Given a paper of size A x B. Task is to cut the paper into squares of any size. Find the minimum number of squares that can be cut from the paper.
Input : 13 x 29 Output : 9 Explanation : 2 (squares of size 13x13) + 4 (squares of size 3x3) + 3 (squares of size 1x1)=9 Input : 4 x 5 Output : 5 Explanation : 1 (squares of size 4x4) + 4 (squares of size 1x1)
We know that if we want to cut minimum number of squares from the paper then we would have to cut largest square possible from the paper first and largest square will have same side as smaller side of the paper. For example if paper have the size 13 x 29, then maximum square will be of side 13. so we can cut 2 square of size 13 x 13 (29/13 = 2). Now remaining paper will have size 3 x 13. Similarly we can cut remaining paper by using 4 squares of size 3 x 3 and 3 squares of 1 x 1. So minimum 9 squares can be cut from the Paper of size 13 x 29.
Below is the implementation of above approach.
Note that the above Greedy solution doesn’t always produce optimal result. For example if input is 36 x 30, the above algorithm would produce output 6, but we can cut the paper in 5 squares
1) Three squares of size 12 x 12
2) Two squares of size 18 x 18.
Thanks to Sergey V. Pereslavtsev for pointing out the above case.
This article is contributed by Kuldeep Singh(kulli_d_coder). 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 write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
GeeksforGeeks has prepared a complete interview preparation course with premium videos, theory, practice problems, TA support and many more features. Please refer Placement 100 for details
- Minimum number of squares whose sum equals to given number n
- Minimum number of squares whose sum equals to given number N | set 2
- Minimum Cost to cut a board into squares
- Minimum squares to evenly cut a rectangle
- Minimum squares to cover a rectangle
- Check whether a number can be represented by sum of two squares
- Number of perfect squares between two given numbers
- Square pyramidal number (Sum of Squares)
- Count number of squares in a rectangle
- Number of ways of writing N as a sum of 4 squares
- Number of ways to distribute N Paper Set among M students
- Sum of the count of number of adjacent squares in an M X N grid
- Check whether a number can be represented as difference of two squares
- Check whether a number can be represented by the product of two squares
- Number of squares of maximum area in a rectangle
Improved By : 29AjayKumar