Algorithm


Problem Name: 1253. 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 0 or 1.
  • 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], where colsum is given as an integer array with length n.

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
 

Code Examples

#1 Code Example with Python Programming

Code - Python Programming


class Solution:
    def reconstructMatrix(
        self, upper: int, lower: int, colsum: List[int]
    ) -> List[List[int]]:
        res = [[0] * len(colsum) for _ in range(2)]
        for j, sm in enumerate(colsum):
            if sm == 2:
                if upper == 0 or lower == 0:
                    return []
                upper -= 1
                lower -= 1
                res[0][j] = res[1][j] = 1
            elif sm:
                if upper == lower == 0:
                    return []
                if upper >= lower:
                    upper -= 1
                    res[0][j] = 1
                else:
                    lower -= 1
                    res[1][j] = 1
        return res if upper == lower == 0 else []
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Input

x
+
cmd
upper = 2, lower = 1, colsum = [1,1,1]

Output

x
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cmd
[[1,1,0],[0,0,1]]
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