{
  "translations" :{
    "en": {
     "sc1": "Step 1: Write and define the prototype for the function.",
     "sc2": "Let's look at an example. Here is a function to sum the first $n$ elements of an array.", 
     "sc3": "Step 2: Write out a sample function call. Once you've determined what the function does, then we imagine a function call. This will sum the first $n$ elements of arr.",
     "sc4": "Pick the most generic function call. For example, you don't want to have a call like:",
     "sc5": "The problem with this version is that it is calling with a constant for the number of values summed. You want to use variables when possible, because that's the most general way to call the function.",
     "sc6": "Step 3: Think of the smallest version of the problem. This is called the base case. Here, you pick a small value for $n$, and give its answer. A common mistake is to pick a base case that is too large.",
     "sc7": "So, what is the smallest version of the problem? Here are three choices:",
     "sc8": "Some people pick choice 1, reasoning that if you are to sum elements of an array, then you must have at least two elements to sum.",
     "sc9": "However, it is perfectly valid to have a summation of only one element. You could just return the value for that one element.",
     "sc10":"Some people pick choice 2, because it does not make sense to sum an array of size 0, whereas an array of size 1 seems to make sense.",
     "sc11":"But the real issue is: How small might an array be? Choice 3 is the smallest array size possible (an empty array). You can sum zero elements of an array. What value should it return? It should return 0.",
     "sc12": "Step 4: Think of smaller versions of the function call. Here's the function call: ",
     "sc13":"This means to solve a problem of size $n$. We need to think of a smaller problem, which we will assume can be solved correctly. The next smallest problem is to sum $n-1$ elements.",
     "sc14":"Assume this smaller problem of size $n-1$ has been solved for you. How would you solve the original, larger problem?",
     "sc15":"If the first $n - 1$ elements have already been summed, then only the $n$th element is left to be summed. So, the solution to solving sum(arr,n) is to add sum(arr, n-1) to arr[n-1]. (Remember that the $n$th element is actually at index $n - 1$ because arrays start at index 0).",
     "sc16":"Putting it all together: Writing a recursive function requires putting the base case and the recursive case together. Here is the usual format:",
     "sc17":"It doesn't really matter whether the base case or the recursive part comes first."
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