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**Unformatted text preview: **4. Consider a rectangular array of distinct elements. Each row is given in increasing sorted order. Now sort (in place) the elements in each column into increasing order. Prove that the elements in each row remain sorted. 5. Show that if you have a subroutine for HamP which runs in polynomial time, you can solve the HamC problem in polynomial time. 6. Show that if you have a subroutine for HamP which runs in polynomial time, you can actually ﬁnd a hamiltonian path in polynomial time. Extra Credit: Consider the following recurrence: T (1) = 1 T ( n ) = T ( n/ 5) + T (7 n/ 10) + n. You need not give an exact closed form for this recurrence, but give a tight “big-oh” bound on T . As always, prove your answer is correct....

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