Idea：Parallel Task Partitioning via Control Array Decomposition

[Yusheng-Hu]

Concept: How to efficiently partition permutation generation tasks for multi-core CPUs without synchronization overhead?

Technical Approach:
The Position Pure (PP) algorithm uses a Factorial Control Array C (where C[i] ranges from 0 to i). This array essentially acts as a "factorial-base counter". We can achieve perfectly balanced task distribution by pinning the higher-order indices of the C array to specific CPU cores.

Implementation Example (Dual-Core):
To split the workload across 2 cores, we use the second index of the control array (C[1]) as the partition key:

Core 1: Set C[1]=0 as the initial state and execute while C[1]==0.

Core 2: Set C[1]=1 as the initial state and execute while C[1]==1.

Advantages:

Zero Contention: Each core operates on a strictly disjoint set of the permutation space (N!/2 per core), requiring no mutexes or shared state.

[Yusheng-Hu]

duplicate and already proceed