Leetcode #2906: Construct Product Matrix
In this guide, we solve Leetcode #2906 Construct Product Matrix in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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: 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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Matrix, Prefix Sum
Intuition
Range queries become simple once we precompute cumulative sums.
We can transform subarray conditions into prefix comparisons.
Approach
Compute prefix sums and use a map to find matching prefixes.
This avoids nested loops while keeping the logic clear.
Steps:
- Compute prefix sums.
- Use a map to find valid ranges.
- Update the answer.
Example
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]].
Python Solution
class Solution:
def constructProductMatrix(self, grid: List[List[int]]) -> List[List[int]]:
n, m = len(grid), len(grid[0])
p = [[0] * m for _ in range(n)]
mod = 12345
suf = 1
for i in range(n - 1, -1, -1):
for j in range(m - 1, -1, -1):
p[i][j] = suf
suf = suf * grid[i][j] % mod
pre = 1
for i in range(n):
for j in range(m):
p[i][j] = p[i][j] * pre % mod
pre = pre * grid[i][j] % mod
return p
Complexity
The time complexity is , where and are the number of rows and columns in the matrix, respectively. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.