Reconstruct a 2-Row Binary Matrix
Given the following details of a matrix with n columns and 2 rows:
- The matrix is a binary matrix, which means each element in the matrix can be
0or1. - The sum of elements of the
0-th upper row is given asupper. - The sum of elements of the
1-st lower row is given aslower. - The sum of elements in the
i-th column,0-indexed, iscolsum[i], wherecolsumis given as an integer array with lengthn.
Your task is to reconstruct the matrix with upper, lower, and colsum.
Return it as a 2-D integer array.
If there is more than one valid solution, any of them will be accepted.
If no valid solution exists, return an empty 2-D array.
Example 1
Input
upper = 2, lower = 1, colsum = [1,1,1]Output
[[1,1,0],[0,0,1]]Other matrices such as [[1,0,1],[0,1,0]] and [[0,1,1],[1,0,0]] are also correct answers.
Example 2
Input
upper = 2, lower = 3, colsum = [2,2,1,1]Output
[]No binary matrix can satisfy both row sums and the given column sums.
Constraints
- 1 <= colsum.length <= 10^5
- 0 <= upper, lower <= colsum.length
- 0 <= colsum[i] <= 2