Update README_EN.md

Author: yanglbme

solution/1400-1499/1453.Maximum Number of Darts Inside of a Circular Dartboard/README_EN.md

@@ -60,20 +60,99 @@ tags:
 
 <!-- solution:start -->
 
-### Solution 1
+### 方法一
 
 <!-- tabs:start -->
 
 #### Python3
 
 ```python
-
+class Solution:
+    def numPoints(self, darts: list[list[int]], r: int) -> int:
+        def countDarts(x, y):
+            count = 0
+            for x1, y1 in darts:
+                if dist((x, y), (x1, y1)) <= r + 1e-7:
+                    count += 1
+            return count
+
+        def possibleCenters(x1, y1, x2, y2):
+            dx, dy = x2 - x1, y2 - y1
+            d = sqrt(dx * dx + dy * dy)
+            if d > 2 * r:
+                return []
+            mid_x, mid_y = (x1 + x2) / 2, (y1 + y2) / 2
+            dist_to_center = sqrt(r * r - (d / 2) * (d / 2))
+            offset_x = dist_to_center * dy / d
+            offset_y = dist_to_center * -dx / d
+            return [
+                (mid_x + offset_x, mid_y + offset_y),
+                (mid_x - offset_x, mid_y - offset_y),
+            ]
+
+        n = len(darts)
+        max_darts = 1
+
+        for i in range(n):
+            for j in range(i + 1, n):
+                centers = possibleCenters(
+                    darts[i][0], darts[i][1], darts[j][0], darts[j][1]
+                )
+                for center in centers:
+                    max_darts = max(max_darts, countDarts(center[0], center[1]))
+
+        return max_darts
 ```
 
 #### Java
 
 ```java
-
+class Solution {
+    public int numPoints(int[][] darts, int r) {
+        int n = darts.length;
+        int maxDarts = 1;
+
+        for (int i = 0; i < n; i++) {
+            for (int j = i + 1; j < n; j++) {
+                List<double[]> centers
+                    = possibleCenters(darts[i][0], darts[i][1], darts[j][0], darts[j][1], r);
+                for (double[] center : centers) {
+                    maxDarts = Math.max(maxDarts, countDarts(center[0], center[1], darts, r));
+                }
+            }
+        }
+        return maxDarts;
+    }
+
+    private List<double[]> possibleCenters(int x1, int y1, int x2, int y2, int r) {
+        List<double[]> centers = new ArrayList<>();
+        double dx = x2 - x1;
+        double dy = y2 - y1;
+        double d = Math.sqrt(dx * dx + dy * dy);
+        if (d > 2 * r) {
+            return centers;
+        }
+        double midX = (x1 + x2) / 2.0;
+        double midY = (y1 + y2) / 2.0;
+        double distToCenter = Math.sqrt(r * r - (d / 2.0) * (d / 2.0));
+        double offsetX = distToCenter * dy / d;
+        double offsetY = distToCenter * -dx / d;
+
+        centers.add(new double[] {midX + offsetX, midY + offsetY});
+        centers.add(new double[] {midX - offsetX, midY - offsetY});
+        return centers;
+    }
+
+    private int countDarts(double x, double y, int[][] darts, int r) {
+        int count = 0;
+        for (int[] dart : darts) {
+            if (Math.sqrt(Math.pow(dart[0] - x, 2) + Math.pow(dart[1] - y, 2)) <= r + 1e-7) {
+                count++;
+            }
+        }
+        return count;
+    }
+}
 ```
 
 #### C++