A subsequence is called palindromic if it results in the same sequence when read from left-to-right and right-to-left. For example, in the sequence: A, A,A, T,G, G,T, A,C, G,A
The subsequences A, A,A and A, T,G, G,T, A are palindromic, while A, C,G is not. Give an algorithm to find the length of the longest palindromic subsequence in a sequence a[1 ...n]. Your algorithm should run in O(n2) time. Show the proof of correctness and proof of running time, respectively.

answer: when the substance contain the two parts (polar and non-polar) like soap.

explanation:

soap is produced from the basic hydrolysis of ester "saponification", it is considered as a salt of hydrocarbons. the soap molecule contains the two parts: a polar group   (-coo-na+) and a non-polar group (r-hydrocarbon part). the polar group is called the head and the tail is the non-polar group. the polar group is hydrophilic in nature (water loving) and the non-polar group is hydrophobic in nature (water repelling).the polar/non-polar nature of a substance is useful that it can dissolve the non-polar substances by the polar part and also can dissolve the polar substances by the non-polar part. it commonly used in detergents and soaps.

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Through the process of sedimentation,sediment is turned back to rock to form sedimentation.the process of sedimentation is: > deposition-where fragments were deposited into the river or sea under gravity or travelling agent such as wind or water. > sedimentation-the fragments deposited in the river sedimented and accumulate> compaction-the layers of fragments deposited undergoes compaction due to the weight if the upper layers> cementation-chemical substance of the fragments such as cement dissolved into the water and cement the other fragments together to form sedimentary rock.thus,cementation and compaction are the process.on the other hand, transformation only occur when a rock under goes metamorphism(compaction or extreme heat).while recrystillization occurs when a rock is melted and cooled down,which also requires metamorphism to take place.hope it !

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