Problem 973 (#23)

* add solution and resources

* update readme

Author: curtisbarnard

README.md

@@ -36,7 +36,7 @@ As I work through this list I figure I would make a GitHub repo with my solution
 25. [Maximum Subarray #53](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/medium/maximum-subarray-53.md)
 26. Insert Interval #57
 27. 01 Matrix #542
-28. K Closest Points to Origin #973
+28. [K Closest Points to Origin #973](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/medium/k-closest-origin-973.md)
 29. Longest Substring Without Repeating Characters #3
 30. 3Sum #15
 31. Binary Tree Level Order Traversal #102
@@ -101,6 +101,7 @@ In order to practice with similar data structures I'll be placing each problem i
 - [Maximum Subarray #53](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/medium/maximum-subarray-53.md)
 - [Majority Element #169](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/majority-element-169.md)
 - [Contains Duplicate #217](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/contains-duplicate-217.md)
+- [K Closest Points to Origin #973](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/medium/k-closest-origin-973.md)
 
 ### Queue
 
@@ -145,6 +146,10 @@ In order to practice with similar data structures I'll be placing each problem i
 - [Diameter of Binary Tree #543](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/diameter-binary-tree-543.md)
 - [Maximum Depth of Binary Tree #104](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/depth-binary-tree-104.md)
 
+### Heap
+
+- [K Closest Points to Origin #973](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/medium/k-closest-origin-973.md)
+
 ## Algorithm Patterns
 
 Within the problems above there are several patterns that often occur. I plan to categorize each problem such that if you are having problem with a particular pattern you can look for other similar problems that use the same pattern.

