题目链接: http://acm.hdu.edu.cn/showproblem.php? pid=1573 题目大意: 求在小于等于N的正整数中有多少个X满足:X mod a[0] = b[0], X mod a[1] = b[1], X mod a[2] = b[2], -, X mod a[i] = b[i], - (0 < a[i] <= 10). 思路: 先求出数组b[]中全部数的最小公倍数lcm,再求解出该一元线性同余方程组在lcm范围内的解为a.题目要 求解x是小于等于N的正整数,…
题目:求在小于等于N的正整数中有多少个X满足:X mod a[0] = b[0], X mod a[1] = b[1], X mod a[2] = b[2], -, X mod a[i] = b[i], - (0 < a[i] <= 10). 解法:先同上题一样用拓展欧几里德求出同余方程组的最后一个方程 X=ax+b,再调整 x 来求得 X 的解的个数.一些解释请看下面的代码. 注意--每次联立方程后求最小正整数解,可以提高代码速度. 1 #include<cstdio> 2 #i…
题意:Elina看一本刘汝佳的书(O_O*),里面介绍了一种奇怪的方法表示一个非负整数 m .也就是有 k 对 ( ai , ri ) 可以这样表示--m%ai=ri.问 m 的最小值. 解法:拓展欧几里德求解同余方程组的最小非负整数解.(感觉挺不容易的......+_+@) 先看前2个关系式: m%a1=r1 和 m%a2=r2 → …
套模板,因为要是正整数,所以处理一下x=0的情况. X问题 Time Limit: 1000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 4444 Accepted Submission(s): 1439 Problem Description 求在小于等于N的正整数中有多少个X满足:X mod a[0] = b[0], X mod a[1] = b[1], X…
第一步,和同余方程一样,转化一下 两式相减得 这就转化为了求不定方程,用exgcd 求出x,要化成最小正整数解,避免溢出 然后可以求出P出来. 这个时候要把前两个式子转化成一个式子 设求出来的是P' 则有 这个就转化成了新的m1和b1 然后就一直求下去即可 最终b1就是答案 #include<bits/stdc++.h> #define REP(i, a, b) for(register int i = (a); i < (b); i++) #define _for(i, a, b)…
链接: https://vjudge.net/problem/POJ-2891 题意: Elina is reading a book written by Rujia Liu, which introduces a strange way to express non-negative integers. The way is described as following: Choose k different positive integers a1, a2, -, ak. For some…
同余方程组: 先来看一道题目:有物不知其数,三三数之剩二:五五数之剩三:七七数之剩二.问物几何? 然后我们可以做如下变换,设x为所求的数. x%3=2 x ≡ a1(%m1) ① x%5=3 ===> x ≡ a2(%m2) ② x%7=2 x ≡ a3(%m3) 根据前面两式可以得到 x = a1+m1y1 (1) x = a2+m2y2 两式相减得到 m1y1 - m2y2 = a2 - a1 这是一个线性不定方程,可…
写一下自己的理解,下面附上转载的:若a==b(modk);//这里的==指的是同余,我用=表示相等(a%k=b)a-b=kt(t为整数)以前理解的错误思想:以前认为上面的形式+(a-tb=k)也是成立的,今天一想随便就能举出一个反例11==5(mod3)同样是求这个东西..X mod m1=r1X mod m2=r2.........X mod mn=rn 首先,我们看两个式子的情况X mod m1=r1……………………………………………………………(1)X mod m2=r2…………………………
Hello Kiki Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 2734 Accepted Submission(s): 1010 Problem Description One day I was shopping in the supermarket. There was a cashier counting coins…
一个exgcd解决一个线性同余问题,多个exgcd解决线性同余方程组. Strange Way to Express Integers Time Limit: 1000MS Memory Limit: 131072K Total Submissions: 12001 Accepted: 3797 Description Elina is reading a book written by Rujia Liu, which introduces a strange way to expre…
Elina is reading a book written by Rujia Liu, which introduces a strange way to express non-negative integers. The way is described as following: Choose k different positive integers a1, a2, …, ak. For some non-negative m, divide it by every ai (1 ≤ …
Description Elina is reading a book written by Rujia Liu, which introduces a strange way to express non-negative integers. The way is described as following: Choose k different positive integers a1, a2, -, ak. For some non-negative m, divide it by ev…