Recursion in the form of a Recursive Func<T, T>
- by ToStringTheory
I gotta admit, I am kind of surprised that I didn’t realize I could do this sooner. I recently had a problem which required a recursive function call to come up with the answer. After some time messing around with a recursive method, and creating an API that I was not happy with, I was able to create an API that I enjoy, and seems intuitive. Introduction To bring it to a simple example, consider the summation to n: A mathematically identical formula is: In a .NET function, this can be represented by a function: Func<int, int> summation = x => x*(x+1)/2
Calling summation with an input integer will yield the summation to that number:
var sum10 = summation(4);
//sum10 would be equal to 10
But what if I wanted to get a second level summation… First some to n, and then use that argument as the input to the same function, to find the second level summation:
So as an easy example, calculate the summation to 3, which yields 6. Then calculate the summation to 6 which yields 21.
Represented as a mathematical formula -
So what if I wanted to represent this as .NET functions. I can always do:
//using the summation formula from above
var sum3 = summation(3); //sets sum3 to 6
var sum3_2 = summation(sum3); //sets sum3 to 21
I could always create a while loop to perform the calculations too:
Func<int, int> summation = x => x*(x+1)/2;
//for the interests of a smaller example, using shorthand
int sumResultTo = 3;
int level = 2;
while(level-- > 0)
{
sumResultTo = summation(sumResultTo);
}
//sumResultTo is equal to 21 now.
Or express it as a for-loop, method calls, etc… I really didn’t like any of the options that I tried. Then it dawned on me – since I was using a Func<T, T> anyways, why not use the Func’s output from one call as the input as another directly.
Some Code
So, I decided that I wanted a recursion class. Something that I would be generic and reusable in case I ever wanted to do something like this again. It is limited to only the Func<T1, T2> level of Func, and T1 must be the same as T2.
The first thing in this class is a private field for the function:
private readonly Func<T, T> _functionToRecurse;
So, I since I want the function to be unchangeable, I have defined it as readonly. Therefore my constructor looks like:
public Recursion(Func<T, T> functionToRecurse)
{
if (functionToRecurse == null)
{
throw new ArgumentNullException("functionToRecurse", "The function to recurse can not be null");
}
_functionToRecurse = functionToRecurse;
}
Simple enough. If you have any questions, feel free to post them in the comments, and I will be sure to answer them. Next, I want enough. If be able to get the result of a function dependent on how many levels of recursion:
private Func<T, T> GetXLevel(int level)
{
if (level < 1)
{
throw new ArgumentOutOfRangeException("level", level, "The level of recursion must be greater than 0");
}
if (level == 1)
return _functionToRecurse;
return _GetXLevel(level - 1, _functionToRecurse);
}
So, if you pass in 1 for the level, you get just the Func<T,T> back. If you say that you want to go deeper down the rabbit hole, it calls a method which accepts the level it is at, and the function which it needs to use to recurse further:
private Func<T, T> _GetXLevel(int level, Func<T, T> prevFunc)
{
if (level == 1)
return y => prevFunc(_functionToRecurse(y));
return _GetXLevel(level - 1, y => prevFunc(_functionToRecurse(y)));
}
That is really all that is needed for this class. If I exposed the GetXLevel function publicly, I could use that to get the function for a level, and pass in the argument.. But I wanted something better. So, I used the ‘this’ array operator for the class:
public Func<T,T> this[int level]
{
get
{
if (level < 1)
{
throw new ArgumentOutOfRangeException("level", level, "The level of recursion must be greater than 0");
}
return this.GetXLevel(level);
}
}
So, using the same example above of finding the second recursion of the summation of 3:
var summator = new Recursion<int>(x => (x * (x + 1)) / 2);
var sum_3_level2 = summator[2](3); //yields 21
You can even find just store the delegate to the second level summation, and use it multiple times:
var summator = new Recursion<int>(x => (x * (x + 1)) / 2);
var sum_level2 = summator[2];
var sum_3_level2 = sum_level2(3); //yields 21
var sum_4_level2 = sum_level2(4); //yields 55
var sum_5_level2 = sum_level2(5); //yields 120
Full Code
Don’t think I was just going to hold off on the full file together and make you do the hard work… Copy this into a new class file:
public class Recursion<T>
{
private readonly Func<T, T> _functionToRecurse;
public Recursion(Func<T, T> functionToRecurse)
{
if (functionToRecurse == null)
{
throw new ArgumentNullException("functionToRecurse", "The function to recurse can not be null");
}
_functionToRecurse = functionToRecurse;
}
public Func<T,T> this[int level]
{
get
{
if (level < 1)
{
throw new ArgumentOutOfRangeException("level", level, "The level of recursion must be greater than 0");
}
return this.GetXLevel(level);
}
}
private Func<T, T> GetXLevel(int level)
{
if (level < 1)
{
throw new ArgumentOutOfRangeException("level", level, "The level of recursion must be greater than 0");
}
if (level == 1)
return _functionToRecurse;
return _GetXLevel(level - 1, _functionToRecurse);
}
private Func<T, T> _GetXLevel(int level, Func<T, T> prevFunc)
{
if (level == 1)
return y => prevFunc(_functionToRecurse(y));
return _GetXLevel(level - 1, y => prevFunc(_functionToRecurse(y)));
}
}
Conclusion
The great thing about this class, is that it can be used with any function with same input/output parameters. I strived to find an implementation that I found clean and useful, and I finally settled on this. If you have feedback – good or bad, I would love to hear it!
