Implement an infinite sum function

Mar 27, 2024

The classic infinite sum problem is probably the most repetitive brain teaser problems I have encountered during my interviews focussing on testing knowledge of closures alongside recursion.

It’s arguably one of my favourite questions as well just by the sheer number possible variations it can have 😅.

Variation: Basic implementation

1. Basic implementation

Implement a sum function which can perform addition of the input values passed to it in the given form. In this case, only one argument can be passed at a time.

const result= sum(1)(2)(3)(4)() should yield a result of 10.

function sum(valueA) {
  function curriedSum(valueB) {
    return typeof valueB === 'undefined' ? valueA : sum(valueA + valueB);
  }

  return curriedSum;
}

const result = sum(1)(2)(3)(4)();
console.log(result); // yields 10

Variation: Sporadic input

2. Sporadic input implementation

In this variation, there is no restriction of passing only a single input at a time. Some possible ways to invoke the sum function can be:

const result1=sum(1)(2,3,4)()
const result2=sum(1,2,3)(4)()
const result3=sum(1,2,3,4)()
const result4=sum(1,2)(3)(4)()

function sum(...nums) {
  let mergedNums = nums;

  // incase it is invoked without any arguments, we simply return zero or throw an error
  if (nums.length === 0) {
    return 0;
  }

  function curriedSum(...nextNums) {
    const isEnd = nextNums.length === 0;
    mergedNums = [...mergedNums, ...nextNums];

    // when no arguments are passed we terminate the recursion
    return isEnd ? mergedNums.reduce((acc, val) => acc + val, 0) : curriedSum;
  }

  return curriedSum;
}

// Usage
const result1 = sum(1)(2, 3, 4)(); // yields 10
const result2 = sum(1, 2, 3)(4)(); // yields 10
const result3 = sum(1, 2, 3, 4)(); // yields 10
const result4 = sum(1, 2)(3, 4)(); // yields 10

console.log(result1, result2, result3, result4);

Variation: Sporadic input with fixed arguments length

3. Sporadic input with fixed arguments length implementation

Untill now, all the variations of infinite sum the termination was either no input or empty input passed to the function. However in this variation, we still need to allow sporadic input, but only upto fixed length or size. Some possible invocation in this variation are:

const result1=sum(1)(2,3,4)
const result2=sum(1,2,3)(4)
const result3=sum(1,2,3,4)
const result4=sum(1,2)(3)(4)
const result5=sum(1)()(2)(3)(4)
const result6=sum(1)()()()()(2,3,4)

We assume that the fixed length here is 4, i.e total of 4 arguments;

function sum(...nums) {
  let mergedNums = nums;

  // assuming we are asked to create a curried sum of arguments length of 4 with sporadic input
  const FIXED_ARGS_SIZE = 4;

  // incase it is invoked without any arguments, we simply return zero or throw an error
  if (nums.length === 0) {
    return 0;
  }

  // if all 4 input are passed in first invocations only
  if (nums.length === FIXED_ARGS_SIZE) {
    return nums.reduce((acc, val) => acc + val, 0);
  }

  function curriedSum(...nextNums) {
    mergedNums = [...mergedNums, ...nextNums];
    const isEnd = mergedNums.length === FIXED_ARGS_SIZE;

    // when no arguments are passed we terminate the recursion
    return isEnd ? mergedNums.reduce((acc, val) => acc + val, 0) : curriedSum;
  }

  return curriedSum;
}

// Usage
const result1 = sum(1)(2, 3, 4); // yields 10
const result2 = sum(1, 2, 3)(4); // yields 10
const result3 = sum(1, 2, 3, 4); // yields 10
const result4 = sum(1, 2)(3)(4); // yields 10
const result5 = sum(1)()(2)(3)(4); // yields 10
const result6 = sum(1)()()()()(2, 3, 4); // yields 10
const result7 = sum(1, 2, 3, 4); // yields 10

console.log(result1, result2, result3, result4, result5, result6, result7);

Implement an infinite sum function

1. Basic implementation

2. Sporadic input implementation

3. Sporadic input with fixed arguments length implementation

Further Reading