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var cachedUglyNumbers []int | |
func nthUglyNumber(n int) int { | |
if cachedUglyNumbers != nil { | |
// give the desired ugly number | |
return cachedUglyNumbers[n-1] | |
} | |
// generate all ugly numbers <= MaxInt32, then used cached values for subsequent calls | |
h := NewIntHeap(1690, 0, false) | |
// generates a list of all powers of a given base from 1 .. MaxInt32 | |
pN := func(base int) []int { | |
ps := []int{} | |
for p := 1; p <= math.MaxInt32; p *= base { | |
ps = append(ps, p) | |
} | |
return ps | |
} | |
// generate all powers of all ugly primes | |
p2s := pN(2) | |
p3s := pN(3) | |
p5s := pN(5) | |
// compute all combinations of ugly factors w/short circuiting | |
for _, p2 := range p2s { | |
for _, p3 := range p3s { | |
ugly := p2 * p3 | |
if ugly > math.MaxInt32 { | |
break | |
} | |
for _, p5 := range p5s { | |
ugly := ugly * p5 | |
if ugly > math.MaxInt32 { | |
break | |
} | |
// maintains an ordered heap | |
heap.Push(h, ugly) | |
} | |
} | |
} | |
// convert heap to cache sorted in ascending order | |
cachedUglyNumbers = make([]int, h.Len()) | |
for i := 0; i < len(cachedUglyNumbers); i++ { | |
cachedUglyNumbers[i] = heap.Pop(h).(int) | |
} | |
// give the desired ugly number | |
return cachedUglyNumbers[n-1] | |
} | |
// Helper IntHeap | |
func NewIntHeap(initialSize int, maxSize int, desc bool) *IntHeap { | |
return &IntHeap{ | |
data: make([]int, initialSize)[0:0], | |
desc: desc, | |
maxSize: maxSize, | |
} | |
} | |
type IntHeap struct { | |
data []int | |
desc bool // true = descending, false = ascending | |
initialSize int | |
maxSize int | |
} | |
func (h *IntHeap) resetData() { | |
h.data = make([]int, h.initialSize)[0:0] | |
heap.Init(h) | |
} | |
func (h IntHeap) Len() int { | |
return len(h.data) | |
} | |
func (h IntHeap) Less(i, j int) bool { | |
if h.desc { | |
return h.data[i] > h.data[j] | |
} | |
return h.data[i] < h.data[j] | |
} | |
func (h IntHeap) Swap(i, j int) { | |
h.data[i], h.data[j] = h.data[j], h.data[i] | |
} | |
func (h *IntHeap) Push(x interface{}) { | |
h.data = append(h.data, x.(int)) | |
} | |
func (h *IntHeap) Prune() { | |
if h.maxSize == 0 || h.Len() < h.maxSize { | |
return | |
} | |
// pop the desired values | |
r := make([]int, h.maxSize) | |
for i := 0; i < h.maxSize; i++ { | |
r[i] = heap.Pop(h).(int) | |
} | |
// reset heap data | |
h.resetData() | |
// push back | |
for _, v := range r { | |
heap.Push(h, v) | |
} | |
} | |
func (h *IntHeap) Peek() int { | |
return h.data[h.Len()-1] | |
} | |
func (h *IntHeap) Pop() interface{} { | |
n := h.Len() | |
x := h.data[n-1] | |
h.data = h.data[0:n-1] | |
return x | |
} |
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