Interval Inversion Count Given an array of length n with elements bounded by a small constant (≤ 50), we need to answer m queries of the form: count the number of inversions inside subarray [l, r]. A naive O(n2) per query is too slow, and a Mo’s algorithm solution, while feasible for moderate constr...
Alternative Approach A key observation is that a subarray [l,r] is valid when max(l,r) - min(l,r) = r - l. This problem appears challenging to maintain efficiently, leading us to consider block decomposition techniques (given the constraints of 1.2e5 elements and 7-second time limit). Let's divide t...
Given an array of $n$ integers $a_1, a_2, \ldots, a_n$, process $q$ range operations: Type 1 l r d: add $d$ to all elements in $[l, r]$ Type 2 l r d: multiply all elements in $[l, r]$ by $d$ Type 3 l r d: assign all elements in $[l, r]$ to $d$ Type 4 l r: query the sum of elements in $[l, r]$ modulo...
Standard segment tree compositions assume that a node's summary statistics depend exclusively on its immediate children. However, problems involving prefix constraints or running extrema require contextual awarreness—aggregation of the right subtree depends on specific values emanating from the left...
The problem requires maintaining a sequence of n initial preferences and processing m dynamic updates. Each query defines a subarray [L, R], a fallback identifier F, and a list of K positions. The task is to identify whether any value appears strictly more than (R - L + 1) / 2 times within the speci...