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Merged
merged 1 commit into from
Jul 28, 2023
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feat: add solutions to lc problem: No.0469 #1325

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2 changes: 1 addition & 1 deletion solution/0400-0499/0418.Sentence Screen Fitting/README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -144,7 +144,7 @@ class Solution {
public:
int wordsTyping(vector<string>& sentence, int rows, int cols) {
string s;
for (auto& t: sentence) {
for (auto& t : sentence) {
s += t;
s += " ";
}
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2 changes: 1 addition & 1 deletion solution/0400-0499/0418.Sentence Screen Fitting/README_EN.md
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Original file line number Diff line number Diff line change
Expand Up @@ -106,7 +106,7 @@ class Solution {
public:
int wordsTyping(vector<string>& sentence, int rows, int cols) {
string s;
for (auto& t: sentence) {
for (auto& t : sentence) {
s += t;
s += " ";
}
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95 changes: 94 additions & 1 deletion solution/0400-0499/0469.Convex Polygon/README.md
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Expand Up @@ -47,22 +47,115 @@

<!-- 这里可写通用的实现逻辑 -->

**方法一：数学（向量叉积）**

假设当前连续的三个顶点分别为 $p_1, p_2, p_3$，我们可以计算向量 $\overrightarrow{p_1p_2}$ 和 $\overrightarrow{p_1p_3}$ 的叉积，记为 $cur$。如果 $cur$ 的方向与之前的 $pre$ 方向不一致，说明多边形不是凸多边形。否则，我们更新 $pre = cur$，继续遍历下一个顶点。

遍历结束，如果没有发现不一致的情况，说明多边形是凸多边形。

时间复杂度 $O(n)$，其中 $n$ 是顶点的数量。空间复杂度 $O(1)$。

<!-- tabs:start -->

### **Python3**

<!-- 这里可写当前语言的特殊实现逻辑 -->

```python

class Solution:
def isConvex(self, points: List[List[int]]) -> bool:
n = len(points)
pre = cur = 0
for i in range(n):
x1 = points[(i + 1) % n][0] - points[i][0]
y1 = points[(i + 1) % n][1] - points[i][1]
x2 = points[(i + 2) % n][0] - points[i][0]
y2 = points[(i + 2) % n][1] - points[i][1]
cur = x1 * y2 - x2 * y1
if cur != 0:
if cur * pre < 0:
return False
pre = cur
return True
```

### **Java**

<!-- 这里可写当前语言的特殊实现逻辑 -->

```java
class Solution {
public boolean isConvex(List<List<Integer>> points) {
int n = points.size();
long pre = 0, cur = 0;
for (int i = 0; i < n; ++i) {
var p1 = points.get(i);
var p2 = points.get((i + 1) % n);
var p3 = points.get((i + 2) % n);
int x1 = p2.get(0) - p1.get(0);
int y1 = p2.get(1) - p1.get(1);
int x2 = p3.get(0) - p1.get(0);
int y2 = p3.get(1) - p1.get(1);
cur = x1 * y2 - x2 * y1;
if (cur != 0) {
if (cur * pre < 0) {
return false;
}
pre = cur;
}
}
return true;
}
}
```

### **C++**

```cpp
class Solution {
public:
bool isConvex(vector<vector<int>>& points) {
int n = points.size();
long long pre = 0, cur = 0;
for (int i = 0; i < n; ++i) {
int x1 = points[(i + 1) % n][0] - points[i][0];
int y1 = points[(i + 1) % n][1] - points[i][1];
int x2 = points[(i + 2) % n][0] - points[i][0];
int y2 = points[(i + 2) % n][1] - points[i][1];
cur = 1L * x1 * y2 - x2 * y1;
if (cur != 0) {
if (cur * pre < 0) {
return false;
}
pre = cur;
}
}
return true;
}
};
```

### **Go**

```go
func isConvex(points [][]int) bool {
n := len(points)
pre, cur := 0, 0
for i := range points {
x1 := points[(i+1)%n][0] - points[i][0]
y1 := points[(i+1)%n][1] - points[i][1]
x2 := points[(i+2)%n][0] - points[i][0]
y2 := points[(i+2)%n][1] - points[i][1]
cur = x1*y2 - x2*y1
if cur != 0 {
if cur*pre < 0 {
return false
}
pre = cur
}
}
return true
}
```

### **...**
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87 changes: 86 additions & 1 deletion solution/0400-0499/0469.Convex Polygon/README_EN.md
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Expand Up @@ -42,13 +42,98 @@
### **Python3**

```python

class Solution:
def isConvex(self, points: List[List[int]]) -> bool:
n = len(points)
pre = cur = 0
for i in range(n):
x1 = points[(i + 1) % n][0] - points[i][0]
y1 = points[(i + 1) % n][1] - points[i][1]
x2 = points[(i + 2) % n][0] - points[i][0]
y2 = points[(i + 2) % n][1] - points[i][1]
cur = x1 * y2 - x2 * y1
if cur != 0:
if cur * pre < 0:
return False
pre = cur
return True
```

