Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 8 potx

... 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

... contains max[x] = max endpoint value in subtree rooted at x . int max M 8 [17,19] 23 M 8 [21,23] 23 M 8 [5,11] 18 M 8 [15, 18] 18 M 8 [4 ,8] 8 M 8 [7,10] 10 [leave on board] max[x] = max ⎧ ⎨ ⎩ high[int[x]] ... nodes (ancestors of 14-2 Lecture Notes for Chapter 14: Augmenting Data Structures M 8 B B B B R R R R i=5 r=6 i=3 r=2 i=1 r=1 i=5 r=2 M 8 M 8 P 2 M 8 Q 1 M 8...

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... 101 Half-cleaner: 0 0 1 1 1 0 0 0 0 0 0 1 0 1 01 bitonic clean bitonic 0 0 1 1 1 1 1 0 0 1 0 1 1 1 01 bitonic clean bitonic Depth = 1. Lemma If the input to a half-cleaner is a bitonic 0-1 sequence, then for the output: • both the top and ... Networks A bitonic sorting network Constructing a sorting network Step 1: Construct a “bitonic sorter.” It sorts any bitonic sequence. A sequence is b...

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... Structures Lecture Notes 14-1 Solutions 14-9 Preface This document is an instructor’s manual to accompany Introduction to Algorithms, Second Edition, by Thomas H. Cormen, Charles E. Leiserson, Ronald L. ... invariants is like mathematical induction: Instructor’s Manual by Thomas H. Cormen Clara Lee Erica Lin to Accompany Introduction to Algorithms Second Edition...

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... 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 = (n) We ... 5. • MAX-HEAPIFY is applied to subtrees rooted at nodes (in order): 16, 2, 3, 1, 4. 1 23 4567 89 10 1 23 4567 89 10 4 13 2910 14 8 7 16 41 23 16 9 10 14...

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... Notes for Chapter 7: Quicksort 7-3 81 640395 p,j ri 81 640395 prj 186 40395 p,i rj 186 40395 p,i rj 186 4 0395 prji 186 40 395 prji 13640 89 5 prji 13640 89 5 pri 16540 89 3 pri i A[r]: pivot A[j r–1]: not ... Chapter 8: Sorting in Linear Time 8- 11 Solution to Exercise 8. 3-2 Insertion sort is stable. When inserting A[ j] into the sorted sequence A[1 j −1], we do it the followi...

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... CLRS: • ASCII values: C = 67, L = 76, R = 82 , S = 83 . • There are 1 28 basic ASCII values. • So interpret CLRS as (67 ·1 28 3 ) +(76 ·1 28 2 ) + (82 ·1 28 1 ) + (83 ·1 28 0 ) = 141,764,947. Division method h(k) ... 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 usu...

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... 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 ... long it takes to get through S 1,1 . • If j ≥ 2, have two choices of how to get to S 1, j : • Through S 1, j −1 , then directly to S 1, j . • Through S 2, j −1 , then transfer ove...

Ngày tải lên: 13/08/2014, 18:20

... 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.  increases from 0 to size. ... 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 } ∪ (s...

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...

Ngày tải lên: 13/08/2014, 18:20