Solved

# Lattice Multiplication Algorithm in C#

Posted on 2013-02-06
1,131 Views
I have a problem I need answered ASAP. I was tasked with writing a simple C# form that does a fundamentally simple but from a coding standpoint, complex mathematical task. The method is called Lattice Multiplication, and it is a simple, matrix-based way to multiply large numbers. Here is a video that will easily explain it if you are not familiar: http://www.youtube.com/watch?v=VoXJA-9WzNI

I have attached what I came up with thus far. The code is commented and fleshed out up to the point where I multiply the digits to get a linear array of two characters (the products of each multiple) per index. I am completely stumped what to do next. I came here as a last resort because I simply cannot figure this out.

This is a time sensitive matter so I would appreciate any and all help in advance.

Thank you.
default.aspx
default.aspx.cs
0
Question by:mikerowaves
[X]
###### Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

• Help others & share knowledge
• Earn cash & points
• Learn & ask questions
• 7
• 4

LVL 42

Expert Comment

ID: 38858506
i'm half there, let me dig the code and see if it's working properly for all numbers.
be back to you with code
0

Author Comment

ID: 38858521
Thank you.
0

LVL 42

Assisted Solution

sedgwick earned 500 total points
ID: 38858642
see the screenshot, i've tested 10k random calculations so i'm sure its working smooooooooothly :)

``````void TestFigures()
{
var rnd = new Random();
int iterations = 1000;
for (int i = 0; i < iterations; i++)
{
var d1 = (int)Math.Floor(rnd.NextDouble() * rnd.NextDouble() * Math.Pow(10, rnd.Next(0, 5)));
var d2 = (int)Math.Floor(rnd.NextDouble() * rnd.NextDouble() * Math.Pow(10, rnd.Next(0, 5)));
double simple_multiply = d1 * d2;
double lattice_multiply = LatticeMultiplication(int.Parse(d1.ToString()), int.Parse(d2.ToString()));
Debug.Equals(simple_multiply, lattice_multiply);
}
}

private double LatticeMultiplication(int num1, int num2)
{
if (num1 == 0 && num2 == 0) return 0;
int[] num1Array = ConvertToIntArray(num1);
int[] num2Array = ConvertToIntArray(num2);
int num1arrSize = num1Array.Count();
int num2arrSize = num2Array.Count();

int[] accumulators = new int[num1arrSize + num2arrSize];

int i, j, accIndex = accumulators.Count() - 1;
for (i = 0; i < num2arrSize; i++)
{
for (j = 0; j < num1arrSize; j++)
{
int result = num1Array[j] * num2Array[i];
if (result > 9)
{
accumulators[accIndex] += result % 10;
int tenth = accumulators[accIndex];
if (tenth > 9)
{
accumulators[accIndex] = tenth % 10;
accumulators[accIndex - 1] += tenth / 10;
}
accumulators[accIndex - 1] += result / 10;
tenth = accumulators[accIndex - 1];
if (tenth > 9)
{
accumulators[accIndex - 1] = tenth % 10;
accumulators[accIndex - 2] += tenth / 10;
}
}
else
{
accumulators[accIndex] += result;
int tenth = accumulators[accIndex];
if (tenth > 9)
{
accumulators[accIndex] = tenth % 10;
accumulators[accIndex - 1] += tenth / 10;
}
}
accIndex--;
}
accIndex = accumulators.Count() - 2 - i;
}

return double.Parse(string.Join("", accumulators.Select(n => n.ToString()).ToArray()));
}

private int[] ConvertToIntArray(int num)
{
List<int> listOfInts = new List<int>();
while (num > 0)
{
num = num / 10;
}

return listOfInts.ToArray();
}
``````
0

Author Comment

ID: 38860151
This works, but there are a few instances where it doesn't. For example, if you take 1000x1000, it gives you a result of 1. 1000x12 gives you a result of 21.
0

Author Comment

ID: 38860163
I think the main goal of the Lattice process is to transverse a diagonal matrix as opposed to doing it this way, although this still works. Do you know what I mean?
0

Author Comment

ID: 38862274
Any update on this?
0

LVL 42

Expert Comment

ID: 38862850
This is basically what i do. Ill post a screenshot with explanation
0

