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Task/Heronian-triangles/Nim/heronian-triangles.nim

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+import math, algorithm, strfmt, sequtils
+
+type
+  HeronianTriangle = tuple
+    a: int
+    b: int
+    c: int
+    s: float
+    A: int
+
+proc `$` (t: HeronianTriangle): string =
+  fmt("{:3d}, {:3d}, {:3d}\t{:7.3f}\t{:3d}", t.a, t.b, t.c, t.s, t.A)
+
+proc hero(a:int, b:int, c:int): tuple[s, A: float] =
+  let s: float = (a + b + c) / 2
+  result = (s, sqrt( s * (s - float(a)) * (s - float(b)) * (s - float(c)) ))
+
+proc isHeronianTriangle(x: float): bool = ceil(x) == x and x.toInt > 0
+
+proc gcd(x: int, y: int): int =
+  var
+    (dividend, divisor) = if x > y: (x, y) else: (y, x)
+    remainder = dividend mod divisor
+
+  while remainder != 0:
+    dividend = divisor
+    divisor = remainder
+    remainder = dividend mod divisor
+  result = divisor
+
+
+var list = newSeq[HeronianTriangle]()
+const max = 200
+
+for c in 1..max:
+  for b in 1..c:
+    for a in 1..b:
+      let (s, A) = hero(a, b, c)
+      if isHeronianTriangle(A) and gcd(a, gcd(b, c)) == 1:
+        let t:HeronianTriangle = (a, b, c, s, A.toInt)
+        list.add(t)
+
+echo "Numbers of Heronian Triangle : ", list.len
+
+list.sort do (x, y: HeronianTriangle) -> int:
+  result = cmp(x.A, y.A)
+  if result == 0:
+    result = cmp(x.s, y.s)
+    if result == 0:
+      result = cmp(max(x.a, x.b, x.c), max(y.a, y.b, y.c))
+
+echo "Ten first Heronian triangle ordered : "
+echo "Sides          Perimeter Area"
+for t in list[0 .. <10]:
+  echo t
+
+echo "Heronian triangle ordered with Area 210 : "
+echo "Sides          Perimeter Area"
+for t in list.filter(proc (x: HeronianTriangle): bool = x.A == 210):
+  echo t