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Explain the Arrays in Ruby
Ruby arrays are dynamic arrays which expand automatically whenever a value is stored in a location beyond current end of the array. To the programmer, it's as if arrays are unbounded and as many locations as are needed are available. Locations not assigned a value in an expanded array are initialized to nil by default. Ruby also has an interesting indexing mechanism for arrays. Array indices begin at 0 so, for instance, a[13] is the value in the 14th position of the array. Negative numbers are indices of elements counting from current end of the array, so a[-1] is the last element, a[-2] is the second to last element, and so forth. Array references which use an out-of-bound index return nil. These features combine to make it difficult to write an array reference which causes an indexing error. This is apparently a great convenience to the programmer however actually it's not since it makes it so hard to find bugs: many unintended and erroneous array references are legal.
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How many recursive calls are called by the naïve recursive algorithm for binomial coefficients, C(10, 5) and C(21, 12) C(n,k){c(n-1,k)+c(n-1,k-1) if 1 1 if k = n or k = 0
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