## Introduction to Algorithms: A Creative ApproachThis book emphasizes the creative aspects of algorithm design by examining steps used in the process of algorithm development. The heart of the creative process lies in an analogy between proving mathematical theorems by induction and designing combinatorial algorithms. The book contains hundreds of problems and examples. It is designed to enhance the reader's problem-solving abilities and understanding of the principles behind algorithm design. |

### From inside the book

Results 1-3 of 19

Page 50

In a divide-and-conquer algorithm, the problem is divided into smaller

used to solve the original problem. Assume that there are a

size 1 /b ...

In a divide-and-conquer algorithm, the problem is divided into smaller

**subproblems**, each**subproblem**is solved recursively, and a combine algorithm isused to solve the original problem. Assume that there are a

**subproblems**, each ofsize 1 /b ...

Page 109

We have reduced the problem to two smaller

kn). To complete the solution, we have to strengthen the hypothesis. We need to

solve the problem not only for knapsacks of size K, but also for knapsacks of all ...

We have reduced the problem to two smaller

**subproblems**: P(n-\,K) and P(n- \,K -kn). To complete the solution, we have to strengthen the hypothesis. We need to

solve the problem not only for knapsacks of size K, but also for knapsacks of all ...

Page 157

Fortunately, in this case there is no need to solve each

The key to this observation is that there are not too many different

altogether. Each possible

in ...

Fortunately, in this case there is no need to solve each

**subproblem**separately.The key to this observation is that there are not too many different

**subproblems**altogether. Each possible

**subproblem**involves computing C(i, j) for some i and jin ...

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### Common terms and phrases

algorithm to find arbitrary array assume augmenting path AVL tree biconnected components binary search Boolean chapter clique problem colors compute Consider constant contains convex hull corresponding cost cycle data structure defined delete denote Design an algorithm DFS numbers discussed efficient algorithm elements end Figure example Exercise given in Fig graph G Gray code heap induction hypothesis input insert integer intersection Let G logn lower bound matching matrix multiplication maximal maximum MCST mergesort minimal multiset node NP-complete number of comparisons number of edges operations Output parallel algorithm partition perform pointer points polygon polynomial possible Problem Given processors proof prove quicksort real numbers recurrence relation reduction remove requires root running satisfies Section sequence shortest paths simple solution solve sorting spanning tree straightforward strongly connected component subgraph subproblems subset subtree techniques theorem total number traversal undirected graph variables vertex cover weighted