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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
0
or1
. - The sum of elements of the 0-th(upper) row is given as
upper
. - The sum of elements of the 1-st(lower) row is given as
lower
. - The sum of elements in the i-th column(0-indexed) is
colsum[i]
, wherecolsum
is 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 are 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]] Explanation: [[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: []
Example 3:
Input: upper = 5, lower = 5, colsum = [2,1,2,0,1,0,1,2,0,1] Output: [[1,1,1,0,1,0,0,1,0,0],[1,0,1,0,0,0,1,1,0,1]]
Constraints:
1 <= colsum.length <= 10^5
0 <= upper, lower <= colsum.length
0 <= colsum[i] <= 2
Give you a 2
line of n
binary array columns:
- Matrix is a binary matrix, which means that each element of the matrix is not
0
that1
. - The first
0
element of the row and isupper
. - The first
1
element of the row and islower
. - The first
i
column (from the0
elements of the numbered) and iscolsum[i]
,colsum
is a lengthn
of an array of integers.
You need to use upper
, lower
and colsum
to reconstruct this matrix, and return it in the form of a two-dimensional array of integers.
If there are several different answers, so any one can by this question.
If there is no satisfactory answer, please return to an empty two-dimensional array.
Example 1:
Input: upper = 2, lower = 1 , colsum = [1,1,1] Output: [[1,1,0], [0,0,1]] Explanation: [[1,0,1], [ 0,1,0]] and [[0,1,1], [1,0,0]] is the correct answer.
Example 2:
Input: upper = 2, lower = 3 , colsum = [2,2,1,1] Output: []
Example 3:
Input: upper = 5, lower = 5 , colsum = [2,1,2,0,1,0,1,2,0,1] Output: [[1,1,1,0,1,0,0 , 1,0,0], [1,0,1,0,0,0,1,1,0,1]]
prompt:
1 <= colsum.length <= 10^5
0 <= upper, lower <= colsum.length
0 <= colsum[i] <= 2