Rain Water Trap (2D Version)

This was discussed in http://www.mitbbs.com/article/JobHunting/32342353_3.html.
and http://leetcode.com/groups/twitter-interview/forum/topic/rain-water-trap-2d-version/

Here is my solution:

 

// ----------------------------------------------------------------------------
// Copyright (c) SimpleCoder 2013
// ----------------------------------------------------------------------------
int FindMaxWater2D(int[,] matrix, int m, int n)
{
    //Two extra 2d array with same size as matrix
    int[,] potentialWaterRows = new int[m, n];
    int[,] potentialWaterCol = new int[m, n];
    FindMaxHeightRows(matrix, potentialWaterRows, m, n);
    FindMaxHeightCols(matrix, potentialWaterCol, m, n);
    int sum = 0;
    for (int i = 0; i < m; ++i)
    {
        for (int j = 0; j < n; ++j)
        {
            Debug.Assert(Math.Min(potentialWaterRows[i, j], potentialWaterCol[i, j]) >= matrix[i, j]);
            sum += Math.Min(potentialWaterRows[i, j], potentialWaterCol[i, j]) - matrix[i, j];
        }
    }
    return sum;
}

void FindMaxHeightRows(int [,] matrix, int[,] newMatrixRows, int m, int n)
{
    for (int i = 0; i < m; ++i)
    {
        // Find the ascending sequence from left to right
        int[] ascL_R = new int[n];
        ascL_R[0] = matrix[i, 0];
        for (int j = 1; j < n; ++j)
        {
            ascL_R[j] =Math.Max(ascL_R[j-1], matrix[i,j]);
        }
        // Find the ascending sequence from Right to Left
        int[] ascR_L = new int[n];
        ascR_L[n-1] = matrix[i, n-1];
        for (int j = n-2; j >=0; --j)
        {
            ascR_L[j]= Math.Max(ascR_L[j+1], matrix[i,j]);
        }
              
        for(int j = 0; j < n; ++j)
        {
            newMatrixRows[i, j] = Math.Min(ascR_L[j], ascL_R[j]);
        }
    }
}
    
void FindMaxHeightCols(int [,] matrix, int[,] newMatrixCols, int m, int n)
{     
    for (int j = 0; j < n; ++j)
    {
        // Find the ascending sequence from Top to bottom
        int[] ascT_B = new int[n];
        ascT_B[0] =matrix[0, j];
        for (int i = 1; i < m; ++i)
        {
            ascT_B[i] =Math.Max(ascT_B[i-1], matrix[i,j]);
        }
        // Find the ascending sequence from Top to bottom
        int[] ascB_T = new int[n];
        ascB_T[m-1] = matrix[m-1, j];
        for (int i = m-2; i >=0; --i)
        {
            ascB_T[i] = (Math.Max(ascB_T[i+1], matrix[i, j]));
        }
              
        for(int i = 0; i < n; ++i)
        {
            newMatrixCols[i, j] = Math.Min(ascB_T[i], ascT_B[i]);
        }
    }
}