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feat: add solutions to lc problems: No.1515,1654 (doocs#1543)
* No.1515.Best Position for a Service Centre * No.1654.Minimum Jumps to Reach Home
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+697
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Diff for: ‎solution/1500-1599/1515.Best Position for a Service Centre/README.md

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Original file line numberDiff line numberDiff line change
@@ -52,22 +52,200 @@
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<!-- 这里可写通用的实现逻辑 -->
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**方法一：梯度下降法**
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我们可以先设定一个初始的服务中心位置为所有客户坐标的几何中心 $(x, y)$。接下来，使用梯度下降法不断迭代，设定一个学习率 $\alpha=0.5$，衰减率 $decay=0.999$。每次一次迭代，计算当前位置到所有客户的距离之和，然后计算当前位置的梯度，最后更新当前位置。当梯度的绝对值都小于 $10^{-6}$ 时，停止迭代，返回当前位置到所有客户的距离之和。
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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 getMinDistSum(self, positions: List[List[int]]) -> float:
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n = len(positions)
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x = y = 0
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for x1, y1 in positions:
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x += x1
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y += y1
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x, y = x / n, y / n
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decay = 0.999
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eps = 1e-6
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alpha = 0.5
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while 1:
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grad_x = grad_y = 0
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dist = 0
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for x1, y1 in positions:
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a = x - x1
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b = y - y1
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c = sqrt(a * a + b * b)
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grad_x += a / (c + 1e-8)
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grad_y += b / (c + 1e-8)
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dist += c
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dx = grad_x * alpha
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dy = grad_y * alpha
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x -= dx
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y -= dy
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alpha *= decay
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if abs(dx) <= eps and abs(dy) <= eps:
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return dist
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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 double getMinDistSum(int[][] positions) {
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int n = positions.length;
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double x = 0, y = 0;
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for (int[] p : positions) {
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x += p[0];
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y += p[1];
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}
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x /= n;
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y /= n;
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double decay = 0.999;
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double eps = 1e-6;
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double alpha = 0.5;
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while (true) {
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double gradX = 0, gradY = 0;
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double dist = 0;
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for (int[] p : positions) {
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double a = x - p[0], b = y - p[1];
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double c = Math.sqrt(a * a + b * b);
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gradX += a / (c + 1e-8);
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gradY += b / (c + 1e-8);
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dist += c;
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}
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double dx = gradX * alpha, dy = gradY * alpha;
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if (Math.abs(dx) <= eps && Math.abs(dy) <= eps) {
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return dist;
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}
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x -= dx;
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y -= dy;
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alpha *= decay;
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}
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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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double getMinDistSum(vector<vector<int>>& positions) {
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int n = positions.size();
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double x = 0, y = 0;
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for (auto& p : positions) {
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x += p[0];
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y += p[1];
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}
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x /= n;
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y /= n;
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double decay = 0.999;
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double eps = 1e-6;
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double alpha = 0.5;
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while (true) {
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double gradX = 0, gradY = 0;
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double dist = 0;
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for (auto& p : positions) {
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double a = x - p[0], b = y - p[1];
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double c = sqrt(a * a + b * b);
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gradX += a / (c + 1e-8);
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gradY += b / (c + 1e-8);
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dist += c;
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}
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double dx = gradX * alpha, dy = gradY * alpha;
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if (abs(dx) <= eps && abs(dy) <= eps) {
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return dist;
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}
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x -= dx;
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y -= dy;
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alpha *= decay;
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}
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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 getMinDistSum(positions [][]int) float64 {
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n := len(positions)
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var x, y float64
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for _, p := range positions {
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x += float64(p[0])
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y += float64(p[1])
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}
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x /= float64(n)
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y /= float64(n)
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const decay float64 = 0.999
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const eps float64 = 1e-6
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var alpha float64 = 0.5
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for {
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var gradX, gradY float64
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var dist float64
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for _, p := range positions {
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a := x - float64(p[0])
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b := y - float64(p[1])
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c := math.Sqrt(a*a + b*b)
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gradX += a / (c + 1e-8)
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gradY += b / (c + 1e-8)
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dist += c
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}
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dx := gradX * alpha
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dy := gradY * alpha
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if math.Abs(dx) <= eps && math.Abs(dy) <= eps {
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return dist
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}
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x -= dx
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y -= dy
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alpha *= decay
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}
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}
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```
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### **TypeScript**
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```ts
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function getMinDistSum(positions: number[][]): number {
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const n = positions.length;
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let [x, y] = [0, 0];
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for (const [px, py] of positions) {
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x += px;
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y += py;
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}
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x /= n;
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y /= n;
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const decay = 0.999;
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const eps = 1e-6;
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let alpha = 0.5;
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while (true) {
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let [gradX, gradY] = [0, 0];
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let dist = 0;
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for (const [px, py] of positions) {
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const a = x - px;
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const b = y - py;
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const c = Math.sqrt(a * a + b * b);
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gradX += a / (c + 1e-8);
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gradY += b / (c + 1e-8);
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dist += c;
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}
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const dx = gradX * alpha;
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const dy = gradY * alpha;
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if (Math.abs(dx) <= eps && Math.abs(dy) <= eps) {
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return dist;
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}
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x -= dx;
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y -= dy;
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alpha *= decay;
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}
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}
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```
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### **...**

Diff for: ‎solution/1500-1599/1515.Best Position for a Service Centre/README_EN.md

