Data commit

Task/Polynomial-long-division/Swift/polynomial-long-division.swift

@@ -0,0 +1,130 @@
+protocol Dividable {
+  static func / (lhs: Self, rhs: Self) -> Self
+}
+
+extension Int: Dividable { }
+
+struct Solution<T> {
+  var quotient: [T]
+  var remainder: [T]
+}
+
+func polyDegree<T: SignedNumeric>(_ p: [T]) -> Int {
+  for i in stride(from: p.count - 1, through: 0, by: -1) where p[i] != 0 {
+    return i
+  }
+
+  return Int.min
+}
+
+func polyShiftRight<T: SignedNumeric>(p: [T], places: Int) -> [T] {
+  guard places > 0 else {
+    return p
+  }
+
+  let deg = polyDegree(p)
+
+  assert(deg + places < p.count, "Number of places to shift too large")
+
+  var res = p
+
+  for i in stride(from: deg, through: 0, by: -1) {
+    res[i + places] = res[i]
+    res[i] = 0
+  }
+
+  return res
+}
+
+func polyMul<T: SignedNumeric>(_ p: inout [T], by: T) {
+  for i in 0..<p.count {
+    p[i] *= by
+  }
+}
+
+func polySub<T: SignedNumeric>(_ p: inout [T], by: [T]) {
+  for i in 0..<p.count {
+    p[i] -= by[i]
+  }
+}
+
+func polyLongDiv<T: SignedNumeric & Dividable>(numerator n: [T], denominator d: [T]) -> Solution<T>? {
+  guard n.count == d.count else {
+    return nil
+  }
+
+  var nDeg = polyDegree(n)
+  let dDeg = polyDegree(d)
+
+  guard dDeg >= 0, nDeg >= dDeg else {
+    return nil
+  }
+
+  var n2 = n
+  var quo = [T](repeating: 0, count: n.count)
+
+  while nDeg >= dDeg {
+    let i = nDeg - dDeg
+    var d2 = polyShiftRight(p: d, places: i)
+
+    quo[i] = n2[nDeg] / d2[nDeg]
+
+    polyMul(&d2, by: quo[i])
+    polySub(&n2, by: d2)
+
+    nDeg = polyDegree(n2)
+  }
+
+  return Solution(quotient: quo, remainder: n2)
+}
+
+func polyPrint<T: SignedNumeric & Comparable>(_ p: [T]) {
+  let deg = polyDegree(p)
+
+  for i in stride(from: deg, through: 0, by: -1) where p[i] != 0 {
+    let coeff = p[i]
+
+    switch coeff {
+    case 1 where i < deg:
+      print(" + ", terminator: "")
+    case 1:
+      print("", terminator: "")
+    case -1 where i < deg:
+      print(" - ", terminator: "")
+    case -1:
+      print("-", terminator: "")
+    case _ where coeff < 0 && i < deg:
+      print(" - \(-coeff)", terminator: "")
+    case _ where i < deg:
+      print(" + \(coeff)", terminator: "")
+    case _:
+      print("\(coeff)", terminator: "")
+    }
+
+    if i > 1 {
+      print("x^\(i)", terminator: "")
+    } else if i == 1 {
+      print("x", terminator: "")
+    }
+  }
+
+  print()
+}
+
+let n = [-42, 0, -12, 1]
+let d = [-3, 1, 0, 0]
+
+print("Numerator: ", terminator: "")
+polyPrint(n)
+print("Denominator: ", terminator: "")
+polyPrint(d)
+
+guard let sol = polyLongDiv(numerator: n, denominator: d) else {
+  fatalError()
+}
+
+print("----------")
+print("Quotient: ", terminator: "")
+polyPrint(sol.quotient)
+print("Remainder: ", terminator: "")
+polyPrint(sol.remainder)