Chapter 1. Introduction. Why Do We Need to Study Algorithms?. To learn strategies to design efficient algorithms. To understand the difficulty of designing good algorithms for some problems, namely NP-complete problems. Consider the Sorting Problem. Sorting problem:
To sort a set of elements into increasing or decreasing order.
11, 7, 14, 1, 5, 9, 10
1, 5, 7, 9, 10, 11, 14
a good algorithm implemented on a slow computer.
M(weight limit) = 14
best solution: P1, P2, P3, P5 (optimal)
This problem is NP-complete.
Find: A closed tour which includes all points exactly once such that its total length is minimized.
Find S1 and S2 such that S1S2=, S1S2=S,
(Partition into S1 and S2 such that the sum of S1 is equal to that of S2)
Determine: min # of guards and their placements such that the entire art gallery can be monitored.