The problem: Planet coords are sorted, how can we reach O(1/k*log(n)) for time Ordo in Dijkstra? The information leaked from Chinese hackers. We got the picture how they do ^^^ :)

Source: A team from Tsinghua University has shattered the long-standing speed barrier in shortest path algorithms by designing a new solution that beats Dijkstra’s classical approach—without relying on sorting. Traditionally, Dijkstra’s algorithm finds shortest paths by repeatedly sorting nodes by distance, which imposes a fundamental speed bottleneck linked to sorting time. The new algorithm cleverly sidesteps this restriction by clustering boundary nodes and using selective exploration, reducing the number of candidates at each step and avoiding costly sorts. Their breakthrough also adapts Bellman-Ford techniques for directed graphs, combining randomized and deterministic innovations. This lets them solve shortest path problems faster than ever before—even for arbitrary graph weights—a feat considered impossible for 40 years. Their work won Best Paper at STOC and is set to reshape how developers approach pathfinding and graph optimization. Follow Coding Omega for future updates. Well guys, development appeared in my brain in 10 minutes after I read upper mentioned source. Thanks to everybody interconnected in this process!

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