all your base exercise (#18)

Author: quintuple-mallard

config.json

@@ -125,6 +125,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 2
+      },
+      {
+        "slug": "all-your-base",
+        "name": "All Your Base",
+        "uuid": "b858df1d-c175-4bc2-a6f8-b4f4339d60c2",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5
       }
     ]
   },

exercises/practice/all-your-base/.docs/instructions.md

@@ -0,0 +1,28 @@
+# Instructions
+
+Convert a sequence of digits in one base, representing a number, into a sequence of digits in another base, representing the same number.
+
+~~~~exercism/note
+Try to implement the conversion yourself.
+Do not use something else to perform the conversion for you.
+~~~~
+
+## About [Positional Notation][positional-notation]
+
+In positional notation, a number in base **b** can be understood as a linear combination of powers of **b**.
+
+The number 42, _in base 10_, means:
+
+`(4 × 10¹) + (2 × 10⁰)`
+
+The number 101010, _in base 2_, means:
+
+`(1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰)`
+
+The number 1120, _in base 3_, means:
+
+`(1 × 3³) + (1 × 3²) + (2 × 3¹) + (0 × 3⁰)`
+
+_Yes. Those three numbers above are exactly the same. Congratulations!_
+
+[positional-notation]: https://en.wikipedia.org/wiki/Positional_notation

exercises/practice/all-your-base/.docs/introduction.md

@@ -0,0 +1,8 @@
+# Introduction
+
+You've just been hired as professor of mathematics.
+Your first week went well, but something is off in your second week.
+The problem is that every answer given by your students is wrong!
+Luckily, your math skills have allowed you to identify the problem: the student answers _are_ correct, but they're all in base 2 (binary)!
+Amazingly, it turns out that each week, the students use a different base.
+To help you quickly verify the student answers, you'll be building a tool to translate between bases.

exercises/practice/all-your-base/.meta/config.json

@@ -0,0 +1,17 @@
+{
+  "authors": [
+    "quintuple-mallard"
+  ],
+  "files": {
+    "solution": [
+      "all-your-base.nu"
+    ],
+    "test": [
+      "tests.nu"
+    ],
+    "example": [
+      ".meta/example.nu"
+    ]
+  },
+  "blurb": "Convert a number, represented as a sequence of digits in one base, to any other base."
+}

exercises/practice/all-your-base/.meta/example.nu

@@ -0,0 +1,28 @@
+use std/assert
+def base_ten [base: number]: list<number> -> number {
+    $in | reverse | enumerate | reduce --fold 0 {|el, acc|
+        let i = $el.index
+        let digit = $el.item
+        $acc + $digit * $base ** $i
+    }
+}
+def rebase_from_ten [base: number]: number -> list<number> {
+    mut num = $in
+    mut out = []
+    while $num > 0 {
+        let digit = $num mod $base
+        $out ++= [$digit]
+        $num -= $digit
+        $num /= $base
+    }
+    $out | reverse
+}
+export def rebase [--input-base (-i): number, --output-base (-o): number]: list<number> -> list<number> {
+    assert ($input_base >= 2) "input base must be >= 2"
+    assert ($output_base >= 2) "output base must be >= 2"
+    let number = $in
+    assert ($number | all {|d| 0 <= $d and $d < $input_base }) "all digits must satisfy 0 <= d < input base"
+    let number = $number | base_ten $input_base
+    let rebased = $number | rebase_from_ten $output_base
+    if $rebased == [] { [0] } else $rebased
+}

