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CS 261 – Data Structures
Stacks
Stacks
• Linear data abstraction:
- Elements added only at ends and retain order in which they were
inserted
• Stacks (LIFO) :
- addLast (push)
- removeLast (pop)
- getLast (top)
• Stack applications:
- Web browser back button
- Activation record stack Æ Recursion
- Reverse Polish Notation (RPN) calculator
- Undo, backspace key, searching/backtracking
Stack Implementation
• We’ve already seen two data structures that implement
the stack interface:
- Vector: Stack stk = new Vector();
- LinkedList: Stack stk = new LinkedList();
• We will study another later called IndexedDeque
• Both Vector and LinkedList implement the operations
in constant time:
- In practice, either implementation works well
Stack Applications: Parentheses Checking
// Import statements. public class ParenCheck { private Stack stk = new Vector();
private void push(char c) { stk.addLast(new Character(c)); } private void check(char c) { // Check stack for balanced parentheses. if (stk.isEmpty()) reportError(); // Didn’t balance! Character s = (Character)stk.getLast(); // Get character on stack stk.removeLast(); // and remove it! if (c != s.charValue()) reportError(); // If not same Æ error! }
public static void main(String [] args) { try { ParenCheck world = new ParenCheck(System.in); } catch (IOException e) { System.out.println(“Received IO Exception “ + e); } } ...
Stack Applications: Parentheses Checking
public ParenCheck(InputStream in) throws IOException { int i = in.read(); while (i != -1) { if (i == ‘(‘ ) push (‘)’); else if (i == ‘{‘ ) push (‘}’); else if (i == ‘[‘ ) push (‘]’); else if (i == ‘)’ ) check(‘)’); else if (i == ‘}’ ) check(‘}’); else if (i == ‘]’ ) check(‘]’); i = i.read(); } if (stk.isEmpty()) System.out.println(“Parenthesis Balance”); else reportError(); } } // End of class ParenCheck.
Stack Applications: Towers of Hanoi
- We’ve seen this recursive algorithm
- The algorithm didn’t explicitly use a stack:
- Recursive calls use activation record stack to keep track of
parameters and local variables
- Stacks used for visualization to keep track of the size of the
disks on each pole
Move disks one at a time from A to B without placing a larger disk
on top of smaller one
A B C
Place 8 queens on a chessboard so that none can capture
another (no two in the same row, column, or diagonal) :
Implemented using a Stack to backtrack when it gets stuck
Stack Applications: 8 Queens
1 Q
a b c d e f g h
Stack:Stack:
1a
Q
Q
Q
Q
Stack:
2c
1a
Stack:
3e
2c
1a
Stack:
4b
3e
2c
1a
Stack:
5d
4b
3e
2c
1a
No Free Squares in 6:
- Backup Æ Pop stack
- Try another square in row 5 (to right of 5d)
Place 8 queens on a chessboard so that none can capture
another (no two in the same row, column, or diagonal) :
Implemented using a Stack to backtrack when it gets stuck
Stack Applications: 8 Queens
1 Q
a b c d e f g h
Stack:Stack:
1a
Q
Q
Q
Q
Stack:
2c
1a
Stack:
3e
2c
1a
Stack:
4b
3e
2c
1a
Stack:
5h
4b
3e
2c
1a
Still No Free Squares:
- Backup Æ Pop stack
- Try another square in row 5 (to right of 5h)
Place 8 queens on a chessboard so that none can capture
another (no two in the same row, column, or diagonal) :
Implemented using a Stack to backtrack when it gets stuck
Stack Applications: 8 Queens
1 Q
a b c d e f g h
Stack:Stack:
1a
Q
Q
Q
Q
Stack:
2c
1a
Stack:
3e
2c
1a
Stack:
4b
3e
2c
1a
No More Squares in 5:
- Backup Æ Pop stack
- Try another square in row 4 (to right of 4b)
Place 8 queens on a chessboard so that none can capture
another (no two in the same row, column, or diagonal) :
Implemented using a Stack to backtrack when it gets stuck
Stack Applications: 8 Queens
1 Q
a b c d e f g h
Stack:Stack:
1a
Q
Q
Q
Q
Q
Q
Stack:
2c
1a
Stack:
3e
2c
1a
Stack:
4g
3e
2c
1a
Stack:
5b
4b
3e
2c
1a
Stack:
6d
5b
4b
3e
2c
1a
Stack:
7f
6d
5b
4b
3e
2c
1a
No Free Squares in 8:
Place 8 queens on a chessboard so that none can capture
another (no two in the same row, column, or diagonal) :
Implemented using a Stack to backtrack when it gets stuck
Stack Applications: 8 Queens
Q
Q
Q
Q
Q
Q
Q
Q
a b c d e f g h
Eventually, you will
find a solution (though
you may have to backup all the way to the first row)
Stack Applications: Knight’s Tour
Can a knight visit each square on the chessboard exactly
once (using only legal chess moves) :
Implemented using a Stack to backtrack when it gets stuck
