Another strategy for the STACK_FULL(i) condition of section 3.4 is to redistribute all the free space in proportion to the rate of growth of individual stacks since the last call to STACK_FULL. This would

require the use of another array LT(1:n) where LT(j) is the value of T(j) at the last call to

STACK_FULL. Then the amount by which each stack has grown since the last call is T(j) - LT(j). The figure for stack i is actually T(i) - LT(i) + 1, since we are now attempting to add another element to i.

Write algorithm STACK_FULL (i) to redistribute all the stacks so that the free space between stacks j and j + 1 is in proportion to the growth of stack j since the last call to STACK_FULL. STACK_FULL (i) should assign at least 1 free location to stack i.

25. Design a data representation sequentially mapping n queues into all array V(1:m). Represent each queue as a circular queue within V. Write algorithms ADDQ, DELETEQ and QUEUE-FULL for this representation.

26. Design a data representation, sequentially mapping n data objects into an array V(1:m). n₁ of these data objects are stacks and the remaining n₂ = n - n₁ are queues. Write algorithms to add and delete elements from these objects. Use the same SPACE_FULL algorithm for both types of data objects. This algorithm should provide space for the i-th data object if there is some space not currently being used.

Note that a circular queue with space for r elements can hold only r - 1.

27. [Landweber]

People have spent so much time playing card games of solitaire that the gambling casinos are now

capitalizing on this human weakness. A form of solitaire is described below. Your assignment is to write a computer program to play the game thus freeing hours of time for people to return to more useful endeavors.

To begin the game, 28 cards are dealt into 7 piles. The leftmost pile has 1 card, the next two cards, and so forth up to 7 cards in the rightmost pile. Only the uppermost card of each of the 7 piles is turned face up. The cards are dealt left to right, one card to each pile, dealing to one less pile each time, and turning the first card in each round face up.

On the top-most face up card of each pile you may build in descending sequences red on black or black on red. For example, on the 9 of spades you may place either the 8 of diamonds or the 8 of hearts. All face up cards on a pile are moved as a unit and may be placed on another pile according to the

bottommost face up card. For example, the 7 of clubs on the 8 of hearts may be moved as a unit onto the 9 of clubs or the 9 of spades.

Whenever a face down card is uncovered, it is turned face up. If one pile is removed completely, a face-up King may be moved from a pile (together with all cards above it) or the top of the waste pile (see below)) into the vacated space. There are four output piles, one for each suit, and the object of the game is to get as many cards as possible into the output piles. Each time an Ace appears at the top of a pile or the top of the stack it is moved into the appropriate output pile. Cards are added to the output piles in sequence, the suit for each pile being determined by the Ace on the bottom.

From the rest of the deck, called the stock, cards are turned up one by one and placed face up on a waste pile. You may always play cards off the top of the waste pile, but only one at a time. Begin by moving a card from the stock to the top of the waste pile. If there is ever more than one possible play to be made, the following order must be observed:

i) Move a card from the top of a playing pile or from the top of the waste pile to an output pile. If the waste pile becomes empty, move a card from the stock to the waste pile.

ii) Move a card from the top of the waste pile to the leftmost playing pile to which it can be moved. If the waste pile becomes empty move a card from the stock to the waste pile.

iii) Find the leftmost playing pile which can be moved and place it on top of the leftmost playing pile to which it can be moved.

iv) Try i), ii) and iii) in sequence, restarting with i) whenever a move is made.

v) If no move is made via (i)-(iv) move a card from the stock to the waste pile and retry (i).

Only the topmost card of the playing piles or the waste pile may be played to an output pile. Once played on an output pile, a card may not be withdrawn to help elsewhere. The game is over when either i) all the cards have been played to the output or

ii) the stock pile has been exhausted and no more cards can be moved

When played for money, the player pays the house $52 at the beginning and wins $5 for every card played to the output piles.

Write your program so that it will play several games, and determine your net winnings. Use a random number generator to shuffle the deck.

Output a complete record of two games in easily understood form. Include as output the number of games played and the net winning (+ or -).

Go to Chapter 4 Back to Table of Contents

CHAPTER 4: LINKED LISTS