Once the suffix array is constructed, the short routine shown in Figure 1 can be invoked f...

Once the suffix array is constructed, the short routine shown in Figure 1 can be invoked from Figure 2 to create the longest common prefix array.

a. In the code, what does rank[i] represent?

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b. Suppose that LCP[rank[i] ] = h. Show that LCP[rank[i+1] ] ≥ h − 1.

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c. Show that the algorithm in Figure 1 correctly computes the LCP array.

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d. Prove that the algorithm in Figure 1 runs in linear time.

Figure 1: LCP array construction from suffix array

Figure 2: Code to set up the first call to makeSuffixArray; create appropriate size arrays, and to keep things simple; just use the 256 ASCII character codes