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Advanced 24 game solver
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package main | |
import ( | |
"flag" | |
"fmt" | |
"math" | |
"math/rand" | |
"sort" | |
"strconv" | |
"strings" | |
"time" | |
) | |
type Expression interface { | |
Value() float64 | |
Repr() string | |
} | |
func CompareExpression(e1, e2 Expression) bool { | |
if e1.Value() < e2.Value() { | |
return true | |
} | |
if e1.Value() > e2.Value() { | |
return false | |
} | |
return strings.Compare(e1.Repr(), e2.Repr()) < 0 | |
} | |
func SortExpression(e []Expression) { | |
sort.Slice(e, func(i, j int) bool { | |
return CompareExpression(e[i], e[j]) | |
}) | |
} | |
type AddGroup struct { | |
Pos []Expression | |
Neg []Expression | |
} | |
type MulGroup struct { | |
Pos []Expression | |
Neg []Expression | |
} | |
type Number struct { | |
Val float64 | |
Str string | |
} | |
func (e *AddGroup) Value() float64 { | |
var s float64 = 0 | |
for _, ee := range e.Pos { | |
s += ee.Value() | |
} | |
for _, ee := range e.Neg { | |
s -= ee.Value() | |
} | |
return s | |
} | |
func (e *AddGroup) Repr() string { | |
SortExpression(e.Pos) | |
SortExpression(e.Neg) | |
var s strings.Builder | |
for _, ee := range e.Pos { | |
s.WriteString("+" + ee.Repr()) | |
} | |
for _, ee := range e.Neg { | |
s.WriteString("-" + ee.Repr()) | |
} | |
return s.String()[1:] | |
} | |
func (e *MulGroup) Value() float64 { | |
var s float64 = 1 | |
for _, ee := range e.Pos { | |
s *= ee.Value() | |
} | |
for _, ee := range e.Neg { | |
s /= ee.Value() | |
} | |
return s | |
} | |
func (e *MulGroup) Repr() string { | |
SortExpression(e.Pos) | |
SortExpression(e.Neg) | |
var s strings.Builder | |
for _, ee := range e.Pos { | |
if _, ok := ee.(*Number); ok { | |
s.WriteString("*" + ee.Repr()) | |
} else { | |
s.WriteString("*(" + ee.Repr() + ")") | |
} | |
} | |
for _, ee := range e.Neg { | |
if _, ok := ee.(*Number); ok { | |
s.WriteString("/" + ee.Repr()) | |
} else { | |
s.WriteString("/(" + ee.Repr() + ")") | |
} | |
} | |
return s.String()[1:] | |
} | |
func (n *Number) Value() float64 { | |
return n.Val | |
} | |
func (n *Number) Repr() string { | |
return n.Str | |
} | |
func JoinAddGroup(e1, e2 Expression, neg2 bool) *AddGroup { | |
e := new(AddGroup) | |
if a1, ok := e1.(*AddGroup); ok { | |
e.Pos = append(e.Pos, a1.Pos...) | |
e.Neg = append(e.Neg, a1.Neg...) | |
} else { | |
e.Pos = append(e.Pos, e1) | |
} | |
if a2, ok := e2.(*AddGroup); ok { | |
if neg2 { | |
e.Pos = append(e.Pos, a2.Neg...) | |
e.Neg = append(e.Neg, a2.Pos...) | |
} else { | |
e.Pos = append(e.Pos, a2.Pos...) | |
e.Neg = append(e.Neg, a2.Neg...) | |
} | |
} else { | |
if neg2 { | |
e.Neg = append(e.Neg, e2) | |
} else { | |
e.Pos = append(e.Pos, e2) | |
} | |
} | |
return e | |
} | |
func JoinMulGroup(e1, e2 Expression, neg2 bool) *MulGroup { | |
e := new(MulGroup) | |
if a1, ok := e1.(*MulGroup); ok { | |
e.Pos = append(e.Pos, a1.Pos...) | |
e.Neg = append(e.Neg, a1.Neg...) | |
} else { | |
e.Pos = append(e.Pos, e1) | |
} | |
if a2, ok := e2.(*MulGroup); ok { | |
if neg2 { | |
e.Pos = append(e.Pos, a2.Neg...) | |
e.Neg = append(e.Neg, a2.Pos...) | |
} else { | |
e.Pos = append(e.Pos, a2.Pos...) | |
e.Neg = append(e.Neg, a2.Neg...) | |
} | |
} else { | |
if neg2 { | |
e.Neg = append(e.Neg, e2) | |
} else { | |
e.Pos = append(e.Pos, e2) | |
} | |
} | |
return e | |
} | |
var ( | |
target float64 | |
allAnswers bool | |
answers []string | |
) | |
func CompareFloat(a, b, threshold float64) bool { | |
return math.Abs(a-b) < threshold | |
} | |
func EvalResult(e Expression) bool { | |
result := CompareFloat(e.Value(), target, 1e-6) | |
if result { | |
s := e.Repr() | |
duplicate := false | |
for _, ans := range answers { | |
if ans == s { | |
duplicate = true | |
break | |
} | |
} | |
if !duplicate { | |
fmt.Println(s, "=", target) | |
answers = append(answers, s) | |
} | |
} | |
return result && !allAnswers | |
} | |
func Find24(nodes []Expression) bool { | |
if len(nodes) == 1 { | |
return EvalResult(nodes[0]) | |
} | |
result := false | |
for i := 0; i < len(nodes); i++ { | |
for j := 0; j < len(nodes); j++ { | |
if i == j { | |
continue | |
} | |
newNodes := make([]Expression, 0, len(nodes)-1) | |
for k := 0; k < len(nodes); k++ { | |
if k == i || k == j { | |
continue | |
} | |
newNodes = append(newNodes, nodes[k]) | |
} | |
newNodes = append(newNodes, nil) | |
if i < j { | |
newNodes[len(nodes)-2] = JoinAddGroup(nodes[i], nodes[j], false) | |
result = result || Find24(newNodes) | |
newNodes[len(nodes)-2] = JoinMulGroup(nodes[i], nodes[j], false) | |
result = result || Find24(newNodes) | |
} | |
newNodes[len(nodes)-2] = JoinAddGroup(nodes[i], nodes[j], true) | |
result = result || Find24(newNodes) | |
newNodes[len(nodes)-2] = JoinMulGroup(nodes[i], nodes[j], true) | |
result = result || Find24(newNodes) | |
} | |
} | |
return result && !allAnswers | |
} | |
func main() { | |
flag.Float64Var(&target, "t", 24.0, "target value") | |
flag.BoolVar(&allAnswers, "a", false, "find all solutions") | |
flag.Parse() | |
nums := make([]Expression, len(flag.Args())) | |
for i, arg := range flag.Args() { | |
value, err := strconv.ParseFloat(arg, 64) | |
if err != nil { | |
panic(err) | |
} | |
nums[i] = &Number{Val: value, Str: arg} | |
} | |
rand.Seed(time.Now().UnixNano()) | |
for i := range nums { | |
j := rand.Intn(i + 1) | |
nums[i], nums[j] = nums[j], nums[i] | |
} | |
Find24(nums) | |
if len(answers) == 0 { | |
fmt.Println("No solution") | |
} | |
} |
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