We are given three values , and where is number of rows in matrix, is number of columns in the matrix and is the number that can have only two values -1 and 1. Our aim is to find the number of ways of filling the matrix of such that the product of all the elements in each row and each column is equal to . Since the number of ways can be large we will output
Input : n = 2, m = 4, k = -1 Output : 8 Following configurations satisfy the conditions:- Input : n = 2, m = 1, k = -1 Output : The number of filling the matrix are 0
From the above conditions, it is clear that the only elements that can be entered in the matrix are 1 and -1. Now we can easily deduce some of the corner cases
- If k = -1, then the sum of number of rows and columns cannot be odd because -1 will be present odd number of times in each row and column therefore if the sum is odd then answer is .
- If n = 1 or m = 1 then there is only one way of filling the matrix therefore answer is 1.
- If none of the above cases are applicable then we fill the first rows and the first columns with 1 and -1. Then the remaining numbers can be uniquely identified since the product of each row an each column is already known therefore the answer is .
The time complexity of above solution is .
- Remove first X rows and columns from a matrix
- Remove any corner X rows and columns from a matrix
- Sorting rows of matrix in ascending order followed by columns in descending order
- Sorting rows of matrix in descending order followed by columns in ascending order
- Filling diagonal to make the sum of every row, column and diagonal equal of 3x3 matrix
- Count rows/columns with sum equals to diagonal sum
- Sum of columns of a 2-D Matrix where first element is odd
- Interchange elements of first and last columns in matrix
- Count all the columns in a matrix which are sorted in descending
- Count all sorted rows in a matrix
- Find all permuted rows of a given row in a matrix
- Common elements in all rows of a given matrix
- Interchange elements of first and last rows in matrix
- Maximum difference of sum of elements in two rows in a matrix
- Check if all rows of a matrix are circular rotations of each other
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