1. CSC 172 DATA STRUCTURES

2. BACKTRACKING Read Weiss 10.5

3. BACKTRACKING
Backtracking is a recursive strategy to explore possible solutions.
Every possible solution – exhaustive search
“Depth first search”
“Branch & Bound”

4. BACKTRACKING METHODOLOGY
View picking a solution as a sequence of choices
For each choice, consider every option recursively
Return the best solution found

5. BACKTRACKING Generic enough to be applied to most problems.
Probably still take exponential time
Exact time analysis of backtracking algorithms can be extremely difficult
simpler upperbounds that may not be tight are given.

6. Design Example

7. Design Example

8. Design Example The “N-queens” problem
Given an n-by-n checkerboard place n queens on the board in such a way that no two queens are mutually attacking each other.
Issues:
What data structure?
What algorithm?

9. Data
Board
Location
Level

10. placeQueen(int [][] board, int x, int y) {
board[x][y]++;
for (int k=0; k<board[x].length;k++)
board[x][k]++ ;
removeQueen(int [][] board, int x, int y) {
board[x][y]--;
board[x][k]--;

11. boolean nQueen(int [][] board,
int[]result, int level) {
if (level >= board.length) return true;
for (int k=0; k<board[level].length;k++){
if(board[level][k] <= 0) {
placeQueen(board,level,k);
result[level] = k;
if (nQueen(board,result,level+1))
return true ;
else //BACKTRACK
removeQueen(board,level,k); }
return false ;