469. Convex Polygon

Description

You are given an array of points on the X-Y plane points where points[i] = [xi, yi]. The points form a polygon when joined sequentially.

Return true if this polygon is convex and false otherwise.

You may assume the polygon formed by given points is always a simple polygon. In other words, we ensure that exactly two edges intersect at each vertex and that edges otherwise don't intersect each other.

 

Example 1:

Input: points = [[0,0],[0,5],[5,5],[5,0]]
Output: true

Example 2:

Input: points = [[0,0],[0,10],[10,10],[10,0],[5,5]]
Output: false

 

Constraints:

  • 3 <= points.length <= 104
  • points[i].length == 2
  • -104 <= xi, yi <= 104
  • All the given points are unique.

Solutions

Solution 1

Python Code
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class Solution:
    def isConvex(self, points: List[List[int]]) -> bool:
        n = len(points)
        pre = cur = 0
        for i in range(n):
            x1 = points[(i + 1) % n][0] - points[i][0]
            y1 = points[(i + 1) % n][1] - points[i][1]
            x2 = points[(i + 2) % n][0] - points[i][0]
            y2 = points[(i + 2) % n][1] - points[i][1]
            cur = x1 * y2 - x2 * y1
            if cur != 0:
                if cur * pre < 0:
                    return False
                pre = cur
        return True

Java Code
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class Solution {
    public boolean isConvex(List<List<Integer>> points) {
        int n = points.size();
        long pre = 0, cur = 0;
        for (int i = 0; i < n; ++i) {
            var p1 = points.get(i);
            var p2 = points.get((i + 1) % n);
            var p3 = points.get((i + 2) % n);
            int x1 = p2.get(0) - p1.get(0);
            int y1 = p2.get(1) - p1.get(1);
            int x2 = p3.get(0) - p1.get(0);
            int y2 = p3.get(1) - p1.get(1);
            cur = x1 * y2 - x2 * y1;
            if (cur != 0) {
                if (cur * pre < 0) {
                    return false;
                }
                pre = cur;
            }
        }
        return true;
    }
}

C++ Code
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class Solution {
public:
    bool isConvex(vector<vector<int>>& points) {
        int n = points.size();
        long long pre = 0, cur = 0;
        for (int i = 0; i < n; ++i) {
            int x1 = points[(i + 1) % n][0] - points[i][0];
            int y1 = points[(i + 1) % n][1] - points[i][1];
            int x2 = points[(i + 2) % n][0] - points[i][0];
            int y2 = points[(i + 2) % n][1] - points[i][1];
            cur = 1L * x1 * y2 - x2 * y1;
            if (cur != 0) {
                if (cur * pre < 0) {
                    return false;
                }
                pre = cur;
            }
        }
        return true;
    }
};

Go Code
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func isConvex(points [][]int) bool {
	n := len(points)
	pre, cur := 0, 0
	for i := range points {
		x1 := points[(i+1)%n][0] - points[i][0]
		y1 := points[(i+1)%n][1] - points[i][1]
		x2 := points[(i+2)%n][0] - points[i][0]
		y2 := points[(i+2)%n][1] - points[i][1]
		cur = x1*y2 - x2*y1
		if cur != 0 {
			if cur*pre < 0 {
				return false
			}
			pre = cur
		}
	}
	return true
}