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Commit 24e3158

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feat: add solutions to lc problem: No.0786
No.0786 K-th Smallest Prime Fraction
1 parent d2e6a2b commit 24e3158

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6 files changed

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-3
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6 files changed

+283
-3
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‎solution/0700-0799/0786.K-th Smallest Prime Fraction/README.md‎

Lines changed: 98 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -18,7 +18,7 @@
1818
<pre>
1919
<strong>输入:</strong>arr = [1,2,3,5], k = 3
2020
<strong>输出:</strong>[2,5]
21-
<strong>解释:</strong>已构造好的分数,排序后如下所示:
21+
<strong>解释:</strong>已构造好的分数,排序后如下所示:
2222
1/5, 1/3, 2/5, 1/2, 3/5, 2/3
2323
很明显第三个最小的分数是 2/5
2424
</pre>
@@ -55,15 +55,111 @@
5555
<!-- 这里可写当前语言的特殊实现逻辑 -->
5656

5757
```python
58-
58+
class Solution:
59+
def kthSmallestPrimeFraction(self, arr: List[int], k: int) -> List[int]:
60+
h = [(1 / y, 0, j + 1) for j, y in enumerate(arr[1:])]
61+
heapq.heapify(h)
62+
for _ in range(k - 1):
63+
_, i, j = heapq.heappop(h)
64+
if i + 1 < j:
65+
heapq.heappush(h, (arr[i + 1] / arr[j], i + 1, j))
66+
return [arr[h[0][1]], arr[h[0][2]]]
5967
```
6068

6169
### **Java**
6270

6371
<!-- 这里可写当前语言的特殊实现逻辑 -->
6472

6573
```java
74+
class Solution {
75+
public int[] kthSmallestPrimeFraction(int[] arr, int k) {
76+
int n = arr.length;
77+
Queue<Frac> pq = new PriorityQueue<>();
78+
for (int i = 1; i < n; i++) {
79+
pq.offer(new Frac(1, arr[i], 0, i));
80+
}
81+
for (int i = 1; i < k; i++) {
82+
Frac f = pq.poll();
83+
if (f.i + 1 < f.j) {
84+
pq.offer(new Frac(arr[f.i + 1], arr[f.j], f.i + 1, f.j));
85+
}
86+
}
87+
Frac f = pq.peek();
88+
return new int[] { f.x, f.y };
89+
}
90+
91+
static class Frac implements Comparable {
92+
int x, y, i, j;
93+
94+
public Frac(int x, int y, int i, int j) {
95+
this.x = x;
96+
this.y = y;
97+
this.i = i;
98+
this.j = j;
99+
}
100+
101+
@Override
102+
public int compareTo(Object o) {
103+
return x * ((Frac) o).y - ((Frac) o).x * y;
104+
}
105+
}
106+
}
107+
```
108+
109+
### **Go**
110+
111+
```go
112+
type frac struct{ x, y, i, j int }
113+
type hp []frac
114+
115+
func (a hp) Len() int { return len(a) }
116+
func (a hp) Swap(i, j int) { a[i], a[j] = a[j], a[i] }
117+
func (a hp) Less(i, j int) bool { return a[i].x*a[j].y < a[j].x*a[i].y }
118+
func (a *hp) Push(x interface{}) { *a = append(*a, x.(frac)) }
119+
func (a *hp) Pop() interface{} { l := len(*a); tmp := (*a)[l-1]; *a = (*a)[:l-1]; return tmp }
120+
121+
func kthSmallestPrimeFraction(arr []int, k int) []int {
122+
n := len(arr)
123+
h := make(hp, 0, n-1)
124+
for i := 1; i < n; i++ {
125+
h = append(h, frac{1, arr[i], 0, i})
126+
}
127+
heap.Init(&h)
128+
for i := 1; i < k; i++ {
129+
f := heap.Pop(&h).(frac)
130+
if f.i+1 < f.j {
131+
heap.Push(&h, frac{arr[f.i+1], arr[f.j], f.i + 1, f.j})
132+
}
133+
}
134+
return []int{h[0].x, h[0].y}
135+
}
136+
```
66137

