Special Section: Building Your Own Compiler

(The Simple Language) Before we begin building the compiler, we discuss a simple, yet powerful, high-level language similar to early versions of the popular language BASIC. We call the language Simple. Every Simple statement consists of a line number and a Simple instruction. Line numbers must appear in ascending order. Each instruction begins with one of the following Simple commands: rem, input, let, print, goto, if...goto and end (see Fig. 21.25). All commands except end can be used repeatedly. Simple evaluates only integer expressions using the +, -, * and / operators. These operators have the same precedence as in C++. Parentheses can be used to change the order of evaluation of an expression.

Our Simple compiler recognizes only lowercase letters. All characters in a Simple file should be lowercase (uppercase letters result in a syntax error unless they appear in a rem statement, in which case they are ignored). A variable name is a single letter. Simple does not allow descriptive variable names, so variables should be explained in remarks to indicate their use in a program. Simple uses only integer variables. Simple does not have variable declarationsmerely mentioning a variable name in a program causes the variable to be declared and initialized to zero automatically. The syntax of Simple does not allow string manipulation (reading a string, writing a string, comparing strings, etc.). If a string is encountered in a Simple program (after a command other than rem), the compiler generates a syntax error. The first version of our compiler will assume that Simple programs are entered correctly. Exercise 21.29 asks the student to modify the compiler to perform syntax error checking.

Simple uses the conditional if...goto statement and the unconditional goto statement to alter the flow of control during program execution. If the condition in the if...goto statement is true, control is transferred to a specific line of the program. The following relational and equality operators are valid in an if...goto statement: <, >, <=, >=, == and !=. The precedence of these operators is the same as in C++.

Let us now consider several programs that demonstrate Simple's features. The first program (Fig. 21.26) reads two integers from the keyboard, stores the values in variables a and b and computes and prints their sum (stored in variable c).

Figure 21.26. Simple program that determines the sum of two integers.

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The program of Fig. 21.27 determines and prints the larger of two integers. The integers are input from the keyboard and stored in s and t. The if...goto statement tests the condition s >= t. If the condition is true, control is transferred to line 90 and s is output; otherwise, t is output and control is transferred to the end statement in line 99, where the program terminates.

Figure 21.27. Simple program that finds the larger of two integers.

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Simple does not provide a repetition statement (such as C++'s for, while or do...while). However, Simple can simulate each of C++'s repetition statements using the if...goto and goto statements. Figure 21.28 uses a sentinel-controlled loop to calculate the squares of several integers. Each integer is input from the keyboard and stored in variable j. If the value entered is the sentinel value - 9999, control is transferred to line 99, where the program terminates. Otherwise, k is assigned the square of j, k is output to the screen and control is passed to line 20, where the next integer is input.

Figure 21.28. Calculate the squares of several integers.

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Using the sample programs of Fig. 21.26, Fig. 21.27 and Fig. 21.28 as your guide, write a Simple program to accomplish each of the following:

1. Input three integers, determine their average and print the result.
2. Use a sentinel-controlled loop to input 10 integers and compute and print their sum.
3. Use a counter-controlled loop to input seven integers, some positive and some negative, and compute and print their average.
4. Input a series of integers and determine and print the largest. The first integer input indicates how many numbers should be processed.
5. Input 10 integers and print the smallest.
6. Calculate and print the sum of the even integers from 2 to 30.
7. Calculate and print the product of the odd integers from 1 to 9.

(Building a Compiler; Prerequisite: Complete Exercises 8.18, 8.19, 21.12, 21.13 and 21.26) Now that the Simple language has been presented (Exercise 21.26), we discuss how to build a Simple compiler. First, we consider the process by which a Simple program is converted to SML and executed by the Simpletron simulator (see Fig. 21.29). A file containing a Simple program is read by the compiler and converted to SML code. The SML code is output to a file on disk, in which SML instructions appear one per line. The SML file is then loaded into the Simpletron simulator, and the results are sent to a file on disk and to the screen. Note that the Simpletron program developed in Exercise 8.19 took its input from the keyboard. It must be modified to read from a file so it can run the programs produced by our compiler.

Figure 21.29. Writing, compiling and executing a Simple language program.

The Simple compiler performs two passes of the Simple program to convert it to SML. The first pass constructs a symbol table (object) in which every line number (object), variable name (object) and constant (object) of the Simple program is stored with its type and corresponding location in the final SML code (the symbol table is discussed in detail below). The first pass also produces the corresponding SML instruction object(s) for each of the Simple statements (object, etc.). As we will see, if the Simple program contains statements that transfer control to a line later in the program, the first pass results in an SML program containing some "unfinished" instructions. The second pass of the compiler locates and completes the unfinished instructions, and outputs the SML program to a file.

