119. Magic Pairs time limit per test: 0.5 sec. memory limit per test: 4096 KB “Prove that for any integer X and Y if 5X+4Y is divided by 23 than 3X+7Y is divided by 23 too.” The task is from city Olympiad in mathematics in Saratov, Russia for schoolc…

Magic Pairs Problem's Link Mean: 已知N.A0.B0,对于给定X.Y,若A0X+B0Y能被N整除,则AX+BY也能被N整除,求所有的A.B.(0<=A.B<N) analyse: 这道题目就是先把A0和B0和N都除以他们的最大公约数,然后就是枚举A0和B0的0到N-1倍. 最后快排,注意一下有0的情况. Time complexity: O(N) view code /** * ------------------------------------------…

题目大意:如果A0*X + B0*Y能够整除 N,求出来多有少A*X+B*Y 也能够整除去N,求出所有的A,B(0<=A,B<N) 分析:有条件可以知道 A*X+B*Y = K *(A0*X + B0*Y)% N ====> (K * A0) % N = A, (K * B0) % N = B, (k=[0....N)). ps.记得排序去重复...... 代码如下: ============================================================…

题意: 对于给出的一个整数N,和一对(A0,B0) 找到所有的整数对(A,B)满足 : 对于任意 X,Y 当 A0 * X + B0 * Y 能被 N 整除时 A * X + B * Y 也能被 N 整除 Solution:               如果AX+BY能被N整除,则dAX+dBY也能,因A,B<N,所以(dA mod N)X+(dB mod N)Y也能,把所有情况枚举完排序输出 参考代码:              #include <stdio.h> #include…

127. Telephone directory time limit per test: 0.25 sec. memory limit per test: 4096 KB CIA has decided to create a special telephone directory for its agents. The first 2 pages of the directory contain the name of the directory and instructions for a…

126. Boxes time limit per test: 0.25 sec. memory limit per test: 4096 KB There are two boxes. There are A balls in the first box, and B balls in the second box (0 < A + B < 2147483648). It is possible to move balls from one box to another. From one…

123. The sum time limit per test: 0.25 sec. memory limit per test: 4096 KB The Fibonacci sequence of numbers is known: F1 = 1; F2 = 1; Fn+1 = Fn + Fn-1, for n>1. You have to find S - the sum of the first K Fibonacci numbers. Input First line contains…

120. Archipelago time limit per test: 0.25 sec. memory limit per test: 4096 KB Archipelago Ber-Islands consists of N islands that are vertices of equiangular and equilateral N-gon. Islands are clockwise numerated. Coordinates of island N1 are (x1, y1…

118. Digital Root time limit per test: 0.25 sec. memory limit per test: 4096 KB Let f(n) be a sum of digits for positive integer n. If f(n) is one-digit number then it is a digital root for n and otherwise digital root of n is equal to digital root o…

117. Counting time limit per test: 0.25 sec. memory limit per test: 4096 KB Find amount of numbers for given sequence of integer numbers such that after raising them to the M-th power they will be divided by K. Input Input consists of two lines. Ther…