Suppose we also wish to compute the vertices on shortest paths in the algorithms of this section. Show how to compute the predecessor matrix ... from the completed matrix L of shortest-path weights in O. n3/ time.

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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