### **Java**

```java
class Solution {
public boolean isConvex(List<List<Integer>> points) {
int n = points.size();
long pre = 0, cur = 0;
for (int i = 0; i < n; ++i) {
var p1 = points.get(i);
var p2 = points.get((i + 1) % n);
var p3 = points.get((i + 2) % n);
int x1 = p2.get(0) - p1.get(0);
int y1 = p2.get(1) - p1.get(1);
int x2 = p3.get(0) - p1.get(0);
int y2 = p3.get(1) - p1.get(1);
cur = x1 * y2 - x2 * y1;
if (cur != 0) {
if (cur * pre < 0) {
return false;
}
pre = cur;
}
}
return true;
}
}
```

### **C++**

```cpp
class Solution {
public:
bool isConvex(vector<vector<int>>& points) {
int n = points.size();
long long pre = 0, cur = 0;
for (int i = 0; i < n; ++i) {
int x1 = points[(i + 1) % n][0] - points[i][0];
int y1 = points[(i + 1) % n][1] - points[i][1];
int x2 = points[(i + 2) % n][0] - points[i][0];
int y2 = points[(i + 2) % n][1] - points[i][1];
cur = 1L * x1 * y2 - x2 * y1;
if (cur != 0) {
if (cur * pre < 0) {
return false;
}
pre = cur;
}
}
return true;
}
};
```

### **Go**

```go
func isConvex(points [][]int) bool {
n := len(points)
pre, cur := 0, 0
for i := range points {
x1 := points[(i+1)%n][0] - points[i][0]
y1 := points[(i+1)%n][1] - points[i][1]
x2 := points[(i+2)%n][0] - points[i][0]
y2 := points[(i+2)%n][1] - points[i][1]
cur = x1*y2 - x2*y1
if cur != 0 {
if cur*pre < 0 {
return false
}
pre = cur
}
}
return true
}
```

### **...**
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21 changes: 21 additions & 0 deletions solution/0400-0499/0469.Convex Polygon/Solution.cpp
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Original file line number Diff line number Diff line change
@@ -0,0 +1,21 @@
class Solution {
public:
bool isConvex(vector<vector<int>>& points) {
int n = points.size();
long long pre = 0, cur = 0;
for (int i = 0; i < n; ++i) {
int x1 = points[(i + 1) % n][0] - points[i][0];
int y1 = points[(i + 1) % n][1] - points[i][1];
int x2 = points[(i + 2) % n][0] - points[i][0];
int y2 = points[(i + 2) % n][1] - points[i][1];
cur = 1L * x1 * y2 - x2 * y1;
if (cur != 0) {
if (cur * pre < 0) {
return false;
}
pre = cur;
}
}
return true;
}
};
18 changes: 18 additions & 0 deletions solution/0400-0499/0469.Convex Polygon/Solution.go
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Original file line number Diff line number Diff line change
@@ -0,0 +1,18 @@
func isConvex(points [][]int) bool {
n := len(points)
pre, cur := 0, 0
for i := range points {
x1 := points[(i+1)%n][0] - points[i][0]
y1 := points[(i+1)%n][1] - points[i][1]
x2 := points[(i+2)%n][0] - points[i][0]
y2 := points[(i+2)%n][1] - points[i][1]
cur = x1*y2 - x2*y1
if cur != 0 {
if cur*pre < 0 {
return false
}
pre = cur
}
}
return true
}
23 changes: 23 additions & 0 deletions solution/0400-0499/0469.Convex Polygon/Solution.java
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Original file line number Diff line number Diff line change
@@ -0,0 +1,23 @@
class Solution {
public boolean isConvex(List<List<Integer>> points) {
int n = points.size();
long pre = 0, cur = 0;
for (int i = 0; i < n; ++i) {
var p1 = points.get(i);
var p2 = points.get((i + 1) % n);
var p3 = points.get((i + 2) % n);
int x1 = p2.get(0) - p1.get(0);
int y1 = p2.get(1) - p1.get(1);
int x2 = p3.get(0) - p1.get(0);
int y2 = p3.get(1) - p1.get(1);
cur = x1 * y2 - x2 * y1;
if (cur != 0) {
if (cur * pre < 0) {
return false;
}
pre = cur;
}
}
return true;
}
}
15 changes: 15 additions & 0 deletions solution/0400-0499/0469.Convex Polygon/Solution.py
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Original file line number Diff line number Diff line change
@@ -0,0 +1,15 @@
class Solution:
def isConvex(self, points: List[List[int]]) -> bool:
n = len(points)
pre = cur = 0
for i in range(n):
x1 = points[(i + 1) % n][0] - points[i][0]
y1 = points[(i + 1) % n][1] - points[i][1]
x2 = points[(i + 2) % n][0] - points[i][0]
y2 = points[(i + 2) % n][1] - points[i][1]
cur = x1 * y2 - x2 * y1
if cur != 0:
if cur * pre < 0:
return False
pre = cur
return True