Add solution #1515

Author: JoshCrozier

README.md

@@ -1,4 +1,4 @@
-# 1,341 LeetCode solutions in JavaScript
+# 1,342 LeetCode solutions in JavaScript
 
 [https://leetcodejavascript.com](https://leetcodejavascript.com)
 
@@ -1158,6 +1158,7 @@
 1512|[Number of Good Pairs](./solutions/1512-number-of-good-pairs.js)|Easy|
 1513|[Number of Substrings With Only 1s](./solutions/1513-number-of-substrings-with-only-1s.js)|Medium|
 1514|[Path with Maximum Probability](./solutions/1514-path-with-maximum-probability.js)|Medium|
+1515|[Best Position for a Service Centre](./solutions/1515-best-position-for-a-service-centre.js)|Hard|
 1519|[Number of Nodes in the Sub-Tree With the Same Label](./solutions/1519-number-of-nodes-in-the-sub-tree-with-the-same-label.js)|Medium|
 1524|[Number of Sub-arrays With Odd Sum](./solutions/1524-number-of-sub-arrays-with-odd-sum.js)|Medium|
 1528|[Shuffle String](./solutions/1528-shuffle-string.js)|Easy|

solutions/1515-best-position-for-a-service-centre.js

@@ -0,0 +1,72 @@
+/**
+ * 1515. Best Position for a Service Centre
+ * https://leetcode.com/problems/best-position-for-a-service-centre/
+ * Difficulty: Hard
+ *
+ * A delivery company wants to build a new service center in a new city. The company knows the
+ * positions of all the customers in this city on a 2D-Map and wants to build the new center in
+ * a position such that the sum of the euclidean distances to all customers is minimum.
+ *
+ * Given an array positions where positions[i] = [xi, yi] is the position of the ith customer on
+ * the map, return the minimum sum of the euclidean distances to all customers.
+ *
+ * In other words, you need to choose the position of the service center [xcentre, ycentre] such
+ * that the following formula is minimized:
+ * - Answers within 10-5 of the actual value will be accepted.
+ */
+
+/**
+ * @param {number[][]} positions
+ * @return {number}
+ */
+var getMinDistSum = function(positions) {
+  const n = positions.length;
+  let xSum = 0;
+  let ySum = 0;
+
+  for (const [x, y] of positions) {
+    xSum += x;
+    ySum += y;
+  }
+
+  let xCenter = xSum / n;
+  let yCenter = ySum / n;
+  const epsilon = 1e-7;
+  const maxIterations = 1000;
+
+  for (let iter = 0; iter < maxIterations; iter++) {
+    let xNumerator = 0;
+    let yNumerator = 0;
+    let denominator = 0;
+
+    for (const [x, y] of positions) {
+      const dx = xCenter - x;
+      const dy = yCenter - y;
+      const dist = Math.sqrt(dx * dx + dy * dy);
+      if (dist < epsilon) continue;
+      const weight = 1 / dist;
+      xNumerator += x * weight;
+      yNumerator += y * weight;
+      denominator += weight;
+    }
+
+    if (denominator < epsilon) break;
+
+    const newX = xNumerator / denominator;
+    const newY = yNumerator / denominator;
+
+    if (Math.abs(newX - xCenter) < epsilon && Math.abs(newY - yCenter) < epsilon) {
+      break;
+    }
+
+    xCenter = newX;
+    yCenter = newY;
+  }
+
+  let sumDist = 0;
+  for (const [x, y] of positions) {
+    sumDist += Math.sqrt((xCenter - x) ** 2 + (yCenter - y) ** 2);
+  }
+
+  return sumDist;
+};