First Pass

The compiler begins by reading one statement of the Simple program into memory. The line must be separated into its individual tokens (i.e., "pieces" of a statement) for processing and compilation (standard library function strtok can be used to facilitate this task). Recall that every statement begins with a line number followed by a command. As the compiler breaks a statement into tokens, if the token is a line number, a variable or a constant, it is placed in the symbol table. A line number is placed in the symbol table only if it is the first token in a statement. The symbolTable object is an array of tableEntry objects representing each symbol in the program. There is no restriction on the number of symbols that can appear in the program. Therefore, the symbolTable for a particular program could be large. Make the symbolTable a 100-element array for now. You can increase or decrease its size once the program is working.

Each tableEntry object contains three members. Member symbol is an integer containing the ASCII representation of a variable (remember that variable names are single characters), a line number or a constant. Member type is one of the following characters indicating the symbol's type: 'C' for constant, 'L' for line number and 'V' for variable. Member location contains the Simpletron memory location (00 to 99) to which the symbol refers. Simpletron memory is an array of 100 integers in which SML instructions and data are stored. For a line number, the location is the element in the Simpletron memory array at which the SML instructions for the Simple statement begin. For a variable or constant, the location is the element in the Simpletron memory array in which the variable or constant is stored. Variables and constants are allocated from the end of Simpletron's memory backward. The first variable or constant is stored in location at 99, the next in location at 98, etc.

The symbol table plays an integral part in converting Simple programs to SML. We learned in Chapter 8 that an SML instruction is a four-digit integer composed of two partsthe operation code and the operand. The operation code is determined by commands in Simple. For example, the simple command input corresponds to SML operation code 10 (read), and the Simple command print corresponds to SML operation code 11 (write). The operand is a memory location containing the data on which the operation code performs its task (e.g., operation code 10 reads a value from the keyboard and stores it in the memory location specified by the operand). The compiler searches symbolTable to determine the Simpletron memory location for each symbol so the corresponding location can be used to complete the SML instructions.

The compilation of each Simple statement is based on its command. For example, after the line number in a rem statement is inserted in the symbol table, the remainder of the statement is ignored by the compiler because a remark is for documentation purposes only. The input, print, goto and end statements correspond to the SML read, write, branch (to a specific location) and halt instructions. Statements containing these Simple commands are converted directly to SML (note that a goto statement may contain an unresolved reference if the specified line number refers to a statement further into the Simple program file; this is sometimes called a forward reference).

When a goto statement is compiled with an unresolved reference, the SML instruction must be flagged to indicate that the second pass of the compiler must complete the instruction. The flags are stored in 100-element array flags of type int in which each element is initialized to -1. If the memory location to which a line number in the Simple program refers is not yet known (i.e., it is not in the symbol table), the line number is stored in array flags in the element with the same subscript as the incomplete instruction. The operand of the incomplete instruction is set to 00 temporarily. For example, an unconditional branch instruction (making a forward reference) is left as +4000 until the second pass of the compiler. The second pass of the compiler is described shortly.

Compilation of if...goto and let statements is more complicated than for other statementsthey are the only statements that produce more than one SML instruction. For an if...goto, the compiler produces code to test the condition and to branch to another line if necessary. The result of the branch could be an unresolved reference. Each of the relational and equality operators can be simulated using SML's branch zero or branch negative instructions (or a combination of both).

For a let statement, the compiler produces code to evaluate an arbitrarily complex arithmetic expression consisting of integer variables and/or constants. Expressions should separate each operand and operator with spaces. Exercise 21.12 and Exercise 21.13 presented the infix-to-postfix conversion algorithm and the postfix evaluation algorithm used by compilers to evaluate expressions. Before proceeding with your compiler, you should complete each of these exercises. When a compiler encounters an expression, it converts the expression from infix notation to postfix notation and then evaluates the postfix expression.

How is it that the compiler produces the machine language to evaluate an expression containing variables? The postfix evaluation algorithm contains a "hook" where the compiler can generate SML instructions rather than actually evaluating the expression. To enable this "hook" in the compiler, the postfix evaluation algorithm must be modified to search the symbol table for each symbol it encounters (and possibly insert it), determine the symbol's corresponding memory location and push the memory location onto the stack (instead of the symbol). When an operator is encountered in the postfix expression, the two memory locations at the top of the stack are popped and machine language for effecting the operation is produced, using the memory locations as operands. The result of each subexpression is stored in a temporary location in memory and pushed back onto the stack so that the evaluation of the postfix expression can continue. When postfix evaluation is complete, the memory location containing the result is the only location left on the stack. This is popped, and SML instructions are generated to assign the result to the variable at the left of the let statement.

