Codeforces 1178D (思维+数学) 题面 给出正整数n(不一定是质数),构造一个边数为质数的无向连通图(无自环重边),且图的每个节点的度数为质数 分析 我们先构造一个环,每个点的度数都是2.但由于n不一定是质数,我们还需要再加k条边.然后对于\(i \in [1,k]\),我们加边(i,i+n/2).当\(k\leq \frac{n}{2}\)的时候,只会把一些点的度数由2变成3,否则会出现重边问题.假设新图的边数为m,那\(m \in [n,n+\frac{n}{2}]\),如果…

传送门 首先每个点至少要有两条边连接 那么容易想到先保证这一点然后再慢慢加边 那么先构成一个环即可:$(1,2),(2,3),(3,4)...(n,1)$ 然后考虑加边,发现一个点加一条边还是合法的,那么不妨直接 $(1,4),(2,5),(3,6)$ ,然后一旦边数为质数了就直接输出答案 那么现在问题就是能否保证在 $[n,n+\left \lfloor \frac {n-3} {2} \right \rfloor]$ 范围内一定有质数 打个表发现在 $n \in [3,1000]$ 内唯一不…

D. Relatively Prime Graph time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output Let's call an undirected graph G=(V,E)G=(V,E) relatively prime if and only if for each edge (v,u)∈E(v,u)∈E  GCD(v,…

Relatively Prime Graph time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output Let's call an undirected graph G=(V,E)G=(V,E) relatively prime if and only if for each edge (v,u)∈E(v,u)∈E  GCD(v,u)=…

Let's call an undirected graph G=(V,E)G=(V,E) relatively prime if and only if for each edge (v,u)∈E(v,u)∈E  GCD(v,u)=1GCD(v,u)=1 (the greatest common divisor of vv and uu is 11). If there is no edge between some pair of vertices vv and uu then the va…

题目描述: Prime Gift time limit per test 3.5 seconds memory limit per test 256 megabytes input standard input output standard output Opposite to Grisha's nice behavior, Oleg, though he has an entire year at his disposal, didn't manage to learn how to sol…

Every person likes prime numbers. Alice is a person, thus she also shares the love for them. Bob wanted to give her an affectionate gift but couldn't think of anything inventive. Hence, he will be giving her a graph. How original, Bob! Alice will sur…

题目链接:http://codeforces.com/contest/1036/problem/F 题意: 题解:求在[2,n]中,x != a ^ b(b >= 2 即为gcd)的个数,那么实际上就是要求x = a ^ b的个数,然后用总数减掉就好了,答案即为.(pow会丢失精度,学习避免精度丢失的方法) #include <bits/stdc++.h> using namespace std; #define ll long long #define LL __int128 #def…

ACM思维题训练集合 To confuse the opponents, the Galactic Empire represents fractions in an unusual format. The fractions are represented as two sets of integers. The product of numbers from the first set gives the fraction numerator, the product of numbers…

A. Anastasia and pebbles time limit per test:1 second memory limit per test:256 megabytes input:standard input output:standard output Anastasia loves going for a walk in Central Uzhlyandian Park. But she became uninterested in simple walking, so she…