minimum-cost-to-hire-k-workers

heap/minimum-cost-to-hire-k-workers.js

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+/**
+857. Minimum Cost to Hire K Workers
+
+There are n workers. You are given two integer arrays quality and wage where quality[i] is the quality of the ith worker and wage[i] is the minimum wage expectation for the ith worker.
+
+We want to hire exactly k workers to form a paid group. To hire a group of k workers, we must pay them according to the following rules:
+
+Every worker in the paid group should be paid in the ratio of their quality compared to other workers in the paid group.
+Every worker in the paid group must be paid at least their minimum wage expectation.
+Given the integer k, return the least amount of money needed to form a paid group satisfying the above conditions. Answers within 10-5 of the actual answer will be accepted.
+
+Example 1:
+Input: quality = [10,20,5], wage = [70,50,30], k = 2
+Output: 105.00000
+Explanation: We pay 70 to 0th worker and 35 to 2nd worker.
+
+Example 2:
+Input: quality = [3,1,10,10,1], wage = [4,8,2,2,7], k = 3
+Output: 30.66667
+Explanation: We pay 4 to 0th worker, 13.33333 to 2nd and 3rd workers separately.
+
+Constraints:
+n == quality.length == wage.length
+1 <= k <= n <= 104
+1 <= quality[i], wage[i] <= 104
+*/
+
+const mincostToHireWorkers = function (quality, wage, K) {
+  const workers = wage
+    .map((w, i) => ({ ratio: w / quality[i], quality: quality[i] }))
+    .sort((a, b) => b.ratio - a.ratio);
+
+  const pq = new Heap((a, b) => a.quality < b.quality);
+
+  let qualitySum = 0;
+  let result = Number.POSITIVE_INFINITY;
+
+  while (workers.length) {
+    const worker = workers.pop();
+    qualitySum += worker.quality;
+    pq.insert(worker);
+    if (pq.getLength() > K) {
+      qualitySum -= pq.pop().quality;
+    }
+    if (pq.getLength() === K) {
+      result = Math.min(result, worker.ratio * qualitySum);
+    }
+  }
+
+  return result;
+};
+
+class Heap {
+  constructor(comparator) {
+    this.arr = [];
+    this.comparator = comparator;
+  }
+
+  siftDown(i) {
+    const { arr } = this;
+    const left = 2 * i + 1;
+    const right = 2 * i + 2;
+
+    if (left >= arr.length) return;
+
+    if (right >= arr.length) {
+      if (this.comparator(arr[i], arr[left])) this.swap(i, left);
+      return;
+    }
+    if (
+      this.comparator(arr[left], arr[i]) &&
+      this.comparator(arr[right], arr[i])
+    ) {
+      return;
+    }
+
+    if (this.comparator(arr[right], arr[left])) {
+      this.swap(i, left);
+      this.siftDown(left);
+      return;
+    }
+
+    this.swap(i, right);
+    this.siftDown(right);
+  }
+
+  bubbleUp(i) {
+    const parent = Math.floor((i - 1) / 2);
+    if (parent !== -1 && this.comparator(this.arr[parent], this.arr[i])) {
+      this.swap(i, parent);
+      this.bubbleUp(parent);
+    }
+  }
+
+  insert(value) {
+    this.arr.push(value);
+    this.bubbleUp(this.arr.length - 1);
+  }
+
+  pop() {
+    const { arr } = this;
+    if (arr.length === 0) return -1;
+
+    const popValue = arr[0];
+    arr[0] = arr[arr.length - 1];
+    arr.pop();
+    this.siftDown(0);
+    return popValue;
+  }
+
+  getLength() {
+    return this.arr.length;
+  }
+
+  swap(a, b) {
+    [this.arr[a], this.arr[b]] = [this.arr[b], this.arr[a]];
+  }
+
+  empty() {
+    return this.arr.length === 0;
+  }
+}