134 lines
3.3 KiB
Go
134 lines
3.3 KiB
Go
package main
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import "fmt"
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// representation of an expression in x, y, and z
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type expr struct {
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x, y, z float64 // coefficients
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c float64 // constant term
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}
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// add two expressions
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func addExpr(a, b expr) expr {
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return expr{a.x + b.x, a.y + b.y, a.z + b.z, a.c + b.c}
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}
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// subtract two expressions
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func subExpr(a, b expr) expr {
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return expr{a.x - b.x, a.y - b.y, a.z - b.z, a.c - b.c}
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}
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// multiply expression by a constant
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func mulExpr(a expr, c float64) expr {
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return expr{a.x * c, a.y * c, a.z * c, a.c * c}
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}
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// given a row of expressions, produce the next row up, by the given
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// sum relation between blocks
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func addRow(l []expr) []expr {
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if len(l) == 0 {
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panic("wrong")
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}
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r := make([]expr, len(l)-1)
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for i := range r {
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r[i] = addExpr(l[i], l[i+1])
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}
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return r
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}
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// given expression b in a variable, and expression a,
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// take b == 0 and substitute to remove that variable from a.
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func substX(a, b expr) expr {
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if b.x == 0 {
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panic("wrong")
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}
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return subExpr(a, mulExpr(b, a.x/b.x))
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}
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func substY(a, b expr) expr {
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if b.y == 0 {
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panic("wrong")
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}
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return subExpr(a, mulExpr(b, a.y/b.y))
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}
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func substZ(a, b expr) expr {
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if b.z == 0 {
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panic("wrong")
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}
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return subExpr(a, mulExpr(b, a.z/b.z))
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}
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// given an expression in a single variable, return value of that variable
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func solveX(a expr) float64 {
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if a.x == 0 || a.y != 0 || a.z != 0 {
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panic("wrong")
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}
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return -a.c / a.x
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}
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func solveY(a expr) float64 {
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if a.x != 0 || a.y == 0 || a.z != 0 {
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panic("wrong")
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}
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return -a.c / a.y
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}
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func solveZ(a expr) float64 {
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if a.x != 0 || a.y != 0 || a.z == 0 {
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panic("wrong")
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}
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return -a.c / a.z
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}
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func main() {
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// representation of given information for bottom row
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r5 := []expr{{x: 1}, {c: 11}, {y: 1}, {c: 4}, {z: 1}}
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fmt.Println("bottom row:", r5)
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// given definition of brick sum relation
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r4 := addRow(r5)
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fmt.Println("next row up:", r4)
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r3 := addRow(r4)
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fmt.Println("middle row:", r3)
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// given relation y = x + z
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xyz := subExpr(expr{y: 1}, expr{x: 1, z: 1})
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fmt.Println("xyz relation:", xyz)
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// remove z from third cell using xyz relation
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r3[2] = substZ(r3[2], xyz)
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fmt.Println("middle row after substituting for z:", r3)
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// given cell = 40,
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b := expr{c: 40}
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// this gives an xy relation
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xy := subExpr(r3[0], b)
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fmt.Println("xy relation:", xy)
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// substitute 40 for cell
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r3[0] = b
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// remove x from third cell using xy relation
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r3[2] = substX(r3[2], xy)
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fmt.Println("middle row after substituting for x:", r3)
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// continue applying brick sum relation to get top cell
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r2 := addRow(r3)
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fmt.Println("next row up:", r2)
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r1 := addRow(r2)
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fmt.Println("top row:", r1)
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// given top cell = 151, we have an equation in y
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y := subExpr(r1[0], expr{c: 151})
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fmt.Println("y relation:", y)
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// using xy relation, we get an equation in x
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x := substY(xy, y)
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fmt.Println("x relation:", x)
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// using xyz relation, we get an equation in z
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z := substX(substY(xyz, y), x)
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fmt.Println("z relation:", z)
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// show final answers
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fmt.Println("x =", solveX(x))
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fmt.Println("y =", solveY(y))
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fmt.Println("z =", solveZ(z))
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}
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