138+
### **C++**
139+
140+
```cpp
141+
class Solution {
142+
public:
143+
vector<int> kthSmallestPrimeFraction(vector<int>& arr, int k) {
144+
using pii = pair<int, int>;
145+
int n = arr.size();
146+
auto cmp = [&](const pii &a, const pii &b) {
147+
return arr[a.first] * arr[b.second] > arr[b.first] * arr[a.second];
148+
};
149+
priority_queue<pii, vector<pii>, decltype(cmp)> pq(cmp);
150+
for (int i = 1; i < n; ++i) {
151+
pq.push({0, i});
152+
}
153+
for (int i = 1; i < k; ++i) {
154+
pii f = pq.top();
155+
pq.pop();
156+
if (f.first + 1 < f.second) {
157+
pq.push({f.first + 1, f.second});
158+
}
159+
}
160+
return {arr[pq.top().first], arr[pq.top().second]};
161+
}
162+
};
67163
```
68164
69165
### **...**

‎solution/0700-0799/0786.K-th Smallest Prime Fraction/README_EN.md‎

Lines changed: 97 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -48,13 +48,109 @@ The third fraction is 2/5.
4848
### **Python3**
4949

5050
```python
51-
51+
class Solution:
52+
def kthSmallestPrimeFraction(self, arr: List[int], k: int) -> List[int]:
53+
h = [(1 / y, 0, j + 1) for j, y in enumerate(arr[1:])]
54+
heapq.heapify(h)
55+
for _ in range(k - 1):
56+
_, i, j = heapq.heappop(h)
57+
if i + 1 < j:
58+
heapq.heappush(h, (arr[i + 1] / arr[j], i + 1, j))
59+
return [arr[h[0][1]], arr[h[0][2]]]
5260
```
5361

5462
### **Java**
5563

5664
```java
65+
class Solution {
66+
public int[] kthSmallestPrimeFraction(int[] arr, int k) {
67+
int n = arr.length;
68+
Queue<Frac> pq = new PriorityQueue<>();
69+
for (int i = 1; i < n; i++) {
70+
pq.offer(new Frac(1, arr[i], 0, i));
71+
}
72+
for (int i = 1; i < k; i++) {
73+
Frac f = pq.poll();
74+
if (f.i + 1 < f.j) {
75+
pq.offer(new Frac(arr[f.i + 1], arr[f.j], f.i + 1, f.j));
76+
}
77+
}
78+
Frac f = pq.peek();
79+
return new int[] { f.x, f.y };
80+
}
81+
82+
static class Frac implements Comparable {
83+
int x, y, i, j;
84+
85+
public Frac(int x, int y, int i, int j) {
86+
this.x = x;
87+
this.y = y;
88+
this.i = i;
89+
this.j = j;
90+
}
91+
92+
@Override
93+
public int compareTo(Object o) {
94+
return x * ((Frac) o).y - ((Frac) o).x * y;
95+
}
96+
}
97+
}
98+
```
99+
100+
### **Go**
101+
102+
```go
103+
type frac struct{ x, y, i, j int }
104+
type hp []frac
105+
106+
func (a hp) Len() int { return len(a) }
107+
func (a hp) Swap(i, j int) { a[i], a[j] = a[j], a[i] }
108+
func (a hp) Less(i, j int) bool { return a[i].x*a[j].y < a[j].x*a[i].y }
109+
func (a *hp) Push(x interface{}) { *a = append(*a, x.(frac)) }
110+
func (a *hp) Pop() interface{} { l := len(*a); tmp := (*a)[l-1]; *a = (*a)[:l-1]; return tmp }
111+
112+
func kthSmallestPrimeFraction(arr []int, k int) []int {
113+
n := len(arr)
114+
h := make(hp, 0, n-1)
115+
for i := 1; i < n; i++ {
116+
h = append(h, frac{1, arr[i], 0, i})
117+
}
118+
heap.Init(&h)
119+
for i := 1; i < k; i++ {
120+
f := heap.Pop(&h).(frac)
121+
if f.i+1 < f.j {
122+
heap.Push(&h, frac{arr[f.i+1], arr[f.j], f.i + 1, f.j})
123+
}
124+
}
125+
return []int{h[0].x, h[0].y}
126+
}
127+
```
57128

