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Commit bd03a95

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feat: add solutions to lc problem: No.0812 (doocs#4750)
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‎solution/0800-0899/0812.Largest Triangle Area/README.md‎

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<!-- solution:start -->
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### 方法一
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### 方法一:枚举三点面积公式
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给定平面上三点 $(x_1, y_1),ドル $(x_2, y_2),ドル $(x_3, y_3),ドル其面积公式为:
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$$S = \frac{1}{2} \left| x_1y_2 + x_2y_3 + x_3y_1 - x_1y_3 - x_2y_1 - x_3y_2 \right|$$
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我们可以枚举所有的三点组合,计算面积的最大值。
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时间复杂度 $O(n^3),ドル其中 $n$ 是点的数量。空间复杂度 $O(1)$。
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<!-- tabs:start -->
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}
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```
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#### TypeScript
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```ts
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function largestTriangleArea(points: number[][]): number {
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let ans = 0;
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for (const [x1, y1] of points) {
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for (const [x2, y2] of points) {
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for (const [x3, y3] of points) {
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const u1 = x2 - x1,
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v1 = y2 - y1;
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const u2 = x3 - x1,
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v2 = y3 - y1;
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const t = Math.abs(u1 * v2 - u2 * v1) / 2;
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ans = Math.max(ans, t);
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}
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}
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}
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return ans;
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}
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```
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#### Rust
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```rust
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impl Solution {
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pub fn largest_triangle_area(points: Vec<Vec<i32>>) -> f64 {
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let mut ans: f64 = 0.0;
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for point1 in &points {
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let (x1, y1) = (point1[0], point1[1]);
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for point2 in &points {
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let (x2, y2) = (point2[0], point2[1]);
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for point3 in &points {
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let (x3, y3) = (point3[0], point3[1]);
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let u1 = x2 - x1;
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let v1 = y2 - y1;
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let u2 = x3 - x1;
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let v2 = y3 - y1;
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let t = ((u1 * v2 - u2 * v1) as f64).abs() / 2.0;
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ans = ans.max(t);
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}
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}
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}
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ans
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}
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}
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```
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<!-- tabs:end -->
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<!-- solution:end -->

‎solution/0800-0899/0812.Largest Triangle Area/README_EN.md‎

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<!-- solution:start -->
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### Solution 1
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### Solution: Enumerate Triangle Area Formula
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Given three points $(x_1, y_1),ドル $(x_2, y_2),ドル $(x_3, y_3)$ on a plane, the area formula is:
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$$S = \frac{1}{2} \left| x_1y_2 + x_2y_3 + x_3y_1 - x_1y_3 - x_2y_1 - x_3y_2 \right|$$
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We can enumerate all combinations of three points and calculate the maximum area.
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The time complexity is $O(n^3),ドル where $n$ is the number of points. The space complexity is $O(1)$.
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<!-- tabs:start -->
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```
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#### TypeScript
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```ts
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function largestTriangleArea(points: number[][]): number {
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let ans = 0;
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for (const [x1, y1] of points) {
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for (const [x2, y2] of points) {
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for (const [x3, y3] of points) {
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const u1 = x2 - x1,
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v1 = y2 - y1;
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const u2 = x3 - x1,
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v2 = y3 - y1;
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const t = Math.abs(u1 * v2 - u2 * v1) / 2;
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ans = Math.max(ans, t);
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}
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}
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}
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return ans;
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}
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```
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#### Rust
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```rust
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impl Solution {
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pub fn largest_triangle_area(points: Vec<Vec<i32>>) -> f64 {
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let mut ans: f64 = 0.0;
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for point1 in &points {
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let (x1, y1) = (point1[0], point1[1]);
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for point2 in &points {
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let (x2, y2) = (point2[0], point2[1]);
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for point3 in &points {
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let (x3, y3) = (point3[0], point3[1]);
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let u1 = x2 - x1;
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let v1 = y2 - y1;
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let u2 = x3 - x1;
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let v2 = y3 - y1;
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let t = ((u1 * v2 - u2 * v1) as f64).abs() / 2.0;
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ans = ans.max(t);
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}
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}
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}
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ans
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}
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}
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```
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<!-- tabs:end -->
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<!-- solution:end -->
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impl Solution {
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pub fn largest_triangle_area(points: Vec<Vec<i32>>) -> f64 {
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let mut ans: f64 = 0.0;
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for point1 in &points {
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let (x1, y1) = (point1[0], point1[1]);
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for point2 in &points {
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let (x2, y2) = (point2[0], point2[1]);
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for point3 in &points {
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let (x3, y3) = (point3[0], point3[1]);
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let u1 = x2 - x1;
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let v1 = y2 - y1;
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let u2 = x3 - x1;
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let v2 = y3 - y1;
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let t = ((u1 * v2 - u2 * v1) as f64).abs() / 2.0;
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ans = ans.max(t);
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}
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}
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}
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ans
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}
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}
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function largestTriangleArea(points: number[][]): number {
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let ans = 0;
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for (const [x1, y1] of points) {
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for (const [x2, y2] of points) {
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for (const [x3, y3] of points) {
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const u1 = x2 - x1,
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v1 = y2 - y1;
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const u2 = x3 - x1,
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v2 = y3 - y1;
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const t = Math.abs(u1 * v2 - u2 * v1) / 2;
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ans = Math.max(ans, t);
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}
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}
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}
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return ans;
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}

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