Accepted Solution

mikerowaves earned 0 total points
ID: 38862875
I actually figured out the pattern and did it myself. Here is the final code:

``````    // Main Multiplication Function
private int LatticeMultiplication(int num1, int num2)
{
// Create integer list for total number.
List<int> total = new List<int>();

if (num1 != 0 && num2 != 0) // Proceed if no zeroes.
{
// Convert numbers to linear arrays and then to a matrix.
int[] num1Array = ConvertToIntArray(num1);
int[] num2Array = ConvertToIntArray(num2);
string[,] mLattice = ConvertToMatrix(num1Array, num2Array); // String preserves zeroes.

// Set x/y coordinates.
int wall = num1Array.Count() - 1; // Right side of matrix.
int floor = num2Array.Count() - 1; // Bottom of matrix.
int ceiling = 0; // Top of matrix.
int door = 0; // Left side of matrix.
int xPos = floor;
int yPos = wall;
int tempX = floor;
int tempY = wall;

int sum = 0;
int carry = 0;
bool isFirst = false;

// Transverse bottom diagonals.
while (yPos > door - 1)
{
// Reset temporary values.
tempX = xPos;
tempY = yPos;
isFirst = false;
sum = carry;

while (tempX >= ceiling && tempY <= wall)
{
if (isFirst == false)
{
sum += GetValue(mLattice[tempX, tempY], 1); // Get first or second number.
isFirst = true; // Set alternate.
tempY++; // Set next diagonal position.
}
else
{
sum += GetValue(mLattice[tempX, tempY], 0);
isFirst = false;
tempX--;
}
}

// Check for tenths spot and add ones to total.
if (sum > 9)
{
carry = GetValue(sum.ToString(), 0);
}
else
{
}

// Move left to next diagonal.
yPos--;
}

// Reset values for left side diagonals.
xPos = floor;
yPos = door;
sum = 0;

// Transverse left diagonals.
while (xPos > ceiling - 1)
{
// Reset temporary values.
tempX = xPos;
tempY = yPos;
isFirst = true;
sum = carry;

while (tempX >= ceiling && tempY <= wall)
{
if (isFirst == false)
{
sum += GetValue(mLattice[tempX, tempY], 1);
isFirst = true;
tempY++;
}
else
{
sum += GetValue(mLattice[tempX, tempY], 0);
isFirst = false;
tempX--;
}
}

if (sum > 9)
{
carry = GetValue(sum.ToString(), 0);
}
else
{
carry = 0;
}

// Move up to next diagonal.
xPos--;
}

// Return a joined final value using LINQ.
return Convert.ToInt32(string.Join("", total.Select(n => n.ToString()).ToArray().Reverse()));
}

// Return if zer
return 0;
}

// Main Multiplication Subfunctions
// Convert integer numbers to a split array.
private int[] ConvertToIntArray(int num)
{
List<int> numArray = new List<int>();

// Add digits one by one by looking at mod result.
while(num > 0)
{
num = num / 10;
}

// Reverse array.
numArray.Reverse();
return numArray.ToArray();
}

// Convert arrays to matrix.
private string[,] ConvertToMatrix(int[] num1Array, int[] num2Array)
{
// Establish given array sizes.
int arr1Size = num1Array.Count();
int arr2Size = num2Array.Count();

// Establish array length.
string[] multiplied = new string[arr1Size * arr2Size];
int index = 0;

// Create single array of multiplied numbers.
for (int i = 0; i < arr2Size; i++)
{
for (int j = 0; j < arr1Size; j++)
{
// Multiply numbers and format with a zero if a single digit.
multiplied[index] = (num2Array[i] * num1Array[j]).ToString("00");
index++;
}
}

// Create matrix.
string[,] matrix = new string[arr2Size, arr1Size];

// Add values to matrix.
for (int i = 0; i < multiplied.Count(); i++)
{
matrix[i / arr1Size, i % arr1Size] = multiplied[i];
}

return matrix;
}

private int GetValue(string m, int index)
{
return Convert.ToInt32(m.Substring(index, 1)); // Return number according to index.
}
``````
0

Author Comment

ID: 38862876
Thank you for your help though. I will accept your solution as correct as well because it is, in fact.
0

LVL 42

Expert Comment

ID: 38862921
10x for the points.
0

Author Closing Comment

ID: 38875516
I figured it out using a matrix, which was required by the project. However, sedgwick provided a solution that also works.
0

## Featured Post

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

### Suggested Solutions

Wouldnâ€™t it be nice if you could test whether an element is contained in an array by using a Contains method just like the one available on List objects? Wouldnâ€™t it be good if you could write code like this? (CODE) In .NET 3.5, this is possibleâ€¦
International Data Corporation (IDC) prognosticates that before the current the year gets over disbursing on IT framework products to be sent in cloud environs will be \$37.1B.
The Email Laundry PDF encryption service allows companies to send confidential encrypted  emails to anybody. The PDF document can also contain attachments that are embedded in the encrypted PDF. The password is randomly generated by The Email Laundrâ€¦
In an interesting question (https://www.experts-exchange.com/questions/29008360/) here at Experts Exchange, a member asked how to split a single image into multiple images. The primary usage for this is to place many photographs on a flatbed scannerâ€¦
###### Suggested Courses
Course of the Month1 day, 17 hours left to enroll

#### 710 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.