Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 4 pot

... 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...

Ngày tải lên: 13/08/2014, 18:20

... E [ Y 1 ] ≤ 1 4  1 + 3 3  = 1 4 · 4 = 1 . Inductive step: Assume that E [ Y i ] ≤ 1 4  i + 3 3  for all i < n. Then E [ Y n ] ≤ 4 n n−1  i=0 E [ Y i ] (from before) ≤ 4 n n−1  i=0 1 4  i + ... 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...

Ngày tải lên: 13/08/2014, 18:20

... and path compression, O(m α(n)). n α(n) 0–2 0 31 4 7 2 8–2 047 3 2 048 –A 4 (1) 4 What’s A 4 (1)? See Section 21 .4, if you dare. It’s  10 80 ≈ # of atoms in observ- able universe. This bound is tight—there ... 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 t...

Ngày tải lên: 13/08/2014, 18:20

... 24- 14 Exercise 24. 3 -4, 24- 14 Exercise 24. 3-6, 24- 15 Exercise 24. 3-7, 24- 16 Exercise 24. 4 -4, 24- 17 Exercise 24. 4-7, 24- 18 Exercise 24. 4-10, 24- 18 Exercise 24. 5 -4, 24- 18 Exercise 24. 5-7, 24- 19 Exercise 24. 5-8, ... 13.3 -4, 13-15 Exercise 13 .4- 6, 13-16 Exercise 13 .4- 7, 13-16 Exercise 14. 1-5, 14- 9 Exercise 14. 1-6, 14- 9 Exercise 14. 1-7, 14- 9 Exercise 14. 2-2, 14- 1...

Ngày tải lên: 13/08/2014, 18:20

... April 20 04. 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 the solutions to Problems ... put in the “cost” and “times” columns later.] Example: 12 345 6 5 246 13 12 345 6 2 546 13 12 345 6 245 613 12 345 6 245 613 12 345 6 245 613 12 345 6 2 4 5 61 3 j jj jj...

Ngày tải lên: 13/08/2014, 18:20

... Chapter 4: Recurrences 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 ... 5. • MAX-HEAPIFY is applied to subtrees rooted at nodes (in order): 16, 2, 3, 1, 4. 1 23 45 67 8910 1 23 45 67 8910 4 13 2910 14 8 7 16 41 23 16 9...

Ngày tải lên: 13/08/2014, 18:20

... 7-3 81 640 395 p,j ri 81 640 395 prj 18 640 395 p,i rj 18 640 395 p,i rj 18 64 0395 prji 18 640 395 prji 13 640 895 prji 13 640 895 pri 16 540 893 pri i A[r]: pivot A[j r–1]: not yet examined A[i+1 j–1]: known to ... 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...

Ngày tải lên: 13/08/2014, 18:20

... Programming a 1,1 e 1 enter e 2 a 2,1 a 1,2 a 2,2 t 1,1 t 2,1 t 1,2 t 2,2 a 1,3 a 2,3 t 1,3 t 2,3 a 1 ,4 a 2 ,4 t 1 ,4 t 2 ,4 a 1,5 a 2,5 x 1 x 2 exit S 1,1 S 2,1 S 1,2 S 2,2 S 1,3 S 2,3 S 1 ,4 S 2 ,4 S 1,5 S 2,5 2 4 7 8 2 2 9 3 1 5 348 3 13 22 645 6 Automobile factory with two assembly lines. • Each ... row-major order, i.e., row-by-row from top to bottom, and left to right w...

Ngày tải lên: 13/08/2014, 18:20

... α = 1 /4. • Since α has different distances 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 ... 1/2. • For α to go from 1/ 2to1 /4, num decreases from size /2tosize /4, for a total decrease of size /4.  increases from 0 to size /4. Thus,  needs to increase by 1 for...

Ngày tải lên: 13/08/2014, 18:20

... in { 1, 2, ,k } : 24- 4 Lecture Notes for Chapter 24: Single-Source Shortest Paths RELAX(u,v,w) if d[v] > d[u] + w(u,v) then d[v] ← d[u] + w(u,v) π[v] ← u 3 3 RELAX uv 41 0 47 RELAX 46 46 For all the ... time. Solution to Exercise 24. 4 -4 Let δ(u) be the shortest-path weight from s to u. Then we want to Þnd δ(t). δ must satisfy δ(s) = 0 δ(v) − δ(u) ≤ w(u,v)for all (u,v)∈ E (...

Ngày tải lên: 13/08/2014, 18:20