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The compound relationship between different moving-orders and different plates of 4-peg Hanoi Tower problem is analyzed in this paper, which is regarded as a new cross correlation pattern without fixed span, not the abutting correlation pattern of 3-peg problem. It is rearranged to a binary and hierarchical tree good for understanding and using. A new idea to solve the 4-peg with a non-recursive algorithm is proposed by forming an iteration path with those nodes that are related to the target problem directly and iterating according this path. By abandoning the storage and computing of useless node, the efficiency of the non-recursive algorithm is improved great.

A Non-recursive Algorithm for 4-Peg Hanoi Tower