dot W_{\max})$ overall), we record only the right endpoint in a right array indexed by the start of the matc...

t the intervals in ascending order by their right endpoint (primary key) and ascending order by length (seco...

> 0$ and $j > 0$, there are two cases: The right endpoint of the last line segment is not $j$. This is equi...

s every pair, but the optimal pair always has one endpoint at house 0 or house $n-1$. Suppose the best pair ...

Approach 1: Enumerate the Left Endpoint Intuition We can enumerate all substrings and che...

he subset. Details In the binary search, the left endpoint is $k$, and the right endpoint is $k \times \min{...

an store the length of each interval at its right endpoint. Specifically, we store $d[r]$ at the right endpo...

intervals in $\textit{intervals}$ by their right endpoints in ascending order. Define $\textit{dp}[i][j]$ a...

hin each group are sorted by non-decreasing right endpoint, the right endpoint $R$ only moves monotonically ...

t, consider the range of valid $j$. Fix the right endpoint $i$. As we extend the window leftward, the subarr...