3031 Construct Product Matrix
3031 Construct Product Matrix
Construct Product Matrix 
Given a 0-indexed 2D integer matrix grid of size n * m, we define a 0-indexed 2D matrix p of size n * m as the product matrix of grid if the following condition is met:
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Each element p[i][j] is calculated as the product of all elements in grid except for the element grid[i][j]. This product is then taken modulo 12345.
Return the product matrix of grid.
Example 1:
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**Input:** grid = [[1,2],[3,4]]
**Output:** [[24,12],[8,6]]
**Explanation:** p[0][0] = grid[0][1] * grid[1][0] * grid[1][1] = 2 * 3 * 4 = 24
p[0][1] = grid[0][0] * grid[1][0] * grid[1][1] = 1 * 3 * 4 = 12
p[1][0] = grid[0][0] * grid[0][1] * grid[1][1] = 1 * 2 * 4 = 8
p[1][1] = grid[0][0] * grid[0][1] * grid[1][0] = 1 * 2 * 3 = 6
So the answer is [[24,12],[8,6]].
Example 2:
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**Input:** grid = [[12345],[2],[1]]
**Output:** [[2],[0],[0]]
**Explanation:** p[0][0] = grid[0][1] * grid[0][2] = 2 * 1 = 2.
p[0][1] = grid[0][0] * grid[0][2] = 12345 * 1 = 12345. 12345 % 12345 = 0. So p[0][1] = 0.
p[0][2] = grid[0][0] * grid[0][1] = 12345 * 2 = 24690. 24690 % 12345 = 0. So p[0][2] = 0.
So the answer is [[2],[0],[0]].
Constraints:
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1 <= n == grid.length <= 105
1 <= m == grid[i].length <= 105
2 <= n * m <= 105
1 <= grid[i][j] <= 109
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class Solution:
def constructProductMatrix(self, grid: List[List[int]]) -> List[List[int]]:
MOD = 12345
n, m = len(grid), len(grid[0])
p = [[0] * m for _ in range(n)]
suffix = 1
for i in range(n - 1, -1, -1):
for j in range(m - 1, -1, -1):
p[i][j] = suffix
suffix = (suffix * grid[i][j]) % MOD
prefix = 1
for i in range(n):
for j in range(m):
p[i][j] = (p[i][j] * prefix) % MOD
prefix = (prefix * grid[i][j]) % MOD
return p
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