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feat: add solutions to lc problem: No.0313
No.0313.Super Ugly Number
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‎solution/0300-0399/0313.Super Ugly Number/README.md

Lines changed: 102 additions & 18 deletions
Original file line numberDiff line numberDiff line change
@@ -51,9 +51,15 @@
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<!-- 这里可写通用的实现逻辑 -->
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54-
**方法一：优先队列**
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**方法一：优先队列（小根堆）**
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根据题目要求，模拟第 1 ～ n 个丑数，显然任意一个丑数 `ugly[i]` 乘以 `primes` 数组中的质数 `primes[i]` 仍旧是丑数。已知 `ugly[1]=1`，`ugly[2] = min(ugly[1]*primes[i])`，则 `ugly[3]` 应该等于集合 `ugly[2]*primes[i], ugly[1]*primes[i]` 中排除 `ugly[2]` 之后的最小值，依次类推可以得到 `ugly[n]` 的值。
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我们用一个优先队列（小根堆）维护所有可能的超级丑数，初始时将 $1$ 放入队列中。
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每次从队列中取出最小的超级丑数 $x$，将 $x$ 乘以数组 `primes` 中的每个数，将乘积放入队列中，然后重复上述操作 $n$ 次即可得到第 $n$ 个超级丑数。
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由于题目保证第 $n$ 个超级丑数在 $32$ 位带符号整数范围内，因此，我们将乘积放入队列之前，可以先判断乘积是否超过 $2^{31} - 1$，如果超过，则不需要将乘积放入队列中。另外，可以使用欧拉筛优化。
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时间复杂度 $O(n \times m \times \log (n \times m))$，空间复杂度 $O(n \times m)$。其中 $m$ 和 $n$ 分别为数组 `primes` 的长度和给定的整数 $n$。
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<!-- tabs:start -->
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@@ -62,29 +68,107 @@
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
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from queue import PriorityQueue
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class Solution:
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def nthSuperUglyNumber(self, n: int, primes: List[int]) -> int:
70-
ugly, pq, p = [0]*(n+1), PriorityQueue(), 2
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ugly[1] = 1
72-
for prime in primes:
73-
pq.put([prime, prime, 2])
74-
75-
while p <= n:
76-
top = pq.get()
77-
if top[0] != ugly[p-1]:
78-
ugly[p], p = top[0], p+1
79-
top[0], top[2] = ugly[top[2]]*top[1], top[2]+1
80-
pq.put(top)
81-
return ugly[n]
73+
q = [1]
74+
x = 0
75+
mx = (1 << 31) - 1
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for _ in range(n):
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x = heappop(q)
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for k in primes:
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if x <= mx // k:
80+
heappush(q, k * x)
81+
if x % k == 0:
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break
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return x
8284
```
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84-
### **Go**
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### **Java**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```java
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class Solution {
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public int nthSuperUglyNumber(int n, int[] primes) {
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PriorityQueue<Integer> q = new PriorityQueue<>();
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q.offer(1);
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int x = 0;
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while (n-- > 0) {
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x = q.poll();
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while (!q.isEmpty() && q.peek() == x) {
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q.poll();
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}
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for (int k : primes) {
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if (k <= Integer.MAX_VALUE / x) {
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q.offer(k * x);
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}
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if (x % k == 0) {
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break;
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}
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}
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}
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return x;
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
120+
int nthSuperUglyNumber(int n, vector<int>& primes) {
121+
priority_queue<int, vector<int>, greater<int>> q;
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q.push(1);
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int x = 0;
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while (n--) {
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x = q.top();
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q.pop();
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for (int& k : primes) {
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if (x <= INT_MAX / k) {
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q.push(k * x);
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}
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if (x % k == 0) {
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break;
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}
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}
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}
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return x;
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}
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};
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```
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### **Go**
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```go
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func nthSuperUglyNumber(n int, primes []int) (x int) {
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q := hp{[]int{1}}
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for n > 0 {
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n--
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x = heap.Pop(&q).(int)
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for _, k := range primes {
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if x <= math.MaxInt32/k {
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heap.Push(&q, k*x)
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}
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if x%k == 0 {
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break
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}
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}
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}
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return
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}
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type hp struct{ sort.IntSlice }
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func (h *hp) Push(v interface{}) { h.IntSlice = append(h.IntSlice, v.(int)) }
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func (h *hp) Pop() interface{} {
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a := h.IntSlice
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v := a[len(a)-1]
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h.IntSlice = a[:len(a)-1]
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return v
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}
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```
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88172
```go
89173
type Ugly struct{ value, prime, index int }
90174
type Queue []Ugly

