LightOJ 1077 How Many Points?

Description

Given two points A and B on the X-Y plane, output the number of the lattice points on the segment AB. Note that A and B are also lattice point. Those who are confused with the definition of lattice point, lattice points are those points which have both x and y co-ordinate as integer.

For example, for A (3, 3) and B (-1, -1) the output is 5. The points are: (-1, -1), (0, 0), (1, 1), (2, 2) and (3, 3).

Input

Input starts with an integer T (≤ 125), denoting the number of test cases.

Each case contains four integers, A_x, A_y, B_x and B_y. Each of them will be fit into a 32 bit signed integer.

Output

For each test case, print the case number and the number of lattice points between AB.

Sample Input

2

3 3 -1 -1

0 0 5 2

Sample Output

Case 1: 5

Case 2: 2

题目很简单,就是让你求两个整数点连成的线段上的整数点（包括两端）有多少个

比如（1，1）（3，3）之间的点有（1，1），（2，2），（3，3）三个点；

看到这个题我想用斜率来做，结果做了两个小时还是不对，后来才知道思路不对，求下公约数就能出来；

#include<stdio.h>#include<stdlib.h>#include<algorithm>using namespace std;int main(){    int tCase,t=1;    long long x1,y1,y2,x2;    scanf("%d",&tCase);    while(tCase--)    {        scanf("%lld%lld%lld%lld",&x1,&y1,&x2,&y2);        printf("Case %d: %lld\n",t++,(long long)__gcd(abs(y2-y1),abs(x2-x1))+1);    }    return 0;}