Data commit

Task/N-smooth-numbers/Go/n-smooth-numbers.go

@@ -0,0 +1,99 @@
+package main
+
+import (
+    "fmt"
+    "log"
+    "math/big"
+)
+
+var (
+    primes      []*big.Int
+    smallPrimes []int
+)
+
+// cache all primes up to 521
+func init() {
+    two := big.NewInt(2)
+    three := big.NewInt(3)
+    p521 := big.NewInt(521)
+    p29 := big.NewInt(29)
+    primes = append(primes, two)
+    smallPrimes = append(smallPrimes, 2)
+    for i := three; i.Cmp(p521) <= 0; i.Add(i, two) {
+        if i.ProbablyPrime(0) {
+            primes = append(primes, new(big.Int).Set(i))
+            if i.Cmp(p29) <= 0 {
+                smallPrimes = append(smallPrimes, int(i.Int64()))
+            }
+        }
+    }
+}
+
+func min(bs []*big.Int) *big.Int {
+    if len(bs) == 0 {
+        log.Fatal("slice must have at least one element")
+    }
+    res := bs[0]
+    for _, i := range bs[1:] {
+        if i.Cmp(res) < 0 {
+            res = i
+        }
+    }
+    return res
+}
+
+func nSmooth(n, size int) []*big.Int {
+    if n < 2 || n > 521 {
+        log.Fatal("n must be between 2 and 521")
+    }
+    if size < 1 {
+        log.Fatal("size must be at least 1")
+    }
+    bn := big.NewInt(int64(n))
+    ok := false
+    for _, prime := range primes {
+        if bn.Cmp(prime) == 0 {
+            ok = true
+            break
+        }
+    }
+    if !ok {
+        log.Fatal("n must be a prime number")
+    }
+
+    ns := make([]*big.Int, size)
+    ns[0] = big.NewInt(1)
+    var next []*big.Int
+    for i := 0; i < len(primes); i++ {
+        if primes[i].Cmp(bn) > 0 {
+            break
+        }
+        next = append(next, new(big.Int).Set(primes[i]))
+    }
+    indices := make([]int, len(next))
+    for m := 1; m < size; m++ {
+        ns[m] = new(big.Int).Set(min(next))
+        for i := 0; i < len(indices); i++ {
+            if ns[m].Cmp(next[i]) == 0 {
+                indices[i]++
+                next[i].Mul(primes[i], ns[indices[i]])
+            }
+        }
+    }
+    return ns
+}
+
+func main() {
+    for _, i := range smallPrimes {
+        fmt.Printf("The first 25 %d-smooth numbers are:\n", i)
+        fmt.Println(nSmooth(i, 25), "\n")
+    }
+    for _, i := range smallPrimes[1:] {
+        fmt.Printf("The 3,000th to 3,202nd %d-smooth numbers are:\n", i)
+        fmt.Println(nSmooth(i, 3002)[2999:], "\n")
+    }
+    for _, i := range []int{503, 509, 521} {
+        fmt.Printf("The 30,000th to 30,019th %d-smooth numbers are:\n", i)
+        fmt.Println(nSmooth(i, 30019)[29999:], "\n")
+    }
+}