题意: 给定n,求问由2n个字母B,n个字母A构成的字符串中 任意前缀B的个数大于A的个数且任意后缀B的个数大于A的个数的 字符串个数. 解法: 注意到答案不易于直接计算,所以我们考虑应用容斥原理. 注意到本题非常类似卡特兰数. 卡特兰数等价于从棋盘上$(1,1)$走到$(n,n)$且不穿过对角线的方案数. 1.先考虑求存在前缀B的个数<A的个数的方案数. 等价于从棋盘上$(1,1)$上走到$(2n,n)$ 且 穿过从$(1,1)$开始,以$(1,1)$为方向向量的直线$L$ 的 方案数. 当第…

Intuitive one to learn about Grundy basic :) Now every pile becomes a game, so we need to use Sprague-Grundy Theory. Calculation is quite intuitive - and if you print them out, you will find these Grundy numbers loops by 9. def firstMissing(s): ret =…

Codeforces 382E Ksenia and Combinatorics Ksenia has her winter exams. Today she is learning combinatorics. Here's one of the problems she needs to learn to solve. How many distinct trees are there consisting of n vertices, each with the following pro…

Change language : Manasa 和 她的朋友出去徒步旅行.她发现一条小河里边顺序排列着带有数值的石头.她开始沿河而走,发现相邻两个石头上的数值增加 a 或者 b. 这条小河的尽头有一个宝藏,如果Manasa能够猜出来最后一颗石头上的数值,那么宝藏就是她的.假设第一个石头的上数值为0,找出最后一个石头的可能的所有数值. 输入格式 第一行包含整数 T, 代表测试数据的组数. 每组数组包含三行: 第一行包含 n,代表石头的个数 第二行包含 a 第三行包含 b 输出格式 升序输出最后一…

2.1 Inclusion-Exclusion Roughly speaking, a "sieve method" in enumerative combinatorics is a method for determining the cardinality of a set $S$ that begins with a larger set and somehow subtracts off or cancels out unwanted elements. Sieve meth…

Problem 1: Given an array of real number with length (n2 + 1) A: a1,  a2, ... , an2+1. Prove that there is either an increasing or a decreasing subarray of A with length (n + 1). Proof: In order to prove the proposition, we just need to prove that th…

https://www.hackerrank.com/contests/w2/challenges/manasa-and-stones 简单题. #include<iostream> using namespace std; int main() { int T; cin >> T; while (T--) { int n, a, b; cin >> n >> a >> b; // a < b if ( a > b) { int tm…

from __future__ import print_function def main(): t = int(raw_input()) for _ in range(t): n = int(raw_input()) a = int(raw_input()) b = int(raw_input()) possible_value = [] for _ in range(n): temp_value = (_ * a + (n - 1 - _) * b) # 抽象化理解题目的意思 if tem…

Given a non-negative integer n, count all numbers with unique digits, x, where 0 ≤ x < 10n. Example: Given n = 2, return 91. (The answer should be the total numbers in the range of 0 ≤ x < 100, excluding [11,22,33,44,55,66,77,88,99]) Hint: A direct…

原文:written by Sebastian Raschka on March 14, 2015 中文版译文:伯乐在线 - atmanic 翻译,toolate 校稿 This article offers a brief glimpse of the history and basic concepts of machine learning. We will take a look at the first algorithmically described neural network…