向DDMathParser添加nCr函数（具有可变参数） [英] Adding nCr Function to DDMathParser (with variable parameters)

问题描述

我正在努力向DDMathParser添加新功能（nCr）。我尝试遵循DDMathParser作者的以下指示：

I'm struggling to add a new function (nCr) to DDMathParser. I've tried to follow these instructions by the author of DDMathParser:

https ：//stackoverflow.com/a/15599814/2521277

我的问题：我无法将DDExpressions组合到带有变量的复杂表达式中。 。

My problem: I can't manage to combine DDExpressions to a complex expression with variables...

您能帮我添加函数nCr吗？（ http://en.wikipedia.org/wiki/Binomial_coefficient#Factorial_formula ）

Can you help me to add the function nCr (http://en.wikipedia.org/wiki/Binomial_coefficient#Factorial_formula)

谢谢！

推荐答案

DDMathParser作者在这里。

DDMathParser author here.

所有功能的基本签名是：

The basic signature for all functions is this:

DDExpression* ^(NSArray *arguments, NSDictionary *variables, DDMathEvaluator *evaluator, NSError **error);

因此，您需要创建实现nCr算法的这些块之一。您可以通过以下两种方法进行操作：

So you need to create one of these blocks that implements the nCr algorithm. There are a couple of ways you could do it:

1. 您可以完全按照本文中所示的方式实现该功能，计算阶乘，然后执行


2. 您可以完全根据现有的阶乘，减法和除法函数来实现该功能。


3. 您可以将两者结合起来。

我个人建议使用最后一个，因为它省去了重新评估参数的麻烦，但也意味着您不必自己编写大多数逻辑。

Personally, I'd recommend the last one, because it saves having to re-evaluate the arguments, but also means you don't have to write most of the logic yourself.

应该是这样的：

DDMathFunction nCrFunction = ^(NSArray *args, NSDictionary *vars, DDMathEvaluator *eval, NSError **error) {
  if ([args count] != 2) {
    *error = [NSError errorWithDomain:DDMathParserErrorDomain code:DDErrorCodeInvalidNumberOfArguments userInfo:@{NSLocalizedDescriptionKey : @"nCr requires 2 arguments"}];
    return nil;
  }

  DDExpression *first = [args objectAtIndex:0];
  DDExpression *second = [args objectAtIndex:1];

  NSNumber *n = [first evaluateWithSubstitutions:vars evaluator:eval error:error];
  if (n == nil) { return nil; }

  NSNumber *k = [second evaluateWithSubstitutions:vars evaluator:eval error:error];
  if (k == nil) { return nil; }

  // some validation here to guarantee that 0 ≤ k ≤ n

  // now, re-box the numbers in expressions to pass off to other functions
  DDExpression *nExpression = [DDExpression numberExpressionWithNumber:n];
  DDExpression *kExpression = [DDExpression numberExpressionWithNumber:k];

  // build the algorithm
  DDExpression *f1 = [DDExpression functionExpressionWithFunction:DDOperatorFactorial arguments:@[kExpression] error:error]; // k!

  // the other half of the denominator
  DDExpression *subtract = [DDExpression functionExpressionWithFunction:DDOperatorMinus arguments:@[nExpression, kExpression] error:error]; // (n-k)
  DDExpression *f2 = [DDExpression functionExpressionWithFunction:DDOperatorFactorial arguments:@[subtract] error:error]; // (n-k)!

  // the full denominator
  DDExpression *denominator = [DDExpression functionExpressionWithFunction:DDOperatorMultiply arguments:@[f1, f2] error:error]; // k!(n-k)!

  // the numerator
  DDExpression *numerator = [DDExpression functionExpressionWithFunction:DDOperatorFactorial arguments:@[nExpression] error:error]; // n!

  // the whole thing
  DDExpression *final = [DDExpression functionExpressionWithFunction:DDOperatorDivide arguments:@[numerator, denominator] error:error]; // n!/(k!(n-k)!)

  return final;
};

使用此块，您可以在 DDMathEvaluator ：

[[DDMathEvaluator sharedMathEvaluator] registerFunction:nCrFunction forName:@"nCr"];

就是这样！

现在您可以做：

NSNumber *n = [@"nCr(4, 3)" numberByEvaluatingString];

_{警告：在浏览器中键入但未编译的代码。 Caveat实施器}

如果这是您想要的功能，要查看DDMathParser的内置文件，请在Github上打开新的问题。

Incidentally, if this is a function you'd like to see built-in to DDMathParser, please open a new issue over at Github.

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