A-Backtracking with examples.pptxA-Backtracking with examples.pptx
- 2. Introduction •Overview •Explain with a diagram that has dead-ends •Examples chosen: •N-queens problem •Subset sum problem •Hamiltonian cycle problem
- 3. 3 N-queens Problem • Define the problem • If two queens are placed at positions (i, j) and (k, l) • Then, they are on the same diagonal iff i – j = k – l or i+j = k+l • Here, first equation implies that j – l = i – k • The second equation implies that j – l = k - i • Combining the two, we get |j – l |= |i – k|
- 5. Algorithm for N-queens Problem
- 6. Subset Sum Problem • Problem definition: Find a subset of a given set A = {a1, . . . , an} of n positive integers whose sum is equal to a given positive integer d. • For example, for A = {1, 2, 5, 6, 8} and d = 9, there are two solutions: {1, 2, 6} and {1, 8}. • Of course, some instances of this problem may have no solutions. • It is convenient to sort the set’s elements in increasing order. So, we will assume that a1< a2< . . . < an. • The state-space tree can be constructed as a binary tree like that in Figure shown below for the instance A = {3, 5, 6, 7} and d = 15.
- 8. Hamiltonian Cycle Problem • Informal Definition • Formal Definition • Examples
- 9. Algorithm
- 10. Subroutine