Data commit

Task/Pisano-period/Go/pisano-period.go

@@ -0,0 +1,136 @@
+package main
+
+import "fmt"
+
+func gcd(a, b uint) uint {
+    if b == 0 {
+        return a
+    }
+    return gcd(b, a%b)
+}
+
+func lcm(a, b uint) uint {
+    return a / gcd(a, b) * b
+}
+
+func ipow(x, p uint) uint {
+    prod := uint(1)
+    for p > 0 {
+        if p&1 != 0 {
+            prod *= x
+        }
+        p >>= 1
+        x *= x
+    }
+    return prod
+}
+
+// Gets the prime decomposition of n.
+func getPrimes(n uint) []uint {
+    var primes []uint
+    for i := uint(2); i <= n; i++ {
+        div := n / i
+        mod := n % i
+        for mod == 0 {
+            primes = append(primes, i)
+            n = div
+            div = n / i
+            mod = n % i
+        }
+    }
+    return primes
+}
+
+// OK for 'small' numbers.
+func isPrime(n uint) bool {
+    switch {
+    case n < 2:
+        return false
+    case n%2 == 0:
+        return n == 2
+    case n%3 == 0:
+        return n == 3
+    default:
+        d := uint(5)
+        for d*d <= n {
+            if n%d == 0 {
+                return false
+            }
+            d += 2
+            if n%d == 0 {
+                return false
+            }
+            d += 4
+        }
+        return true
+    }
+}
+
+// Calculates the Pisano period of 'm' from first principles.
+func pisanoPeriod(m uint) uint {
+    var p, c uint = 0, 1
+    for i := uint(0); i < m*m; i++ {
+        p, c = c, (p+c)%m
+        if p == 0 && c == 1 {
+            return i + 1
+        }
+    }
+    return 1
+}
+
+// Calculates the Pisano period of p^k where 'p' is prime and 'k' is a positive integer.
+func pisanoPrime(p uint, k uint) uint {
+    if !isPrime(p) || k == 0 {
+        return 0 // can't do this one
+    }
+    return ipow(p, k-1) * pisanoPeriod(p)
+}
+
+// Calculates the Pisano period of 'm' using pisanoPrime.
+func pisano(m uint) uint {
+    primes := getPrimes(m)
+    primePowers := make(map[uint]uint)
+    for _, p := range primes {
+        primePowers[p]++
+    }
+    var pps []uint
+    for k, v := range primePowers {
+        pps = append(pps, pisanoPrime(k, v))
+    }
+    if len(pps) == 0 {
+        return 1
+    }
+    if len(pps) == 1 {
+        return pps[0]
+    }
+    f := pps[0]
+    for i := 1; i < len(pps); i++ {
+        f = lcm(f, pps[i])
+    }
+    return f
+}
+
+func main() {
+    for p := uint(2); p < 15; p++ {
+        pp := pisanoPrime(p, 2)
+        if pp > 0 {
+            fmt.Printf("pisanoPrime(%2d: 2) = %d\n", p, pp)
+        }
+    }
+    fmt.Println()
+    for p := uint(2); p < 180; p++ {
+        pp := pisanoPrime(p, 1)
+        if pp > 0 {
+            fmt.Printf("pisanoPrime(%3d: 1) = %d\n", p, pp)
+        }
+    }
+    fmt.Println()
+    fmt.Println("pisano(n) for integers 'n' from 1 to 180 are:")
+    for n := uint(1); n <= 180; n++ {
+        fmt.Printf("%3d ", pisano(n))
+        if n != 1 && n%15 == 0 {
+            fmt.Println()
+        }
+    }
+    fmt.Println()
+}