题目链接http://acm.hdu.edu.cn/showproblem.php?pid=1695 看了别人的方法才会做 参考博客http://blog.csdn.net/shiren_Bod/article/details/5787722 题意 a,b,c,d,k五个数,a与c可看做恒为1,求在a到b中选一个数x,c到d中选一个数y,使得gcd(x,y)等于k,求x和y有多少对. 首先可以想到选取的必是k的倍数,假设是x和y倍,则x和y一定是互质的在,那么就变成了求1到b/k和1到d/k的之…

GCD Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 4272    Accepted Submission(s): 1492 Problem Description Given 5 integers: a, b, c, d, k, you're to find x in a...b, y in c...d that GCD(x, y)…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=1695 题意:x位于区间[a, b],y位于区间[c, d],求满足GCD(x, y) = k的(x, y)有多少组,不考虑顺序. 思路:a = c = 1简化了问题,原问题可以转化为在[1, b/k]和[1, d/k]这两个区间各取一个数,组成的数对是互质的数量,不考虑顺序.我们让d > b,我们枚举区间[1, d/k]的数i作为二元组的第二位,因为不考虑顺序我们考虑第一位的值时,只用考虑小于i的情…

GCD Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 5064    Accepted Submission(s): 1818 Problem Description Given 5 integers: a, b, c, d, k, you're to find x in a...b, y in c...d that GCD(x, y)…

Longge's problem Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 6918   Accepted: 2234 Description Longge is good at mathematics and he likes to think about hard mathematical problems which will be solved by some graceful algorithms. Now…

分析 考虑使用欧拉函数的计算公式化简原式,因为有: \[lcm(i_1,i_2,...,i_k)=p_1^{q_{1\ max}} \times p_2^{q_{2\ max}} \times ... \times p_m^{q_{m\ max}}\] 其实就是分解质因数,丢到那个式子里: \[\varphi(lcm(i_1,i_2,...,i_k))=\prod (p_i-1)p_i^{q_{i\ max}-1}\] 容易发现可以分开讨论每个质数,计算每个\(p_i^j\)在多少种\(i_1…

F - GCD Time Limit:3000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u Submit Status Practice HDU 1695 Description Given 5 integers: a, b, c, d, k, you're to find x in a...b, y in c...d that GCD(x, y) = k. GCD(x, y) means the greatest c…

链接:http://acm.hdu.edu.cn/showproblem.php?pid=1695 题意:在[a,b]中的x,在[c,d]中的y,求x与y的最大公约数为k的组合有多少.(a=1, a <= b <= 100000, c=1, c <= d <= 100000, 0 <= k <= 100000) 思路:由于x与y的最大公约数为k,所以xx=x/k与yy=y/k一定互质.要从a/k和b/k之中选择互质的数,枚举1~b/k,当选择的yy小于等于a/k时,能够…

题目 给定两个区间[1, b], [1, d],统计数对的个数(x, y)满足: \(x \in [1, b]\), \(y \in [1, d]\) ; \(gcd(x, y) = k\) HDU1695 题解 我们观察式子\(gcd(x,y)=k\) 很显然,\(gcd(x/k, y/k) = 1\) 我们令b < d,令x<y(避免重复计数) 分类讨论. 1) y < b 可以看出答案就是\(\sum_{i \in [1, b]} \phi(i)\) 2)\(y \in [b, d…

GCD Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 15488    Accepted Submission(s): 5948 Problem Description Given 5 integers: a, b, c, d, k, you're to find x in a...b, y in c...d that GCD(x,…