Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 6 pps

... row-major order, i.e., row-by-row from top to bottom, and left to right within each row. Column- major order (column-by-column from left to right, and top to bottom within each column) would also ... page 365 , we wish to print the sequence p 7 , p 6 , p 4 , p 3 , p 1 , p 2 , p 5 . Our code is recursive. The right -to- left subpath is printed as we go deeper into the recursion, an...

Ngày tải lên: 13/08/2014, 18:20

... 4-13 nn log 4 n n 2 n 4 n 4 n 8 n 8 n 8 n 16 n 16 n 16 n 32 n 32 n 64 log 8 n . . . n( 4+2+1 8 ) = 7 8 n n( 1 4 + 2 8 + 3 16 + 2 32 + 1 64 ) = n 16+ 16+ 12+4+1 64 = n 49 64 = 7 8 2 n log n  i=1  7 8  i n ... 5. • MAX-HEAPIFY is applied to subtrees rooted at nodes (in order): 16, 2, 3, 1, 4. 1 23 4 567 8910 1 23 4 567 8910 4 13 2910 14 8 7 16 41 23 16 9 10 14 8 7 16...

Ngày tải lên: 13/08/2014, 18:20

... sorting A and B into monotoni- cally increasing order works as well. Lecture Notes for Chapter 16: Greedy Algorithms 16- 3 Solution to S ij is (solution to S ik ) ∪ { a k } ∪ (solution to S kj ). Since ... to go to get to 1 or 1/4, starting from 1/2, rate of increase of  differs. • For α to go from 1/ 2to1 ,num increases from size /2tosize, for a total increase of size /2. ...

Ngày tải lên: 13/08/2014, 18:20

... in the “cost” and “times” columns later.] Example: 1234 56 52 461 3 1234 56 25 461 3 1234 56 24 561 3 1234 56 24 561 3 1234 56 24 561 3 1234 56 2 4 5 61 3 j jj jj [Read this Þgure row by row. Each part shows ... 2004. Added solutions to Exercises 5.4 -6, 11.3-5, 12.4-1, 16. 4-2, 16. 4-3, 21.3-4, 26. 4-2, 26. 4-3, and 26. 4 -6 and to Problems 12-3 and 17-4. Made minor changes in t...

Ngày tải lên: 13/08/2014, 18:20

... Notes for Chapter 7: Quicksort 7-3 8 164 0395 p,j ri 8 164 0395 prj 1 864 0395 p,i rj 1 864 0395 p,i rj 1 864 0395 prji 1 864 0 395 prji 1 364 0 895 prji 1 364 0 895 pri 165 40 893 pri i A[r]: pivot A[j r–1]: ... overview [The treatment in the second edition differs from that of the Þrst edition. We use a different partitioning method—known as “Lomuto partitioning”—in the second edit...

Ngày tải lên: 13/08/2014, 18:20

... pointer) to the new slot, and updating the pointer in the slot that pointed to j to point to the new slot. Then insert the new element in the now-empty slot as usual. To update the pointer to j , ... lists. If we want to delete elements, it’s better to use doubly linked lists.] • Slot j contains a pointer to the head of the list of all stored elements that hash to j [or t...

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... O(h) time, analogous to the changes we made for persistence in insertion. But to do so without using parent pointers we need to walk down the tree to the node to be deleted, to build up a stack ... keys are not distinct, because in order to Þnd the path to the node to delete—a particular node with a given key—we have to make some changes to how we store things in the tre...

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... edge it visits to the cycle C, which is then added to the Euler tour T , when we return from a call to VISIT(u), all edges entering or leaving vertex u have been added to the tour. When we advance ... B to the end of A, instead splice B into A right after the Þrst element of A. We have to traverse B to update representative pointers anyway, so we can just make the last element o...

Ngày tải lên: 13/08/2014, 18:20

... + E) to compute G  . • O(VE) to run BELLMAN-FORD. • (E) to compute w. • O(V 2 lg V +VE) to run Dijkstra’s algorithm | V | times (using Fibonacci heap). • (V 2 ) to compute D matrix. Total: ... t (k−1) kj  . T RANSITIVE-CLOSURE(E, n) for i ← 1 to n do for j ← 1 to n do if i = j or (i, j) ∈ E[G] then t (0) ij ← 1 else t (0) ij ← 0 for k ← 1 to n do for i ← 1 to n do for j...

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... 16. 1-2, 16- 9 Exercise 16. 1-3, 16- 9 Exercise 16. 1-4, 16- 10 Exercise 16. 2-2, 16- 11 Exercise 16. 2-4, 16- 12 Exercise 16. 2 -6, 16- 13 Exercise 16. 2-7, 16- 13 Exercise 16. 4-2, 16- 14 Exercise 16. 4-3, 16- 14 Exercise ... 25.2 -6, 25-12 Exercise 25.3-4, 25-13 Exercise 25.3 -6, 25-13 Exercise 26. 1-4, 26- 15 Exercise 26. 1 -6, 26- 16 Exercise 26. 1-7, 26- 16 Exercise 26. 1-9, 26- 17 Ex...

Ngày tải lên: 13/08/2014, 18:20