poj2115 C Looooops 题意: 对于C的for(i=A ; i!=B ;i +=C)循环语句,问在k位存储系统中循环几次才会结束. 若在有限次内结束,则输出循环次数. 否则输出死循环. (k位==mod $2^{k}$) 列出方程:$A+Cx\equiv B(mode\quad 2^{k})$ 转换一下:$Cx+ky=B-A$ 用exgcd解出 $Cx+ky=gcd(C,k)$ 然后把求出的$x*(B-A)/gcd(C,k)$ 再$\% (k/gcd(C,k))$求个最小正整数解…

题目链接. 分析: 数论了解的还不算太多,解的时候,碰到了不小的麻烦. 设答案为x,n = (1<<k), 则 (A+C*x) % n == B 即 (A+C*x) ≡ B (mod n) 化简得 C*x ≡ (B-A) (mod n) 设 a = C, b = (B-A) 则原式变为 ax=b.解 x. 到这里,以为求出来 a 的逆, 然后 x = b*a-1. a 的 逆好求,用<训练指南>上的模板(P122) inv函数. 例如,求 2 模 66536 下的逆, inv(2,…

A Compiler Mystery: We are given a C-language style for loop of type for (variable = A; variable != B; variable += C) statement; I.e., a loop which starts by setting variable to value A and while variable is not equal to B, repeats statement followed…

C Looooops DescriptionA Compiler Mystery: We are given a C-language style for loop of type for (variable = A; variable != B; variable += C) statement;I.e., a loop which starts by setting variable to value A and while variable is not equal to B, repea…

C Looooops Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 24355   Accepted: 6788 Description A Compiler Mystery: We are given a C-language style for loop of type for (variable = A; variable != B; variable += C) statement; I.e., a loop w…

欢迎访问~原文出处——博客园-zhouzhendong 去博客园看该题解 题目传送门 - POJ2115 题意 对于C的for(i=A ; i!=B ;i +=C)循环语句,问在k位存储系统中循环几次才会结束.若在有限次内结束,则输出循环次数.否则输出死循环. 题解 原题题意再次缩略: A + xC Ξ B (mod 2k) 求x的最小正整数值. 我们把式子稍微变一下形: Cx + (2k)y = B-A 然后就变成了一个基础的二元一次方程求解,扩展欧几里德套套就可以了. 至于扩展欧几里德(ex…

题目: http://poj.org/problem?id=2115 要求: 会求最优解,会求这d个解,即(x+(i-1)*b/d)modm;(看最后那个博客的链接地址) 前两天用二元一次线性方程解过,万变不离其宗都是利用扩展欧几里得来接最优解. 分析: 数论了解的还不算太多,解的时候,碰到了不小的麻烦. 设答案为x,n = (1<<k), 则 (A+C*x) % n == B 即 (A+C*x) ≡ B (mod n)//-----结果显而易见两边的(a+cx)%n==b<n 化简得…

C Looooops Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 29262   Accepted: 8441 Description A Compiler Mystery: We are given a C-language style for loop of type for (variable = A; variable != B; variable += C) statement; I.e., a loop w…

题目链接:http://poj.org/problem?id=2115 C Looooops Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 27838   Accepted: 7930 Description A Compiler Mystery: We are given a C-language style for loop of type for (variable = A; variable != B; vari…

无符号k位数溢出就相当于mod 2k,然后设循环x次A等于B,就可以列出方程: $$ Cx+A \equiv B \pmod {2^k} $$ $$ Cx \equiv B-A \pmod {2^k} $$ 最后就用扩展欧几里得算法求出这个线性同余方程的最小非负整数解. #include<cstdio> #include<cstring> #define mod(x,y) (((x)%(y)+(y))%(y)) #define ll long long ll exgcd(ll a,…