Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Convex Polygon in C++
Suppose we have a list of points that form a polygon when joined sequentially, we have to find if this polygon is convex (Convex polygon definition). We have to keep in mind that there are at least 3 and at most 10,000 points. And the coordinates are in the range -10,000 to 10,000.
We can 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. So if the input is like: [[0,0],[0,1],[1,1],[1,0]], then it is convex, so returned value will be true.
To solve this, we will follow these steps −
Define a method calc(), this will take ax, ay, bx, by, cx, cy, this will work as follows −
BAx := ax – bx, BAy := ay – by, BCx := cx – bx, BCy := cy - by
From the main method do the following
neg := false and pos := false, n := size of points array
for i in range 0 to n – 1
a := i, b := (i + 1) mod n and c := (i + 2) mod n
cross_prod := calc(p[a, 0], p[a, 1], p[b, 0], p[b, 1], p[c, 0], p[c, 1])
if cross_prod < 0, then neg := true, otherwise when cross_prod > 0, then pos := true
if neg and pos is true, then return false
return true
Example (C++)
Let us see the following implementation to get a better understanding −
#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
bool isConvex(vector<vector<int>>& points) {
bool neg = false;
bool pos = false;
int n = points.size();
for(int i = 0; i < n; i++){
int a = i;
int b = (i + 1) % n;
int c = (i + 2) % n;
int crossProduct = calc(points[a][0], points[a][1], points[b][0], points[b][1], points[c][0], points[c][1]);
if(crossProduct < 0) neg = true;
else if(crossProduct > 0) pos = true;
if(neg && pos) return false;
}
return true;
}
int calc(int ax, int ay, int bx, int by, int cx, int cy){
int BAx = ax - bx;
int BAy = ay - by;
int BCx = cx - bx;
int BCy = cy - by;
return (BAx * BCy - BAy * BCx);
}
};
main(){
vector<vector<int>> v = {{0,0},{0,1},{1,1},{1,0}};
Solution ob;
cout << (ob.isConvex(v));
}Input
[[0,0],[0,1],[1,1],[1,0]]
Output
1
1K+ Views
To Continue Learning Please Login