In this paper, we propose a novel data structure and the algorithms to build, update and perform range query operations of transitive function. The update and query operation takes O(log(n)) time, and the space required for operating data is also O(cn), where c=3 proving it to be efficient than other data structures such as segment tree and sparse table. Experimental analysis shows the statistical evidence of proposed algorithm and conclude that it provides a good trade-off between space and time complexity in comparison to existent methods.

中文翻译：

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使用二进制索引树的有效传递操作

在本文中，我们提出了一种新颖的数据结构和算法，以建立，更新和执行传递函数的范围查询操作。更新和查询操作需要O（log（n））时间，并且操作数据所需的空间也是O（cn），其中c = 3证明它比其他数据结构（例如段树和稀疏表）有效。实验分析显示了该算法的统计证据，并得出结论，与现有方法相比，该算法在空间和时间复杂度之间取得了良好的折衷。