I. Older Brother Your older brother is an amateur mathematician with lots of experience. However, his memory is very bad. He recently got interested in linear algebra over finite fields, but he does not remember exactly which finite fields exist. For…

L. Sticky Situation While on summer camp, you are playing a game of hide-and-seek in the forest. You need to designate a “safe zone”, where, if the players manage to sneak there without being detected,they beat the seeker. It is therefore of utmost i…

Alice and Bob are playing a simple game. They line up a row of n identical coins, all with the heads facing down onto the table and the tails upward. For exactly mm times they select any k of the coins and toss them into the air, replacing each of th…

All as we know, a mountain is a large landform that stretches above the surrounding land in a limited area. If we as the tourists take a picture of a distant mountain and print it out, the image on the surface of paper will be in the shape of a parti…

Alice and Bob are playing a simple game. They line up a row of nn identical coins, all with the heads facing down onto the table and the tails upward. For exactly mm times they select any kk of the coins and toss them into the air, replacing each of…

A. Coins Alice and Bob are playing a simple game. They line up a row of nnn identical coins, all with the heads facing down onto the table and the tails upward. For exactly mmm times they select any kkk of the coins and toss them into the air, replac…

八数码问题也称为九宫问题.(本想查查历史,结果发现居然没有词条= =,所谓的历史也就不了了之了) 在3×3的棋盘,摆有八个棋子,每个棋子上标有1至8的某一数字,不同棋子上标的数字不相同.棋盘上还有一个空格,与空格相邻的棋子可以移到空格中.要求解决的问题是: 给出一个初始状态和一个目标状态,找出一种从初始转变成目标状态的移动棋子步数最少的移动步骤. 所谓问题的一个状态就是棋子在棋盘上的一种摆法.棋子移动后,状态就会发生改变.解八数码问题就是找出从初状态到目标状态所经过的一系列中间状态.八数码问题一…

挺不错的概率DP,看似基础,实则很考验扎实的功底 这题很明显是个DP,为什么???找规律或者算组合数这种概率,N不可能给的这么友善... 因为DP一般都要在支持N^2操作嘛. 稍微理解一下,这DP[i][j]还是不好想啊,首先是写DP[I][j]的含义 首先我们想这道题是要求一个最优决策下的期望,那么这个我们的最优决策是什么??? 决策就是:我们假设我这一次需要翻转K个硬币,我们不愿翻那些已经在正面的,而去翻那些没有在正面的 而如果剩余的反面的不足,我再去翻转正面的 那么给dp[i][j]一个含…

题目链接:https://www.jisuanke.com/contest/2870?view=challenges 题目大意:给出n个都正面朝下的硬币,操作m次,每次都选取k枚硬币抛到空中,求操作m次后,硬币向上的期望值. 思路: 1.期望跟概率还是有点不同的,期望要枚举出抛的所有的情况,然后求sigma(i * dp[][]) 2.dp[i][j]表示进行i次操作后,有j枚硬币向上的概率.这样就可以求最后的硬币向上的期望了. 3.值得注意的是,预处理的组合数要开 double 型. 代码:…

题目链接 题意,有m种颜色,给2n个位置染色,使左边n个和右边n个没有共同的颜色. 可以先递推求出恰用i种颜色染n个位置的方案数,然后枚举两边的染色数就可以了,代码很简单. #include<bits/stdc++.h> using namespace std; typedef long long LL; //求C(a,b) ,其中,a,b大小大概不超过1e6级别,很多组数据 ; ; LL fac[M+]; //阶乘 LL inv_of_fac[M+]; //阶乘的逆元 LL qpow(LL…