medium/k-closest-origin-973.md

@@ -0,0 +1,237 @@
+# K Closest Points to Origin
+
+Page on leetcode: https://leetcode.com/problems/k-closest-points-to-origin/
+
+## Problem Statement
+
+Given an array of points where points[i] = [xi, yi] represents a point on the X-Y plane and an integer k, return the k closest points to the origin (0, 0). The distance between two points on the X-Y plane is the Euclidean distance (i.e., √(x1 - x2)2 + (y1 - y2)2). You may return the answer in any order. The answer is guaranteed to be unique (except for the order that it is in).
+
+### Constraints
+
+- 1 <= k <= points.length <= 104
+- -104 < xi, yi < 104
+
+### Example
+
+```
+Input: points = [[1,3],[-2,2]], k = 1
+Output: [[-2,2]]
+Explanation:
+The distance between (1, 3) and the origin is sqrt(10).
+The distance between (-2, 2) and the origin is sqrt(8).
+Since sqrt(8) < sqrt(10), (-2, 2) is closer to the origin.
+We only want the closest k = 1 points from the origin, so the answer is just [[-2,2]].
+```
+
+## Solution
+
+Any order so sorting isn't required. This is an optimization problem (minimizing distance to origin) so my mind goes to greedy methods. A heap might be a good data structure. I will need to look at all sets of points so the best conceivable time complexity would be O(n). I'm not sure if that is attainable though.
+
+Edge case would be 1 point provided, with a k of 1. Or k = num of points.
+
+### Pseudocode
+
+1. If points length equals k then return points
+2. Create helper function that returns euclidean distance
+3. Heapify array to Min-Heap
+4. Remove k smallest points from heap to array and return array
+
+### Initial Attempt
+
+```javascript
+const kClosest = function (points, k) {
+  if (points.length === k) {
+    return points;
+  }
+
+  function dist(point) {
+    return Math.sqrt(point[0] ** 2 + point[1] ** 2);
+  }
+
+  function heapify(arr) {
+    for (let i = points.length - 1; i >= 0; i--) {
+      const right = 2 * i + 2;
+      const left = 2 * i + 1;
+      if (arr[right]) {
+        if (dist(arr[right]) < dist(arr[i])) {
+          const temp = arr[i];
+          arr[i] = arr[right];
+          arr[right] = temp;
+        }
+      }
+      if (arr[left]) {
+        if (dist(arr[left]) < dist(arr[i])) {
+          const temp = arr[i];
+          arr[i] = arr[left];
+          arr[left] = temp;
+        }
+      }
+    }
+    return arr;
+  }
+
+  function deleteFromHeap(arr) {
+    const first = arr.shift();
+    const last = arr.pop();
+    arr.unshift(last);
+    bubbleDown(arr, 0);
+    return first;
+  }
+
+  function bubbleDown(arr, point) {
+    if (!arr[point]) {
+      return;
+    }
+    const right = 2 * i + 2;
+    const left = 2 * i + 1;
+    if (arr[left] < arr[right] && arr[left] < arr[point]) {
+      arr[point] = arr[left];
+      arr[left] = bubbleDown(arr, left);
+    } else if (arr[right] < arr[left] && arr[right] < arr[point]) {
+      arr[point] = arr[right];
+      arr[right] = bubbleDown(arr, right);
+    }
+    return;
+  }
+
+  let result = [];
+  for (let i = 0; i < k; i++) {
+    result.push(deleteFromHeap(points));
+  }
+  return result;
+};
+```
+
+### Second Attempt
+
+I've used the max heap approach which has a time complexity of O(nlogk) and a space complexity of O(k).
+
+```javascript
+const kClosest = function (points, k) {
+  if (points.length === k) {
+    return points;
+  }
+
+  const maxHeap = [];
+
+  // Add points to the heap
+  for (let i = 0; i < points.length; i++) {
+    if (maxHeap.length >= k && dist(points[i]) > dist(maxHeap[0])) {
+      continue;
+    }
+
+    addToHeap(points[i]);
+    if (maxHeap.length > k) {
+      removeFromHeap();
+    }
+  }
+
+  // Helper Functions
+  function dist(point) {
+    return point[0] ** 2 + point[1] ** 2;
+  }
+
+  function addToHeap(point) {
+    maxHeap.push(point);
+    heapifyUp(maxHeap, maxHeap.length - 1);
+  }
+
+  function heapifyUp(arr, node) {
+    const parentNode = Math.floor((node - 1) / 2);
+    if (parentNode < 0) {
+      return;
+    }
+    if (dist(arr[node]) > dist(arr[parentNode])) {
+      const temp = arr[parentNode];
+      arr[parentNode] = arr[node];
+      arr[node] = temp;
+      heapifyUp(arr, parentNode);
+    }
+    return;
+  }
+
+  function removeFromHeap() {
+    maxHeap.shift();
+    maxHeap.unshift(maxHeap.pop());
+    heapifyDown(maxHeap, 0);
+  }
+
+  function heapifyDown(arr, node) {
+    const right = 2 * node + 2;
+    const left = 2 * node + 1;
+    if (right <= arr.length - 1) {
+      if (dist(arr[right]) > dist(arr[node])) {
+        const temp = arr[node];
+        arr[node] = arr[right];
+        arr[right] = temp;
+        heapifyDown(arr, right);
+      }
+    }
+    if (left <= arr.length - 1) {
+      if (dist(arr[left]) > dist(arr[node])) {
+        const temp = arr[node];
+        arr[node] = arr[left];
+        arr[left] = temp;
+        heapifyDown(arr, left);
+      }
+    }
+    return;
+  }
+
+  return maxHeap;
+};
+```
+
+### Optimized Solution
+
+There are a few different ways to solve this problem. Good examples and discussion can be seen here: https://leetcode.com/problems/k-closest-points-to-origin/discuss/762781/javascript-sort-minHeap-and-maxHeap-solutions
+
+I would say the min heap approach is the most ideal.
+
+```javascript
+var kClosest = function (points, k) {
+  // we can build the heap in place
+  let p = Math.floor((points.length - 2) / 2); // last parent
+  for (let i = p; i >= 0; i--) {
+    heapifyDown(points, i, distance);
+  }
+
+  // now we need to remove the smallest (points[0]) k times
+  let solution = [];
+  for (let i = 0; i < k; i++) {
+    solution.push(remove(points, distance));
+  }
+
+  return solution;
+
+  // read 0, replace 0 with last position, heapifyDown
+  function remove(heap, weightFunction) {
+    let val = heap[0];
+    heap[0] = heap.pop();
+    heapifyDown(heap, 0, weightFunction);
+    return val;
+  }
+
+  // compare with children, swap with smallest, repeat
+  function heapifyDown(heap, idx, weightFunction) {
+    let left = 2 * idx + 1;
+    let right = 2 * idx + 2;
+    let smallest = left;
+
+    if (left >= heap.length) return;
+
+    if (right < heap.length && weightFunction(heap[left]) > weightFunction(heap[right])) {
+      smallest = right;
+    }
+
+    if (weightFunction(heap[idx]) > weightFunction(heap[smallest])) {
+      [heap[idx], heap[smallest]] = [heap[smallest], heap[idx]];
+      heapifyDown(heap, smallest, weightFunction);
+    }
+  }
+
+  function distance(point) {
+    return point[0] * point[0] + point[1] * point[1];
+  }
+};
+```