数同余的个数显然是要把\(i,j\)分别放到\(\equiv\)的两边 $ (a_i + a_j)(a_i^2 + a_j^2) \equiv k \bmod p $ 左右两边乘上\((a_i-a_j)\) 得:\((a_i^2-a_j^2)(a_i^2+a_j^2)\equiv a_ik-a_jk \bmod p\Longrightarrow a_i^4-a_j^4\equiv a_ik-a_jk \bmod p\Longrightarrow a_i^4-a_ik\equiv a_j^4-a_…

You are given a prime number pp, nn integers a1,a2,…,ana1,a2,…,an, and an integer kk. Find the number of pairs of indexes (i,j)(i,j) (1≤i<j≤n1≤i<j≤n) for which (ai+aj)(a2i+a2j)≡kmodp(ai+aj)(ai2+aj2)≡kmodp. Input The first line contains integers n,p,…

Count Pairs Description You are given n circles centered on Y-aixs. The ith circle’s center is at point (i, 0) and its radius is A[i]. Count the number of pairs of circles that have at least one common point? Input The input should be a list of n pos…

Count Pairs You are given a prime number pp, nn integers a1,a2,…,ana1,a2,…,an, and an integer kk. Find the number of pairs of indexes (i,j)(i,j) (1≤i<j≤n1≤i<j≤n) for which (ai+aj)(a2i+a2j)≡kmodp(ai+aj)(ai2+aj2)≡kmodp. Input The first line contains i…

前言 这道题目是道好题. 第一次div-2进前100,我太弱了. 题解 公式推导 我们观察这个式子. \[(a_i+a_j)(a_i^2+a_j^2)\equiv k \mod p\] 感觉少了点什么,我们想到两边同时乘一个\((a_i-a_j)\). 于是它变成了: \[(a_i^2-a_j^2)(a_i^2+a_j^2) \equiv k(a_i-a_j) \mod p\] 也就是: \[a_i^4-a_j^4 \equiv k(a_i-a_j) \mod p\] 把\(k\)乘进去变成:…

[题目描述] 给定一个质数 \(p\) , 一个长度为 \(n\)n 的序列 \(a = \{ a_1,a_2,\cdots,a_n\}\)一个整数 \(k\). 求所有数对 \((i, j)\) (\(1 \le i .j \le n\))中满足 \((a_i + a_j) \times (a_i^2 + a_j^2 ) \equiv k (\bmod p)\)的个数. [题解] 对于题中的柿子: \[(a_i + a_j) \times (a_i^2 + a_j^2 ) \equiv k (…

链接: https://vjudge.net/problem/Gym-100923I 题意: We don't know how Por Costel the pig arrived at FMI's dance party. All we know is that he did. The dance floor is hot because Por Costel broke the air conditioner. On the dance floor, the boys and girls…

Codeforces 题面传送门 & 洛谷题面传送门 虽说是一个 D1B,但还是想了我足足 20min,所以还是写篇题解罢( 首先注意到这个式子里涉及两个参数,如果我们选择固定一个并动态维护另一个的决策,则相当于我们要求方程 \(ax^3+bx^2+cx+d\equiv k\pmod{p}\) 的根,而这是很难维护的,因此这个思路行不通.考虑 \((x+y)(x^2+y^2)\) 的性质,我们考虑在前面添上一项 \((x-y)\),根据初中数学 \((x-y)(x+y)(x^2+y^2)=x^4…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=4472 Problem Description Prof. Tigris is the head of an archaeological team who is currently in charge of an excavation in a site of ancient relics. This site contains relics of a village where civilizat…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=5056 Problem Description You are given a string S consisting of lowercase letters, and your task is counting the number of substring that the number of each lowercase letter in the substring is no more t…