From fa9478665ea63259b8ad7f5075c57c7a31757935 Mon Sep 17 00:00:00 2001
From: Wesley Kerfoot <wjak56@gmail.com>
Date: Mon, 20 Jan 2020 20:24:00 -0500
Subject: [PATCH] Shunting-Yard implementation in Nim

---
 shunting_yard.nim | 149 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 149 insertions(+)
 create mode 100644 shunting_yard.nim

diff --git a/shunting_yard.nim b/shunting_yard.nim
new file mode 100644
index 0000000..1edf09a
--- /dev/null
+++ b/shunting_yard.nim
@@ -0,0 +1,149 @@
+import deques, parseutils, tables, strutils, math
+
+type
+  RPNKind = enum
+    rpnkNum,
+    rpnkOp
+  RPNVal = ref object
+    case kind: RPNKind
+    of rpnkNum: num: float
+    of rpnkOp: op: string
+
+proc tokenize(expr : string) : seq[string] =
+  var currentTok : string
+  for c in expr:
+    if c in Whitespace:
+      if currentTok.len > 0:
+        result = result & currentTok
+      currentTok = ""
+      continue
+
+    if c == '(' or c == ')':
+      if currentTok.len > 0:
+        result = result & currentTok
+      currentTok = ""
+
+      result = result & $c
+
+    if c in Digits:
+      currentTok = currentTok & c
+
+    if c in "+-*/^":
+      currentTok = ""
+      result = result & $c
+
+  if currentTok.len > 0:
+    result = result & currentTok
+
+proc toRPN(expr : string) : seq[RPNVal] =
+  let prec = {
+    "^" : 0,
+    "+" : 2,
+    "-" : 2,
+    "*" : 1,
+    "/" : 1
+  }.toTable
+
+  let assoc = {
+    "+" : "left",
+    "-" : "left",
+    "*" : "left",
+    "/" : "left",
+    "^" : "right"
+  }.toTable
+
+  var stack : seq[string]
+  var q = initDeque[string]()
+  
+  var tokens = expr.tokenize
+
+  while tokens.len > 0:
+    let tok = tokens[0]
+
+    if tok[0] in Digits:
+      q.addLast(tok)
+
+    if not (tok[0] in Digits):
+      if tok == ")":
+        # Drain the stack onto the queue
+        while stack.len > 0:
+          let op = stack[0]
+          stack = stack[1..^1]
+          if op == "(":
+            break
+          q.addLast(op)
+        tokens = tokens[1..^1]
+        continue
+
+      if stack.len > 0 and (stack[0] in prec) and (tok in prec):
+              # there are ops   the op on the stack has higher prec
+              #                 or the op on the stack is left assoc and == prec
+        while (stack.len > 0 and 
+              ((prec[stack[0]] < prec[tok]) or
+              (assoc[stack[0]] == "left" and prec[stack[0]] == prec[tok]))):
+          # We want to evaluate higher precedence sub-expressions first
+          # This should also check the associativity
+          # If we have 3 ^ 2 + 4, it should be 3 2 ^ 4 +, not 3 2 4 + ^
+          # If the operator is right-associative, that means we will leave it
+          q.addLast(stack[0])
+          stack = stack[1..^1]
+
+      stack = @[tok] & stack
+    tokens = tokens[1..^1]
+
+  while stack.len > 0:
+    q.addLast(stack[0])
+    stack = stack[1..^1]
+
+  while q.len > 0:
+    var numRes : float
+    let tok = q.popFirst
+    let num = tok.parseBiggestFloat(numRes)
+    if numRes == 0:
+      # It's an operator
+      result = result & RPNVal(kind: rpnkOp, op: $tok)
+    else:
+      # It's a number
+      result = result & RPNVal(kind: rpnkNum, num: numRes)
+
+proc operate(stack : seq[float], op : RPNVal) : seq[float] =
+  let a : float = stack[1]
+  let b : float = stack[0]
+
+  var res : float
+
+  if op.op == "+":
+    res = a + b
+  if op.op == "-":
+    res = a - b
+  if op.op == "*":
+    res = a * b
+  if op.op == "/":
+    res = a / b
+  if op.op == "^":
+    res = a.pow(b)
+
+  result = stack[2..^1]
+  result = @[res] & result
+
+proc calculate(expr : string) : float =
+  let tokens = expr.toRPN
+  var stack : seq[float]
+
+  for token in tokens:
+    if token.kind == rpnkNum:
+      # If it's a number, push it onto the stack
+      stack = @[token.num] & stack
+    if token.kind == rpnkOp:
+      # If it's an operator, pop two elements off
+      # Then push the result back on
+      stack = stack.operate(token)
+
+  assert(stack.len == 1)
+  stack[0]
+
+echo "7 / (2 ^ 3) ^ (4 * 2) + 10".calculate
+echo "2 ^ 3 ^ 4".calculate
+echo "3 ^ 2 + 4".calculate
+for tok in "2 ^ 3 ^ 4".toRPN:
+  echo tok.repr