exercises/practice/all-your-base/.meta/tests.toml

@@ -0,0 +1,73 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[5ce422f9-7a4b-4f44-ad29-49c67cb32d2c]
+description = "single bit one to decimal"
+
+[0cc3fea8-bb79-46ac-a2ab-5a2c93051033]
+description = "binary to single decimal"
+
+[f12db0f9-0d3d-42c2-b3ba-e38cb375a2b8]
+description = "single decimal to binary"
+
+[2c45cf54-6da3-4748-9733-5a3c765d925b]
+description = "binary to multiple decimal"
+
+[65ddb8b4-8899-4fcc-8618-181b2cf0002d]
+description = "decimal to binary"
+
+[8d418419-02a7-4824-8b7a-352d33c6987e]
+description = "trinary to hexadecimal"
+
+[d3901c80-8190-41b9-bd86-38d988efa956]
+description = "hexadecimal to trinary"
+
+[5d42f85e-21ad-41bd-b9be-a3e8e4258bbf]
+description = "15-bit integer"
+
+[d68788f7-66dd-43f8-a543-f15b6d233f83]
+description = "empty list"
+
+[5e27e8da-5862-4c5f-b2a9-26c0382b6be7]
+description = "single zero"
+
+[2e1c2573-77e4-4b9c-8517-6c56c5bcfdf2]
+description = "multiple zeros"
+
+[3530cd9f-8d6d-43f5-bc6e-b30b1db9629b]
+description = "leading zeros"
+
+[a6b476a1-1901-4f2a-92c4-4d91917ae023]
+description = "input base is one"
+
+[e21a693a-7a69-450b-b393-27415c26a016]
+description = "input base is zero"
+
+[54a23be5-d99e-41cc-88e0-a650ffe5fcc2]
+description = "input base is negative"
+
+[9eccf60c-dcc9-407b-95d8-c37b8be56bb6]
+description = "negative digit"
+
+[232fa4a5-e761-4939-ba0c-ed046cd0676a]
+description = "invalid positive digit"
+
+[14238f95-45da-41dc-95ce-18f860b30ad3]
+description = "output base is one"
+
+[73dac367-da5c-4a37-95fe-c87fad0a4047]
+description = "output base is zero"
+
+[13f81f42-ff53-4e24-89d9-37603a48ebd9]
+description = "output base is negative"
+
+[0e6c895d-8a5d-4868-a345-309d094cfe8d]
+description = "both bases are negative"

exercises/practice/all-your-base/all-your-base.nu

@@ -0,0 +1,4 @@
+export def rebase [--input-base (-i): number, --output-base (-o): number]: list<number> -> number {
+   error make {msg: "Please implement rebase"}
+   NaN # This is to prevent the typechecker from erroring
+}

exercises/practice/all-your-base/tests.nu

@@ -0,0 +1,23 @@
+use std/assert
+use all-your-base.nu rebase
+assert equal ([1] | rebase -i 2 -o 10) [1]
+assert equal ([1, 0, 1] | rebase -i 2 -o 10) [5]
+assert equal ([5] | rebase -i 10 -o 2) [1, 0, 1]
+assert equal ([1, 0, 1, 0, 1, 0] | rebase -i 2 -o 10) [4, 2]
+assert equal ([4, 2] | rebase -i 10 -o 2) [1, 0, 1, 0, 1, 0]
+assert equal ([1, 1, 2, 0] | rebase -i 3 -o 16) [2, 10]
+assert equal ([2, 10] | rebase -i 16 -o 3) [1, 1, 2, 0]
+assert equal ([3, 46, 60] | rebase -i 97 -o 73) [6, 10, 45]
+assert equal ([] | rebase -i 2 -o 10) [0]
+assert equal ([0] | rebase -i 10 -o 2) [0]
+assert equal ([0, 0, 0] | rebase -i 10 -o 2) [0]
+assert equal ([0, 6, 0] | rebase -i 7 -o 10) [4, 2]
+assert equal (try { [0] | rebase -i 1 -o 10 } catch {|e| $e.msg}) "input base must be >= 2"
+assert equal (try { [] | rebase -i 0 -o 10 } catch {|e| $e.msg}) "input base must be >= 2"
+assert equal (try { [1] | rebase -i -2 -o 10 } catch {|e| $e.msg}) "input base must be >= 2"
+assert equal (try { [1,-1, 1, 0, 1, 0] | rebase -i 2 -o 10 } catch {|e| $e.msg}) "all digits must satisfy 0 <= d < input base"
+assert equal (try { [1, 2, 1, 0, 1, 0] | rebase -i 2 -o 10 } catch {|e| $e.msg}) "all digits must satisfy 0 <= d < input base"
+assert equal (try { [1, 0, 1, 0, 1, 0] | rebase -i 2 -o 1 } catch {|e| $e.msg}) "output base must be >= 2"
+assert equal (try { [7] | rebase -i 10 -o 0 } catch {|e| $e.msg}) "output base must be >= 2"
+assert equal (try { [1] | rebase -i 2 -o -7 } catch {|e| $e.msg}) "output base must be >= 2"
+assert equal (try { [1] | rebase -i -2 -o -7 } catch {|e| $e.msg}) "input base must be >= 2"