Just for learning purposes I try to create a list that looks like this: {{{3, 9}, {4, 16}}, {{5, 25}, {6, 36}}}
One way to do it is by using Table:
Table[{j + 2 i, (j + 2 i)^2}, {i, 0, 1}, {j, 3, 4}]
Now I try it using functional programming, but I failed. This is what I tried:
Nest[Map[{#, #^2} &], Range[3, 4], 2]
Is it possible to create the desired result only using Nest, Map and Range? If not, what other function should I use, without using Table, but using a Pure Function instead?
Partition[{#, # #} & /@ Range[3, 6], 2]
{{{3, 9}, {4, 16}}, {{5, 25}, {6, 36}}}
Array[{#, #^2} & @@ {#2 + 2 #} &, {2, 2}, {0, 3}] (* or *)
Outer[{#, #^2} & @@ {#2 + 2 #} &, {0, 1}, Range[3, 4]]
{{{3, 9}, {4, 16}}, {{5, 25}, {6, 36}}}
Removing hard-coded parameters:
f1 = Module[{x = #[[1]], l = Length@#},
Array[{#, #^2} & @@ {#2 + l #} &, {l, l}, {0, x}]] &;
f1 @ Range[3, 4]
{{{3, 9}, {4, 16}},
{{5, 25}, {6, 36}}}
f1 @ Range[4, 6]
{{{4, 16}, {5, 25}, {6, 36}},
{{7, 49}, {8, 64}, {9, 81}},
{{10, 100}, {11, 121}, {12, 144}}}
And, similarly for Outer:
f2 = Module[{l = Length@#, x = #},
Outer[{#, #^2} & @@ {#2 + l #} &, Range[l] - 1, x]] &;
f2 @ Range[3, 4]
{{{3, 9}, {4, 16}},
{{5, 25}, {6, 36}}}
f2 @ Range[4, 6]
{{{4, 16}, {5, 25}, {6, 36}},
{{7, 49}, {8, 64}, {9, 81}},
{{10, 100}, {11, 121}, {12, 144}}}
Also
☺ = # /. ♯_ :> ({#, #^2} & @@@ ({♯ + #} & /@ {0, (♯♯ = 0; ♯♯++ & /@ #; ♯♯)})) &;
☺ @ {3, 4}
{{{3, 9}, {4, 16}}, {{5, 25}, {6, 36}}}
☺ @ Range[3, 7]
{{{3, 9}, {4, 16}, {5, 25}, {6, 36}, {7, 49}},
{{8, 64}, {9, 81}, {10, 100}, {11, 121}, {12, 144}}}
{{{3, 9}, {4, 16}}, {{5, 25}, {6, 36}}}
– eldo
Jul 16 '17 at 00:26
BlockMap[{{#1[[1]], #[[1]]^2}, {#1[[2]], #[[2]]^2}} &, Range[3, 6], 2]
(* {{{3, 9}, {4, 16}}, {{5, 25}, {6, 36}}} *)
({#, Power[#, 2]} & @ Range[3, 6] // Transpose // ArrayReshape[#, {2, 2, 2}] &) == ({#, # #} & @ Range[3, 6] // Transpose // ArrayReshape[#, {2, 2, 2}] &) == want– user1066 Jul 15 '17 at 22:55