.25 second(s) Memory limit: 262144 kilobytes input: standard output: standard ICPC (International Cardboard Producing Company) is in the business of producing cardboard boxes. Recently the company organized…