DDSA Solutions

2906. Construct Product Matrix

EasyView on LeetCode
ArrayMathMatrixPrefix Sum
Time: O(n)
Space: O(n)

Problem Overview

Construct matrix with column-wise prefix OR sums (each row i is OR of first i+1 elements per column).

Intuition

Construct matrix with column-wise prefix OR sums (each row i is OR of first i+1 elements per column).

Algorithm

  1. 1For each column j: result[i][j] = OR of matrix[0][j]..matrix[i][j]. Prefix OR column-wise.

Common Pitfalls

  • •OR is monotonically non-decreasing (bits only get set). Simple prefix accumulation.
2906.cs
C#
// Approach: Prefix and suffix product arrays modulo p; answer[i] = prefix[i-1] * suffix[i+1].
// Time: O(n) Space: O(n)

public class Solution
{
    public int[][] ConstructProductMatrix(int[][] grid)
    {
        const int kMod = 12345;
        int m = grid.Length;
        int n = grid[0].Length;
        int[][] ans = new int[m][];
        for (int i = 0; i < m; i++)
            ans[i] = new int[n];

        List<int> prefix = new List<int> { 1 };
        int suffix = 1;

        foreach (var row in grid)
        {
            foreach (var num in row)
                prefix.Add((int)((long)prefix[prefix.Count - 1] * num % kMod));
        }

        for (int i = m - 1; i >= 0; i--)
        {
            for (int j = n - 1; j >= 0; j--)
            {
                ans[i][j] = (int)((long)prefix[i * n + j] * suffix % kMod);
                suffix = (int)((long)suffix * grid[i][j] % kMod);
            }
        }

        return ans;
    }
}
Was this solution helpful?

Related Problems