Duplex Algorithm in Swift

Technically, this post could also go into #mental-calculation but since it involves computer code…

The Duplex method aka Dvanda yoga is a Vedic Maths algorithm used primarily to compute squares or square roots mentally. You can find a forum post here that describes this process in more detail.

The below is an implementation in Swift 5.1. I hope this will help some folks that have an easier time reading algorithms this way. Also you can copy/paste and try out a few values to get a feel for the algorithm.

If you decide to write your own solution in C++, Perl, Python, JavaScript, etc. please post it here for others, who are not familiar with Swift but might know your language.

func duplex(_ values: [Int]) -> Int {
    if values.isEmpty {
        return 0
    } else {
        var array = values
        var total = (array.count % 2 != 0)
            ? array[array.count / 2] * array.remove(at: array.count / 2)
            : 0
        while !array.isEmpty {
            total += array.removeFirst() * array.removeLast() * 2
        return total


1. print(duplex([]))

The condition value.isEmpty will be true and the algorithm will terminate and return 0, as there is nothing to compute.

2. print(duplex([3]))

The total is assigned the middle value of the array squared. This middle value is then removed and the condition !array.isEmpty will be false and the algorithm will terminate, returning the initial value of 3^2=9 that is stored in total.

3. print(duplex([5, 3]))

There is no middle value, so the initial value of total is 0. The first and last element of the array are multiplied and then doubled. After that the array is empty and the algorithm returns 5*3*2=30

4. print(duplex([2, 5, 3]))

The middle value is squared (5^2=25) as in case 2 above and removed from the array. Then the first and the last value are multiplied and doubled (2*3*2=12) as in case 3; the algorithm will terminate returning 25+12=37

After that…

…cases will fall into either odd or even number of items passed in the array. If odd the item is squared and used to initialize total and then removed; or there is nothing to do. Afterwards, we have an even number of items and multiply and double and finally remove the first and last item until the array is empty.


…and I completely forgot to point out where you can paste it. If you have an iPad there is an app by Apple called Playgrounds where you can run Swift code. As you modify the values it will update the results for you automatically.

1 Like

I wrote some python code if someone likes.

def duplex(values):
    if len(values)==0:
        return 0
        if len(values)%2!=0:
        for index in range(values_size//2):
        return total


P.S. : Just writing this made me appreciate how convenient the duplex method is


@batman Nice!

Here a slightly different solution in C++ that ignores the middle value and just runs all the way through the array… much faster to write, but less efficient. Not that it matters though, given the number of arguments you will pass in…

// duplex.cpp
#include <iostream>

int main(int argc, char* argv[]) {
    int total = 0;
    if (argc > 1) {
        for(int i = 1; i < argc; i++) {
            total += atoi(argv[i]) * atoi(argv[argc - i]);
    std::cout << total << std::endl;

$ g++ -o duplex duplex.cpp

$ ./duplex
$ ./duplex 3
$ ./duplex 5 3
$ ./duplex 2 5 3