129+
### **C++**
130+
131+
```cpp
132+
class Solution {
133+
public:
134+
vector<int> kthSmallestPrimeFraction(vector<int>& arr, int k) {
135+
using pii = pair<int, int>;
136+
int n = arr.size();
137+
auto cmp = [&](const pii &a, const pii &b) {
138+
return arr[a.first] * arr[b.second] > arr[b.first] * arr[a.second];
139+
};
140+
priority_queue<pii, vector<pii>, decltype(cmp)> pq(cmp);
141+
for (int i = 1; i < n; ++i) {
142+
pq.push({0, i});
143+
}
144+
for (int i = 1; i < k; ++i) {
145+
pii f = pq.top();
146+
pq.pop();
147+
if (f.first + 1 < f.second) {
148+
pq.push({f.first + 1, f.second});
149+
}
150+
}
151+
return {arr[pq.top().first], arr[pq.top().second]};
152+
}
153+
};
58154
```
59155
60156
### **...**
Lines changed: 22 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,22 @@
1+
class Solution {
2+
public:
3+
vector<int> kthSmallestPrimeFraction(vector<int>& arr, int k) {
4+
using pii = pair<int, int>;
5+
int n = arr.size();
6+
auto cmp = [&](const pii &a, const pii &b) {
7+
return arr[a.first] * arr[b.second] > arr[b.first] * arr[a.second];
8+
};
9+
priority_queue<pii, vector<pii>, decltype(cmp)> pq(cmp);
10+
for (int i = 1; i < n; ++i) {
11+
pq.push({0, i});
12+
}
13+
for (int i = 1; i < k; ++i) {
14+
pii f = pq.top();
15+
pq.pop();
16+
if (f.first + 1 < f.second) {
17+
pq.push({f.first + 1, f.second});
18+
}
19+
}
20+
return {arr[pq.top().first], arr[pq.top().second]};
21+
}
22+
};
Lines changed: 24 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,24 @@
1+
type frac struct{ x, y, i, j int }
2+
type hp []frac
3+
4+
func (a hp) Len() int { return len(a) }
5+
func (a hp) Swap(i, j int) { a[i], a[j] = a[j], a[i] }
6+
func (a hp) Less(i, j int) bool { return a[i].x*a[j].y < a[j].x*a[i].y }
7+
func (a *hp) Push(x interface{}) { *a = append(*a, x.(frac)) }
8+
func (a *hp) Pop() interface{} { l := len(*a); tmp := (*a)[l-1]; *a = (*a)[:l-1]; return tmp }
9+
10+
func kthSmallestPrimeFraction(arr []int, k int) []int {
11+
n := len(arr)
12+
h := make(hp, 0, n-1)
13+
for i := 1; i < n; i++ {
14+
h = append(h, frac{1, arr[i], 0, i})
15+
}
16+
heap.Init(&h)
17+
for i := 1; i < k; i++ {
18+
f := heap.Pop(&h).(frac)
19+
if f.i+1 < f.j {
20+
heap.Push(&h, frac{arr[f.i+1], arr[f.j], f.i + 1, f.j})
21+
}
22+
}
23+
return []int{h[0].x, h[0].y}
24+
}
Lines changed: 33 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,33 @@
1+
class Solution {
2+
public int[] kthSmallestPrimeFraction(int[] arr, int k) {
3+
int n = arr.length;
4+
Queue<Frac> pq = new PriorityQueue<>();
5+
for (int i = 1; i < n; i++) {
6+
pq.offer(new Frac(1, arr[i], 0, i));
7+
}
8+
for (int i = 1; i < k; i++) {
9+
Frac f = pq.poll();
10+
if (f.i + 1 < f.j) {
11+
pq.offer(new Frac(arr[f.i + 1], arr[f.j], f.i + 1, f.j));
12+
}
13+
}
14+
Frac f = pq.peek();
15+
return new int[] { f.x, f.y };
16+
}
17+
18+
static class Frac implements Comparable {
19+
int x, y, i, j;
20+
21+
public Frac(int x, int y, int i, int j) {
22+
this.x = x;
23+
this.y = y;
24+
this.i = i;
25+
this.j = j;
26+
}
27+
28+
@Override
29+
public int compareTo(Object o) {
30+
return x * ((Frac) o).y - ((Frac) o).x * y;
31+
}
32+
}
33+
}
Lines changed: 9 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,9 @@
1+
class Solution:
2+
def kthSmallestPrimeFraction(self, arr: List[int], k: int) -> List[int]:
3+
h = [(1 / y, 0, j + 1) for j, y in enumerate(arr[1:])]
4+
heapq.heapify(h)
5+
for _ in range(k - 1):
6+
_, i, j = heapq.heappop(h)
7+
if i + 1 < j:
8+
heapq.heappush(h, (arr[i + 1] / arr[j], i + 1, j))
9+
return [arr[h[0][1]], arr[h[0][2]]]

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