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@@ -45,13 +45,187 @@
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### **Python3**
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```python
48-
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class Solution:
49+
def getMinDistSum(self, positions: List[List[int]]) -> float:
50+
n = len(positions)
51+
x = y = 0
52+
for x1, y1 in positions:
53+
x += x1
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y += y1
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x, y = x / n, y / n
56+
decay = 0.999
57+
eps = 1e-6
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alpha = 0.5
59+
while 1:
60+
grad_x = grad_y = 0
61+
dist = 0
62+
for x1, y1 in positions:
63+
a = x - x1
64+
b = y - y1
65+
c = sqrt(a * a + b * b)
66+
grad_x += a / (c + 1e-8)
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grad_y += b / (c + 1e-8)
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dist += c
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dx = grad_x * alpha
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dy = grad_y * alpha
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x -= dx
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y -= dy
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alpha *= decay
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if abs(dx) <= eps and abs(dy) <= eps:
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return dist
4976
```
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### **Java**
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```java
81+
class Solution {
82+
public double getMinDistSum(int[][] positions) {
83+
int n = positions.length;
84+
double x = 0, y = 0;
85+
for (int[] p : positions) {
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x += p[0];
87+
y += p[1];
88+
}
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x /= n;
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y /= n;
91+
double decay = 0.999;
92+
double eps = 1e-6;
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double alpha = 0.5;
94+
while (true) {
95+
double gradX = 0, gradY = 0;
96+
double dist = 0;
97+
for (int[] p : positions) {
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double a = x - p[0], b = y - p[1];
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double c = Math.sqrt(a * a + b * b);
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gradX += a / (c + 1e-8);
101+
gradY += b / (c + 1e-8);
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dist += c;
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}
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double dx = gradX * alpha, dy = gradY * alpha;
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if (Math.abs(dx) <= eps && Math.abs(dy) <= eps) {
106+
return dist;
107+
}
108+
x -= dx;
109+
y -= dy;
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alpha *= decay;
111+
}
112+
}
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}
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```
115+
116+
### **C++**
117+
118+
```cpp
119+
class Solution {
120+
public:
121+
double getMinDistSum(vector<vector<int>>& positions) {
122+
int n = positions.size();
123+
double x = 0, y = 0;
124+
for (auto& p : positions) {
125+
x += p[0];
126+
y += p[1];
127+
}
128+
x /= n;
129+
y /= n;
130+
double decay = 0.999;
131+
double eps = 1e-6;
132+
double alpha = 0.5;
133+
while (true) {
134+
double gradX = 0, gradY = 0;
135+
double dist = 0;
136+
for (auto& p : positions) {
137+
double a = x - p[0], b = y - p[1];
138+
double c = sqrt(a * a + b * b);
139+
gradX += a / (c + 1e-8);
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gradY += b / (c + 1e-8);
141+
dist += c;
142+
}
143+
double dx = gradX * alpha, dy = gradY * alpha;
144+
if (abs(dx) <= eps && abs(dy) <= eps) {
145+
return dist;
146+
}
147+
x -= dx;
148+
y -= dy;
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alpha *= decay;
150+
}
151+
}
152+
};
153+
```
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155+
### **Go**
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```go
158+
func getMinDistSum(positions [][]int) float64 {
159+
n := len(positions)
160+
var x, y float64
161+
for _, p := range positions {
162+
x += float64(p[0])
163+
y += float64(p[1])
164+
}
165+
x /= float64(n)
166+
y /= float64(n)
167+
const decay float64 = 0.999
168+
const eps float64 = 1e-6
169+
var alpha float64 = 0.5
170+
for {
171+
var gradX, gradY float64
172+
var dist float64
173+
for _, p := range positions {
174+
a := x - float64(p[0])
175+
b := y - float64(p[1])
176+
c := math.Sqrt(a*a + b*b)
177+
gradX += a / (c + 1e-8)
178+
gradY += b / (c + 1e-8)
179+
dist += c
180+
}
181+
dx := gradX * alpha
182+
dy := gradY * alpha
183+
if math.Abs(dx) <= eps && math.Abs(dy) <= eps {
184+
return dist
185+
}
186+
x -= dx
187+
y -= dy
188+
alpha *= decay
189+
}
190+
}
191+
```
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### **TypeScript**
194+
195+
```ts
196+
function getMinDistSum(positions: number[][]): number {
197+
const n = positions.length;
198+
let [x, y] = [0, 0];
199+
for (const [px, py] of positions) {
200+
x += px;
201+
y += py;
202+
}
203+
x /= n;
204+
y /= n;
205+
const decay = 0.999;
206+
const eps = 1e-6;
207+
let alpha = 0.5;
208+
while (true) {
209+
let [gradX, gradY] = [0, 0];
210+
let dist = 0;
211+
for (const [px, py] of positions) {
212+
const a = x - px;
213+
const b = y - py;
214+
const c = Math.sqrt(a * a + b * b);
215+
gradX += a / (c + 1e-8);
216+
gradY += b / (c + 1e-8);
217+
dist += c;
218+
}
219+
const dx = gradX * alpha;
220+
const dy = gradY * alpha;
221+
if (Math.abs(dx) <= eps && Math.abs(dy) <= eps) {
222+
return dist;
223+
}
224+
x -= dx;
225+
y -= dy;
226+
alpha *= decay;
227+
}
228+
}
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```
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### **...**

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