P10281 [USACO24OPEN] Grass Segments G

Bessie is planting some grass on the positive real line. She has $N$ ($2\le N\le 2\cdot 10^5$) different cultivars of grass, and will plant the $i$th cultivar on the interval $[\ell_i, r_i]$ ($0 < \ell_i < r_i \leq 10^9$). In addition, cultivar $i$ grows better when there is some cultivar $j$ ($j\neq i$) such that cultivar $j$ and cultivar $i$ overlap with length at least $k_i$ ($0 < k_i \leq r_i - \ell_i$). Bessie wants to evaluate all of her cultivars. For each $i$, compute the number of $j\neq i$ such that $j$ and $i$ overlap with length at least $k_i$.

The first line contains $N$. The next $N$ lines each contain three space-separated integers $\ell_i$, $r_i$, and $k_i$.

The answers for all cultivars on separate lines.

##### For Sample 1: The overlaps of the cultivars is $[4,6]$, which has length $2$, which is at least $2$ but not at least $3$. #### SCORING: - Input 4-5: $N \leq 5000$. - Inputs 6-11: $k$ is the same for all intervals. - Inputs 12-20: No additional constraints. In addition, for Inputs 5, 7, ..., 19, $r_i \leq 2N$ for all $i$.