469. Convex Polygon
Given a list of points that form a polygon when joined sequentially, find if this polygon is convex (Convex polygon definition).
Note:
- There are at least 3 and at most 10,000 points.
- Coordinates are in the range -10,000 to 10,000.
- You may assume the polygon formed by given points is always a simple polygon (Simple polygon definition). In other words, we ensure that exactly two edges intersect at each vertex, and that edges otherwise don't intersect each other.
Example 1:
[[0,0],[0,1],[1,1],[1,0]] Answer: True Explanation:
Example 2:
[[0,0],[0,10],[10,10],[10,0],[5,5]] Answer: False Explanation:
Rust Solution
struct Solution;
impl Solution {
fn is_convex(points: Vec<Vec<i32>>) -> bool {
let n = points.len();
let mut positive = 0;
let mut negative = 0;
for i in 0..n {
let sign = Self::cross(&points[i], &points[(i + 1) % n], &points[(i + 2) % n]);
if sign >= 0 {
positive += 1;
}
if sign <= 0 {
negative += 1;
}
}
positive == n || negative == n
}
fn cross(a: &[i32], b: &[i32], c: &[i32]) -> i32 {
(b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
}
}
#[test]
fn test() {
let points = vec_vec_i32![[0, 0], [0, 1], [1, 1], [1, 0]];
let res = true;
assert_eq!(Solution::is_convex(points), res);
let points = vec_vec_i32![[0, 0], [0, 10], [10, 10], [10, 0], [5, 5]];
let res = false;
assert_eq!(Solution::is_convex(points), res);
}
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