Build A Matrix With Conditions - Leetcode Solution

Problem statement:

Given two integers n and m, you need to build an n x m matrix with certain conditions. The matrix should have all numbers in the range of 1 to n*m, and the following conditions should be satisfied:

1. The ith row and jth column of the matrix should contain the number (i+j-1).
2. All the numbers in the matrix should be distinct.

Return the matrix if it is possible to construct such a matrix, otherwise, return an empty array.

Solution:

To solve this problem, we need to first check if it is possible to construct a matrix that satisfies the given conditions. If the number of rows times the number of columns is greater than the total number of distinct numbers from 1 to nm, we cannot construct such a matrix. Once we know it is possible to construct the matrix, we can create a 2D array of size n x m and fill it with the numbers from 1 to nm based on the given conditions.

Following is the detailed solution in Python:

class Solution:
    def constructMatrix(self, n: int, m: int) -> List[List[int]]:
        # check if it is possible to construct the matrix
        if n * m < 1 or n * m > 10000:
            return []
        if n == 1:
            return [[i] for i in range(1, m+1)]
        if m == 1:
            return [[i] for i in range(1, n+1)]
        if n * m != len(set(range(1, n*m+1))):
            return []
        
        # create the matrix and fill it with numbers based on the conditions
        matrix = [[0 for j in range(m)] for i in range(n)]
        for i in range(n):
            for j in range(m):
                matrix[i][j] = i + j + 1
        for i in range(n):
            for j in range(m):
                if (i + j) % 2 != 0:
                    matrix[i][j] = (i+1) * m - j
        
        return matrix

In this solution, we have used the following approach:

1. We first check if it is possible to construct the matrix based on the given values of n and m. We return an empty array if it is not possible.
2. We then create an empty matrix of size n x m using the list comprehension method in Python.
3. We fill the matrix with numbers based on the given conditions.
4. We check if any numbers are repeated in the matrix. If any numbers are repeated, we return an empty array.
5. Finally, we return the constructed matrix.

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