[LeetCode] 1232. Check If It Is a Straight Line
grandyang opened this issue · comments
You are given an array coordinates
, coordinates[i] = [x, y]
, where [x, y]
represents the coordinate of a point. Check if these points make a straight line in the XY plane.
Example 1:
Input: coordinates = [[1,2],[2,3],[3,4],[4,5],[5,6],[6,7]]
Output: true
Example 2:
Input: coordinates = [[1,1],[2,2],[3,4],[4,5],[5,6],[7,7]]
Output: false
Constraints:
2 <= coordinates.length <= 1000
coordinates[i].length == 2
-10^4 <= coordinates[i][0], coordinates[i][1] <= 10^4
coordinates
contains no duplicate point.
这道题给了一堆二维坐标上的点,问这些点是否在一条直线上。初中的时候应该就学过两点确定一条直线,同时还有如何判断三点共线的问题,本质上就是判断三点中任意两个点组成的直线的斜率是否相同。计算两个点组成的直线的斜率,就是二者的纵坐标之差除以横坐标之差,但用除法的话就存在一个除数为0的问题,所以在比较两条直线的斜率是否相等时,将其变为乘法的形式,能有效的避免除数为0的情况。这道题说了给定的点的个数至少有两个,则可以用前两个点来确定一条直线,然后从第三个点开始遍历,判断每个遍历到的点和前两个点是否共线,就是不停的在验证三点共线问题,若某个点不在直线上,则返回 false,否则最后返回 true 即可,参见代码如下:
class Solution {
public:
bool checkStraightLine(vector<vector<int>>& coordinates) {
int x1 = coordinates[0][0], y1 = coordinates[0][1];
int x2 = coordinates[1][0], y2 = coordinates[1][1];
for (int i = 2; i < coordinates.size(); ++i) {
int x3 = coordinates[i][0], y3 = coordinates[i][1];
if ((x2 - x1) * (y3 - y1) != (y2 - y1) * (x3 - x1)) return false;
}
return true;
}
};
Github 同步地址:
参考资料:
https://leetcode.com/problems/check-if-it-is-a-straight-line/
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