7. Union-Find Data Structure Using Pointers
The chapter introduces the union-find data structure and its implementation using pointers. It describes operations including make-union-find, find, and union, highlighting the differences between an array-based and a pointer-based implementation. The chapter underscores the efficiency improvements achieved through the use of path compression, ultimately reducing the complexity of find operations from logarithmic to nearly constant time.
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What we have learnt
- The union-find data structure tracks a partition of a set and supports efficient union and find operations.
- Using pointers for implementation results in significant efficiency gains, particularly when combined with path compression techniques.
- The amortized complexity for n find operations can be reduced to O(n α(n)), where α(n) is the inverse Ackermann function.
Key Concepts
- -- UnionFind Data Structure
- A structure that manages partitions of a set and efficiently supports union and find operations.
- -- Path Compression
- A technique used to flatten the structure of the union-find tree, improving the speed of future find operations.
- -- Amortized Analysis
- A method to analyze the time complexity of operations over a sequence of actions, averaging the time taken per operation.
- -- Inverse Ackermann Function α(n)
- A very slowly growing function that helps bound the time complexity of algorithms involving union-find operations.
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