Given an integer N, the task is to divide the number into four parts such that the divided parts can be used to construct a rectangle but not a square. Find how many numbers of ways are there so that the number can be divided fulfilling the condition.
Input: N = 8
Input: N = 10
Approach: As the number has to be divided such that rectangle is formed from the divided four parts, so if the number is odd, then the number of ways will be zero, as perimeter of a rectangle is always even
Now, if n is even, then only (n – 2) / 4 number of ways are there to divide the number, for example,
if 8 has to be divided in four parts then there is only (8 – 2) / 4 = 1 way, i.e., [1, 1, 3, 3], no other way is there. It’s because you can only take sides length < = n/2 – 1 to form a valid rectangle and from those n/2 – 1 rectangles count divide again by 2 to avoid double counting.
Below is the implementation of the above approach:
Time Complexity: O(1)
- Find the number of ways to divide number into four parts such that a = c and b = d
- Count number of ways to divide a number in 4 parts
- Check if an array of 1s and 2s can be divided into 2 parts with equal sum
- Minimum Cuts can be made in the Chessboard such that it is not divided into 2 parts
- Check if any square (with one colored cell) can be divided into two equal parts
- Split a number into 3 parts such that none of the parts is divisible by 3
- Find if there exists multiple ways to draw line through (x, y) to cut rectangle in equal halfs
- Find minimum number to be divided to make a number a perfect square
- Divide N into K unique parts such that gcd of those parts is maximum
- Break the number into three parts
- Divide a number into two parts
- Largest number by which given 3 numbers should be divided such that they leaves same remainder
- Program to find remainder when large number is divided by r
- Number of K's such that the given array can be divided into two sets satisfying the given conditions
- Program to find remainder when large number is divided by 11
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. 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.