tasks a-s

Task/Pascals-triangle-Puzzle/Go/pascals-triangle-puzzle.go

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