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feat: add solutions to lc problem: No.0469 (doocs#1325)
No.0469.Convex Polygon
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‎solution/0400-0499/0418.Sentence Screen Fitting/README.md‎

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@@ -144,7 +144,7 @@ class Solution {
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public:
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int wordsTyping(vector<string>& sentence, int rows, int cols) {
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string s;
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for (auto& t: sentence) {
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for (auto& t : sentence) {
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s += t;
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s += " ";
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}

‎solution/0400-0499/0418.Sentence Screen Fitting/README_EN.md‎

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@@ -106,7 +106,7 @@ class Solution {
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public:
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int wordsTyping(vector<string>& sentence, int rows, int cols) {
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string s;
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for (auto& t: sentence) {
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for (auto& t : sentence) {
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s += t;
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s += " ";
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}

‎solution/0400-0499/0469.Convex Polygon/README.md‎

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<!-- 这里可写通用的实现逻辑 -->
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**方法一：数学（向量叉积）**
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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。
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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。
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时间复杂度 $O(n)$，其中 $n$ 是顶点的数量。空间复杂度 $O(1)$。
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<!-- tabs:start -->
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### **Python3**
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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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class Solution:
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def isConvex(self, points: List[List[int]]) -> bool:
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n = len(points)
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pre = cur = 0
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for i in range(n):
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x1 = points[(i + 1) % n][0] - points[i][0]
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y1 = points[(i + 1) % n][1] - points[i][1]
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x2 = points[(i + 2) % n][0] - points[i][0]
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y2 = points[(i + 2) % n][1] - points[i][1]
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cur = x1 * y2 - x2 * y1
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if cur != 0:
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if cur * pre < 0:
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return False
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pre = cur
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return True
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```
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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 boolean isConvex(List<List<Integer>> points) {
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int n = points.size();
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long pre = 0, cur = 0;
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for (int i = 0; i < n; ++i) {
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var p1 = points.get(i);
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var p2 = points.get((i + 1) % n);
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var p3 = points.get((i + 2) % n);
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int x1 = p2.get(0) - p1.get(0);
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int y1 = p2.get(1) - p1.get(1);
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int x2 = p3.get(0) - p1.get(0);
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int y2 = p3.get(1) - p1.get(1);
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cur = x1 * y2 - x2 * y1;
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if (cur != 0) {
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if (cur * pre < 0) {
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return false;
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}
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pre = cur;
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}
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}
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return true;
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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:
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bool isConvex(vector<vector<int>>& points) {
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int n = points.size();
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long long pre = 0, cur = 0;
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for (int i = 0; i < n; ++i) {
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int x1 = points[(i + 1) % n][0] - points[i][0];
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int y1 = points[(i + 1) % n][1] - points[i][1];
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int x2 = points[(i + 2) % n][0] - points[i][0];
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int y2 = points[(i + 2) % n][1] - points[i][1];
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cur = 1L * x1 * y2 - x2 * y1;
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if (cur != 0) {
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if (cur * pre < 0) {
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return false;
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}
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pre = cur;
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}
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}
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return true;
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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 isConvex(points [][]int) bool {
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n := len(points)
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pre, cur := 0, 0
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for i := range points {
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x1 := points[(i+1)%n][0] - points[i][0]
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y1 := points[(i+1)%n][1] - points[i][1]
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x2 := points[(i+2)%n][0] - points[i][0]
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y2 := points[(i+2)%n][1] - points[i][1]
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cur = x1*y2 - x2*y1
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if cur != 0 {
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if cur*pre < 0 {
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return false
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}
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pre = cur
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}
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}
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return true
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}
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```
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### **...**

‎solution/0400-0499/0469.Convex Polygon/README_EN.md‎

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### **Python3**
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```python
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class Solution:
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def isConvex(self, points: List[List[int]]) -> bool:
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n = len(points)
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pre = cur = 0
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for i in range(n):
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x1 = points[(i + 1) % n][0] - points[i][0]
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y1 = points[(i + 1) % n][1] - points[i][1]
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x2 = points[(i + 2) % n][0] - points[i][0]
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y2 = points[(i + 2) % n][1] - points[i][1]
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cur = x1 * y2 - x2 * y1
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if cur != 0:
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if cur * pre < 0:
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return False
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pre = cur
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return True
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```
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### **Java**
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```java
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class Solution {
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public boolean isConvex(List<List<Integer>> points) {
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int n = points.size();
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long pre = 0, cur = 0;
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for (int i = 0; i < n; ++i) {
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var p1 = points.get(i);
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var p2 = points.get((i + 1) % n);
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var p3 = points.get((i + 2) % n);
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int x1 = p2.get(0) - p1.get(0);
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int y1 = p2.get(1) - p1.get(1);
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int x2 = p3.get(0) - p1.get(0);
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int y2 = p3.get(1) - p1.get(1);
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cur = x1 * y2 - x2 * y1;
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if (cur != 0) {
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if (cur * pre < 0) {
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return false;
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}
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pre = cur;
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}
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}
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return true;
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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:
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bool isConvex(vector<vector<int>>& points) {
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int n = points.size();
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long long pre = 0, cur = 0;
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for (int i = 0; i < n; ++i) {
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int x1 = points[(i + 1) % n][0] - points[i][0];
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int y1 = points[(i + 1) % n][1] - points[i][1];
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int x2 = points[(i + 2) % n][0] - points[i][0];
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int y2 = points[(i + 2) % n][1] - points[i][1];
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cur = 1L * x1 * y2 - x2 * y1;
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if (cur != 0) {
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if (cur * pre < 0) {
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return false;
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}
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pre = cur;
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}
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}
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return true;
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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 isConvex(points [][]int) bool {
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n := len(points)
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pre, cur := 0, 0
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for i := range points {
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x1 := points[(i+1)%n][0] - points[i][0]
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y1 := points[(i+1)%n][1] - points[i][1]
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x2 := points[(i+2)%n][0] - points[i][0]
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y2 := points[(i+2)%n][1] - points[i][1]
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cur = x1*y2 - x2*y1
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if cur != 0 {
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if cur*pre < 0 {
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return false
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}
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pre = cur
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}
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}
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return true
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}
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```
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### **...**

‎solution/0400-0499/0469.Convex Polygon/Solution.cpp‎

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

‎solution/0400-0499/0469.Convex Polygon/Solution.go‎

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

‎solution/0400-0499/0469.Convex Polygon/Solution.java‎

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

‎solution/0400-0499/0469.Convex Polygon/Solution.py‎

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

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