‎solution/0300-0399/0313.Super Ugly Number/README_EN.md

Lines changed: 93 additions & 15 deletions
Original file line numberDiff line numberDiff line change
@@ -47,27 +47,105 @@ Priority Queue.
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### **Python3**
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```python
50-
from queue import PriorityQueue
51-
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class Solution:
5451
def nthSuperUglyNumber(self, n: int, primes: List[int]) -> int:
55-
ugly, pq, p = [0]*(n+1), PriorityQueue(), 2
56-
ugly[1] = 1
57-
for prime in primes:
58-
pq.put([prime, prime, 2])
59-
60-
while p <= n:
61-
top = pq.get()
62-
if top[0] != ugly[p-1]:
63-
ugly[p], p = top[0], p+1
64-
top[0], top[2] = ugly[top[2]]*top[1], top[2]+1
65-
pq.put(top)
66-
return ugly[n]
52+
q = [1]
53+
x = 0
54+
mx = (1 << 31) - 1
55+
for _ in range(n):
56+
x = heappop(q)
57+
for k in primes:
58+
if x <= mx // k:
59+
heappush(q, k * x)
60+
if x % k == 0:
61+
break
62+
return x
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```
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65+
### **Java**
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67+
```java
68+
class Solution {
69+
public int nthSuperUglyNumber(int n, int[] primes) {
70+
PriorityQueue<Integer> q = new PriorityQueue<>();
71+
q.offer(1);
72+
int x = 0;
73+
while (n-- > 0) {
74+
x = q.poll();
75+
while (!q.isEmpty() && q.peek() == x) {
76+
q.poll();
77+
}
78+
for (int k : primes) {
79+
if (k <= Integer.MAX_VALUE / x) {
80+
q.offer(k * x);
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}
82+
if (x % k == 0) {
83+
break;
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}
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}
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}
87+
return x;
88+
}
89+
}
90+
```
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92+
### **C++**
93+
94+
```cpp
95+
class Solution {
96+
public:
97+
int nthSuperUglyNumber(int n, vector<int>& primes) {
98+
priority_queue<int, vector<int>, greater<int>> q;
99+
q.push(1);
100+
int x = 0;
101+
while (n--) {
102+
x = q.top();
103+
q.pop();
104+
for (int& k : primes) {
105+
if (x <= INT_MAX / k) {
106+
q.push(k * x);
107+
}
108+
if (x % k == 0) {
109+
break;
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}
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}
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}
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return x;
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}
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};
67116
```
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### **Go**
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```go
121+
func nthSuperUglyNumber(n int, primes []int) (x int) {
122+
q := hp{[]int{1}}
123+
for n > 0 {
124+
n--
125+
x = heap.Pop(&q).(int)
126+
for _, k := range primes {
127+
if x <= math.MaxInt32/k {
128+
heap.Push(&q, k*x)
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}
130+
if x%k == 0 {
131+
break
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}
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}
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}
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return
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}
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type hp struct{ sort.IntSlice }
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140+
func (h *hp) Push(v interface{}) { h.IntSlice = append(h.IntSlice, v.(int)) }
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func (h *hp) Pop() interface{} {
142+
a := h.IntSlice
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v := a[len(a)-1]
144+
h.IntSlice = a[:len(a)-1]
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return v
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}
147+
```
148+
71149
```go
72150
type Ugly struct{ value, prime, index int }
73151
type Queue []Ugly

‎solution/0300-0399/0313.Super Ugly Number/Solution.cpp

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,21 @@
1+
class Solution {
2+
public:
3+
int nthSuperUglyNumber(int n, vector<int>& primes) {
4+
priority_queue<int, vector<int>, greater<int>> q;
5+
q.push(1);
6+
int x = 0;
7+
while (n--) {
8+
x = q.top();
9+
q.pop();
10+
for (int& k : primes) {
11+
if (x <= INT_MAX / k) {
12+
q.push(k * x);
13+
}
14+
if (x % k == 0) {
15+
break;
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}
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}
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}
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return x;
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}
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};

