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Commit 78287f9

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Added task 699.
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package g0601_0700.s0699_falling_squares;
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// #Hard #Array #Ordered_Set #Segment_Tree
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import java.util.ArrayList;
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import java.util.Collections;
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import java.util.List;
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import java.util.Set;
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import java.util.TreeSet;
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public class Solution {
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public List<Integer> fallingSquares(int[][] positions) {
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// Coordinate compression using TreeSet
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Set<Integer> unique = new TreeSet<>();
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for (int[] square : positions) {
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unique.add(square[0]);
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unique.add(square[0] + square[1] - 1);
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}
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// converted the TreeSet to a List
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List<Integer> sorted = new ArrayList<>(unique);
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// Storing the max heights for compressed coordinates
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int[] heights = new int[sorted.size()];
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// Our answer list
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List<Integer> list = new ArrayList<>(positions.length);
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// Global Max
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int max = 0;
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for (int[] square : positions) {
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// coordinate compression lookup
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int x1 = Collections.binarySearch(sorted, square[0]);
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int x2 = Collections.binarySearch(sorted, square[0] + square[1] - 1);
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// get the current max for the interval between x1 and x2
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int current = 0;
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for (int i = x1; i <= x2; i++) {
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current = Math.max(current, heights[i]);
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}
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// add the new square on the top
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current += square[1];
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// update the interval with the new value
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for (int i = x1; i <= x2; i++) {
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heights[i] = current;
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}
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// recalculate the global max
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max = Math.max(max, current);
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list.add(max);
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}
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return list;
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}
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}
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699\. Falling Squares
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Hard
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There are several squares being dropped onto the X-axis of a 2D plane.
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You are given a 2D integer array `positions` where <code>positions[i] = [left<sub>i</sub>, sideLength<sub>i</sub>]</code> represents the <code>i<sup>th</sup></code> square with a side length of <code>sideLength<sub>i</sub></code> that is dropped with its left edge aligned with X-coordinate <code>left<sub>i</sub></code>.
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Each square is dropped one at a time from a height above any landed squares. It then falls downward (negative Y direction) until it either lands **on the top side of another square** or **on the X-axis**. A square brushing the left/right side of another square does not count as landing on it. Once it lands, it freezes in place and cannot be moved.
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After each square is dropped, you must record the **height of the current tallest stack of squares**.
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Return _an integer array_ `ans` _where_ `ans[i]` _represents the height described above after dropping the_ <code>i<sup>th</sup></code> _square_.
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**Example 1:**
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![](https://assets.leetcode.com/uploads/2021/04/28/fallingsq1-plane.jpg)
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**Input:** positions = [[1,2],[2,3],[6,1]]
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**Output:** [2,5,5]
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**Explanation:**
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After the first drop, the tallest stack is square 1 with a height of 2.
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After the second drop, the tallest stack is squares 1 and 2 with a height of 5.
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After the third drop, the tallest stack is still squares 1 and 2 with a height of 5.
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Thus, we return an answer of [2, 5, 5].
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**Example 2:**
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**Input:** positions = [[100,100],[200,100]]
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**Output:** [100,100]
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**Explanation:**
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After the first drop, the tallest stack is square 1 with a height of 100.
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After the second drop, the tallest stack is either square 1 or square 2, both with heights of 100.
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Thus, we return an answer of [100, 100].
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Note that square 2 only brushes the right side of square 1, which does not count as landing on it.
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**Constraints:**
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* `1 <= positions.length <= 1000`
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* <code>1 <= left<sub>i</sub> <= 10<sup>8</sup></code>
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* <code>1 <= sideLength<sub>i</sub> <= 10<sup>6</sup></code>
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package g0601_0700.s0699_falling_squares;
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import static org.hamcrest.CoreMatchers.equalTo;
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import static org.hamcrest.MatcherAssert.assertThat;
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import java.util.Arrays;
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import org.junit.jupiter.api.Test;
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class SolutionTest {
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@Test
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void fallingSquares() {
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assertThat(
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new Solution().fallingSquares(new int[][] {{1, 2}, {2, 3}, {6, 1}}),
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equalTo(Arrays.asList(2, 5, 5)));
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}
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}

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