Detect Temperature Spike from (timestamp, temperature) pairs

Given a time-ordered list of (timestamp, temperature) data points, detect whether there exists a temperature spike. Definition: a spike occurs if at some index i, the temperature temp[i] increases significantly compared to a previous reading within a short time window. Rules: You are given integers window (seconds) and delta (temperature threshold). If there exist indices j < i such that: timestamp[i] - timestamp[j] <= window temperature[i] - temperature[j] >= delta then output true; otherwise output false. Input (stdin): First line: n window delta Next n lines: t_i temp_i with strictly increasing t_i Output (stdout): One line: true or false Constraints: 1 <= n <= 2e5 0 <= t_i <= 1e9 -1e6 <= temp_i <= 1e6 Requirement: better than O(n^2) time. Example Input 5 10 5 0 30 3 31 6 33 9 40 20 39 Output true