APL Exercises

APL Exercises 9
Power Operator

⎕io←0 throughout.

9.0 Drills I

Predict the result of each expression before evaluating it.

1∘+⍣3 ⊢0

1∘+⍣4 ⊢0

{⍵+1}⍣3 ⊢0

{⍵+1}⍣4 ⊢0

×⍨⍣3 ⊢2

×⍨⍣2 ⊢2

×⍨⍣1 ⊢2

×⍨⍣0 ⊢2

{×⍨⍣⍵⊢2}¨⍳4

9.1 Drills II

Predict the result of each expression before evaluating it.

{2÷⍨⍵+2÷⍵}⍣1⊢ 1

{2÷⍨⍵+2÷⍵}⍣2⊢ 1

{2÷⍨⍵+2÷⍵}⍣3⊢ 1

{{2÷⍨⍵+2÷⍵}⍣⍵⊢1}¨⍳10

{2÷⍨⍵+2÷⍵}⍣≡ 1

3 {2÷⍨⍵+⍺÷⍵}⍣≡ 1

4 {2÷⍨⍵+⍺÷⍵}⍣≡ 1

5 {2÷⍨⍵+⍺÷⍵}⍣≡ 1

9.2 Binomial Coefficients

The binomial coefficients of order ⍵ can be written as a recursion:

   bc←{0=⍵:,1 ⋄ (t,0)+0,t←∇ ⍵-1}

   bc 3
1 3 3 1
   bc 4
1 4 6 4 1
   bc 5
1 5 10 10 5 1

Write a function to compute the binomial coefficients of order ⍵ using the power operator, without recursion.