# Falling Squares LeetCode Solution

Here, We see Falling Squares LeetCode Solution. This Leetcode problem is done in many programming languages like C++, Java, JavaScript, Python, etc. with different approaches.

# List of all LeetCode Solution

## Problem Statement

There are several squares being dropped onto the X-axis of a 2D plane.

You are given a 2D integer array `positions` where `positions[i] = [lefti, sideLengthi]` represents the `ith` square with a side length of `sideLengthi` that is dropped with its left edge aligned with X-coordinate `lefti`.

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.

After each square is dropped, you must record the height of the current tallest stack of squares.

Return an integer array `ans` where `ans[i]` represents the height described above after dropping the `ith` square.

Example 1:

Input: positions = [[1,2],[2,3],[6,1]]
Output: [2,5,5]
Explanation: After the first drop, the tallest stack is square 1 with a height of 2. After the second drop, the tallest stack is squares 1 and 2 with a height of 5. After the third drop, the tallest stack is still squares 1 and 2 with a height of 5. Thus, we return an answer of [2, 5, 5].

Example 2:
Input: positions = [[100,100],[200,100]]
Output: [100,100]
Explanation: After the first drop, the tallest stack is square 1 with a height of 100. After the second drop, the tallest stack is either square 1 or square 2, both with heights of 100. Thus, we return an answer of [100, 100]. Note that square 2 only brushes the right side of square 1, which does not count as landing on it.

## Falling Squares LeetCode Solution C++

``````#include <vector>
#include <algorithm>
#include <iterator>
struct SegmentTree {
SegmentTree(int n) : n(n) {
size = 1;
while (size < n) {
size <<= 1;
}
tree.resize(2*size);
lazy.resize(2*size);
}

void add_range(int l, int r, int h) {
l += size;
r += size;
tree[l] = max(tree[l], h);
tree[r] = max(tree[r], h);
if (l != r) {
if (!(l & 1)) {
lazy[l+1] = max(lazy[l-1], h);
}
if (r & 1) {
lazy[r-1] = max(lazy[r-1], h);
}
}
l >>= 1;
r >>= 1;
while (l != r) {
tree[l] = max(tree[2*l], tree[2*l + 1]);
tree[r] = max(tree[2*r], tree[2*r + 1]);
if (l / 2 != r / 2) {
if (!(l & 1)) {
lazy[l+1] = max(lazy[l+1], h);
}
if (r & 1) {
lazy[r-1] = max(lazy[r-1], h);
}
}
l >>= 1;
r >>= 1;
}
while (l > 0) {
tree[l] = max(tree[2*l], tree[2*l + 1]);
l >>= 1;
}
}
int max_range(int l, int r) {
l += size;
r += size;
int max_val = max(tree[l], tree[r]);
while (l / 2 != r / 2) {
if (!(l & 1)) {
max_val = max(tree[l + 1], max_val);
max_val = max(lazy[l + 1], max_val);
}
if (r & 1) {
max_val = max(tree[r - 1], max_val);
max_val = max(lazy[r - 1], max_val);
}
max_val = max(max_val, lazy[l]);
max_val = max(max_val, lazy[r]);

l >>= 1;
r >>= 1;
}
max_val = max(max_val, lazy[r]);

while (l / 2 > 0) {
max_val = max(lazy[l], max_val);
l >>= 1;
}
return max_val;
}
int global_max() {
return max_range(0, n-1);
}
int size;
int n;
vector<int> tree;
vector<int> lazy;
};

class Solution {
public:
vector<int> fallingSquares(vector<vector<int>>& positions) {
vector<int> points;
for (const auto& rect: positions) {
points.push_back(rect[0]);
points.push_back(rect[0] + rect[1] - 1);
}
sort(begin(points), end(points));
auto new_end = unique(begin(points), end(points));
points.resize(distance(begin(points), new_end));
SegmentTree st(points.size());
vector<int> results;
int max_height = 0;
for (const auto& rect: positions) {
int x_1 = rect[0];
int x_2 = rect[0] + rect[1] - 1;
int l = distance(begin(points), lower_bound(begin(points), end(points), x_1));
int r = distance(begin(points), lower_bound(begin(points), end(points), x_2));
int cur_height = st.max_range(l, r);
int new_height = rect[1] + cur_height;
max_height = max(new_height, max_height);
results.push_back(max_height);
}
return results;
}
};```Code language: PHP (php)```

## Falling Squares LeetCode Solution Java

``````class Solution {
public List<Integer> fallingSquares(int[][] positions) {
SegmentNode root = new SegmentNode(0,Integer.MAX_VALUE,0);
List<Integer> ans = new ArrayList<>();
int max = 0;
for(int[] p : positions){
int left = p[0], height = p[1], right = left + height;
int maxHeight = query(root, left, right) + height;
max = Math.max(max,maxHeight);
}
return ans;
}
public int query(SegmentNode root, int start, int end){
if(start<=root.start && end>=root.end) return root.maxHeight;
if(start>=root.end || end<=root.start) return  0;
if (root.left==null) return root.maxHeight;
int mid = root.start + (root.end - root.start) / 2;
if (end <= mid) {
return query(root.left, start, end);
} else if (start >= mid) {
return query(root.right, start, end);
}
return Math.max(query(root.left,start,mid),query(root.right,mid,end));
}

public void add(SegmentNode root, int start, int end, int maxHeight){
if(start<=root.start && end>=root.end){
root.maxHeight = maxHeight;
root.left = null;
root.right = null;
return;
}
if(start>=root.end || root.start>=end) return;
if(root.left==null){
int mid = root.start + (root.end - root.start) / 2;
root.left = new SegmentNode(root.start,mid,0);
root.right = new SegmentNode(mid,root.end,0);
}
root.maxHeight = Math.max(root.left.maxHeight,root.right.maxHeight);
}
}
class SegmentNode{
public SegmentNode left , right;
public int start, end, maxHeight;
public SegmentNode(int start, int end, int maxHeight){
this.start = start;
this.end = end;
this.maxHeight = maxHeight;
}
}```Code language: PHP (php)```

## Falling Squares LeetCode Solution JavaScript

``````var fallingSquares = function (positions) {
let height = [];

let squares = [[0, 1e10, 0]];
for (let p of positions) {
for (let i = 0; i < squares.length; ++i) {
let l = squares[i][0];
let r = squares[i][1] + l;
if (p[0] < r && ((p[0] + p[1]) > l)) {
let square = [...p, p[1] + squares[i][2]];
for (let j = 0; j < i + 1; ++j) {
if (squares[j][2] < square[2]) {
squares.splice(j, 0, square);
break;
}
}
height.push(squares[0][2]);
break;
}
}
}

return height;
};```Code language: JavaScript (javascript)```

## Falling Squares LeetCode Solution Python

``````class Solution(object):
def fallingSquares(self, positions):
heights, result = [], []
highest = 0
for i, position in enumerate(positions):
left, side_length = position[0], position[1]
base_height = 0
for j in range(i):
prev_left, prev_side = positions[j][0], positions[j][1]
if (left + side_length <= prev_left) or (left >= prev_left + prev_side):
continue
base_height = max(base_height, heights[j])
heights.append(base_height + side_length)
highest = max(highest, heights[-1])
result.append(highest)
return result```Code language: HTML, XML (xml)```
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