Given lower left and upper right coordinates (x1, y1) and (x2, y2) of a square, the task is to count the number of integral coordinates that lies strictly inside the square.
Input: x1 = 1, y1 = 1, x2 = 4, x3 = 4
Approach: The difference between the x and y ordinates of the lower and upper right coordinates of the given squares gives the number integral points of x ordinates and y ordinates between opposite sides of square respectively. The total number of points that strictly lies inside the square is given by:
count = (x2 – x1 – 1) * (y2 – y1 – 1)
In the above figure:
1. The total number of integral points inside base of the square is (x2 – x1 – 1).
2. The total number of integral points inside height of the square is (y2 – y1 – 1).
These (x2 – x1 – 1) integrals points parallel to the base of the square repeats (y2 – y1 – 1) number of times. Therefore the total number of integral points is given by (x2 – x1 – 1)*(y2 – y1 – 1).
Below is the implementation of the above approach:
Time Complexity: O(1)
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Count Integral points inside a Triangle
- Generate all integral points lying inside a rectangle
- Coordinates of rectangle with given points lie inside
- Check whether a given point lies inside a triangle or not
- How to check if a given point lies inside or outside a polygon?
- Find if a point lies inside a Circle
- Check whether a given point lies inside a rectangle or not
- Check if a given circle lies completely inside the ring formed by two concentric circles
- Check whether a point lies inside a sphere or not
- Check if a point lies on or inside a rectangle | Set-2
- Check whether a given point lies on or inside the rectangle | Set 3
- Find a point that lies inside exactly K given squares
- Check if a circle lies inside another circle or not
- Check if the given point lies inside given N points of a Convex Polygon
- Find if a point lies inside, outside or on the circumcircle of three points A, B, C
- Minimum length of square to contain at least half of the given Coordinates
- Sum of Area of all possible square inside a rectangle
- Area of a leaf inside a square
- Find the number of squares inside the given square grid
- Area of largest semicircle that can be drawn inside a square
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.