‎solution/0300-0399/0313.Super Ugly Number/Solution.go

Lines changed: 23 additions & 27 deletions
Original file line numberDiff line numberDiff line change
@@ -1,30 +1,26 @@
1-
type Ugly struct{ value, prime, index int }
2-
type Queue []Ugly
3-
4-
func (u Queue) Len() int { return len(u) }
5-
func (u Queue) Swap(i, j int) { u[i], u[j] = u[j], u[i] }
6-
func (u Queue) Less(i, j int) bool { return u[i].value < u[j].value }
7-
func (u *Queue) Push(v interface{}) { *u = append(*u, v.(Ugly)) }
8-
func (u *Queue) Pop() interface{} {
9-
old, x := *u, (*u)[len(*u)-1]
10-
*u = old[:len(old)-1]
11-
return x
12-
}
13-
14-
func nthSuperUglyNumber(n int, primes []int) int {
15-
ugly, pq, p := make([]int, n+1), &Queue{}, 2
16-
ugly[1] = 1
17-
heap.Init(pq)
18-
for _, v := range primes {
19-
heap.Push(pq, Ugly{value: v, prime: v, index: 2})
20-
}
21-
for p <= n {
22-
top := heap.Pop(pq).(Ugly)
23-
if ugly[p-1] != top.value {
24-
ugly[p], p = top.value, p+1
1+
func nthSuperUglyNumber(n int, primes []int) (x int) {
2+
q := hp{[]int{1}}
3+
for n > 0 {
4+
n--
5+
x = heap.Pop(&q).(int)
6+
for _, k := range primes {
7+
if x <= math.MaxInt32/k {
8+
heap.Push(&q, k*x)
9+
}
10+
if x%k == 0 {
11+
break
12+
}
2513
}
26-
top.value, top.index = ugly[top.index]*top.prime, top.index+1
27-
heap.Push(pq, top)
2814
}
29-
return ugly[n]
15+
return
16+
}
17+
18+
type hp struct{ sort.IntSlice }
19+
20+
func (h *hp) Push(v interface{}) { h.IntSlice = append(h.IntSlice, v.(int)) }
21+
func (h *hp) Pop() interface{} {
22+
a := h.IntSlice
23+
v := a[len(a)-1]
24+
h.IntSlice = a[:len(a)-1]
25+
return v
3026
}

‎solution/0300-0399/0313.Super Ugly Number/Solution.java

Lines changed: 22 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,22 @@
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class Solution {
2+
public int nthSuperUglyNumber(int n, int[] primes) {
3+
PriorityQueue<Integer> q = new PriorityQueue<>();
4+
q.offer(1);
5+
int x = 0;
6+
while (n-- > 0) {
7+
x = q.poll();
8+
while (!q.isEmpty() && q.peek() == x) {
9+
q.poll();
10+
}
11+
for (int k : primes) {
12+
if (k <= Integer.MAX_VALUE / x) {
13+
q.offer(k * x);
14+
}
15+
if (x % k == 0) {
16+
break;
17+
}
18+
}
19+
}
20+
return x;
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}
22+
}

‎solution/0300-0399/0313.Super Ugly Number/Solution.py

Lines changed: 11 additions & 15 deletions
Original file line numberDiff line numberDiff line change
@@ -1,17 +1,13 @@
1-
from queue import PriorityQueue
2-
3-
41
class Solution:
52
def nthSuperUglyNumber(self, n: int, primes: List[int]) -> int:
6-
ugly, pq, p = [0] * (n + 1), PriorityQueue(), 2
7-
ugly[1] = 1
8-
for prime in primes:
9-
pq.put([prime, prime, 2])
10-
11-
while p <= n:
12-
top = pq.get()
13-
if top[0] != ugly[p - 1]:
14-
ugly[p], p = top[0], p + 1
15-
top[0], top[2] = ugly[top[2]] * top[1], top[2] + 1
16-
pq.put(top)
17-
return ugly[n]
3+
q = [1]
4+
x = 0
5+
mx = (1 << 31) - 1
6+
for _ in range(n):
7+
x = heappop(q)
8+
for k in primes:
9+
if x <= mx // k:
10+
heappush(q, k * x)
11+
if x % k == 0:
12+
break
13+
return x

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