Second Pass

The second pass of the compiler performs two tasks: Resolve any unresolved references, and output the SML code to a file. Resolution of references occurs as follows:

1. Search the flags array for an unresolved reference (i.e., an element with a value other than -1).
2. Locate the object in array symbolTable, containing the symbol stored in the flags array (be sure that the type of the symbol is 'L' for line number).
3. Insert the memory location from member location into the instruction with the unresolved reference (remember that an instruction containing an unresolved reference has operand 00).
4. Repeat Steps 1, 2 and 3 until the end of the flags array is reached.

After the resolution process is complete, the entire array containing the SML code is output to a disk file with one SML instruction per line. This file can be read by the Simpletron for execution (after the simulator is modified to read its input from a file). Compiling your first Simple program into an SML file and then executing that file should give you a real sense of personal accomplishment.

A Complete Example

The following example illustrates a complete conversion of a Simple program to SML as it will be performed by the Simple compiler. Consider a Simple program that inputs an integer and sums the values from 1 to that integer. The program and the SML instructions produced by the first pass of the Simple compiler are illustrated in Fig. 21.30. The symbol table constructed by the first pass is shown in Fig. 21.31.

Most Simple statements convert directly to single SML instructions. The exceptions in this program are remarks, the if...goto statement in line 20 and the let statements. Remarks do not translate into machine language. However, the line number for a remark is placed in the symbol table in case the line number is referenced in a goto statement or an if...goto statement. Line 20 of the program specifies that if the condition y == x is true, program control is transferred to line 60. Because line 60 appears later in the program, the first pass of the compiler has not as yet placed 60 in the symbol table (statement line numbers are placed in the symbol table only when they appear as the first token in a statement). Therefore, it is not possible at this time to determine the operand of the SML branch zero instruction at location 03 in the array of SML instructions. The compiler places 60 in location 03 of the flags array to indicate that the second pass completes this instruction.

We must keep track of the next instruction location in the SML array, because there is not a one-to-one correspondence between Simple statements and SML instructions. For example, the if...goto statement of line 20 compiles into three SML instructions. Each time an instruction is produced, we must increment the instruction counter to the next location in the SML array. Note that the size of Simpletron's memory could present a problem for Simple programs with many statements, variables and constants. It is conceivable that the compiler will run out of memory. To test for this case, your program should contain a data counter to keep track of the location at which the next variable or constant will be stored in the SML array. If the value of the instruction counter is larger than the value of the data counter, the SML array is full. In this case, the compilation process should terminate and the compiler should print an error message indicating that it ran out of memory during compilation. This serves to emphasize that, although the programmer is freed from the burdens of managing memory by the compiler, the compiler itself must carefully determine the placement of instructions and data in memory, and must check for such errors as memory being exhausted during the compilation process.

A Step-by-Step View of the Compilation Process

Let us now walk through the compilation process for the Simple program in Fig. 21.30. The compiler reads the first line of the program

5 rem sum 1 to x  

into memory. The first token in the statement (the line number) is determined using strtok (see Chapter 8 and Chapter 21 for a discussion of C++'s C-style string-manipulation functions). The token returned by strtok is converted to an integer using atoi, so the symbol 5 can be located in the symbol table. If the symbol is not found, it is inserted in the symbol table. Since we are at the beginning of the program and this is the first line, no symbols are in the table yet. So 5 is inserted into the symbol table as type L (line number) and assigned the first location in SML array (00). Although this line is a remark, a space in the symbol table is still allocated for the line number (in case it is referenced by a goto or an if...goto). No SML instruction is generated for a rem statement, so the instruction counter is not incremented.

The statement

10 input x  

is tokenized next. The line number 10 is placed in the symbol table as type L and assigned the first location in the SML array (00, because a remark began the program so the instruction counter is currently 00). The command input indicates that the next token is a variable (only a variable can appear in an input statement). Because input corresponds directly to an SML operation code, the compiler has to determine the location of x in the SML array. Symbol x is not found in the symbol table, so it is inserted into the symbol table as the ASCII representation of x, given type V, and assigned location 99 in the SML array (data storage begins at 99 and is allocated backward). SML code can now be generated for this statement. Operation code 10 (the SML read operation code) is multiplied by 100, and the location of x (as determined in the symbol table) is added to complete the instruction. The instruction is then stored in the SML array at location 00. The instruction counter is incremented by 1, because a single SML instruction was produced.

The statement

15 rem check y == x  

is tokenized next. The symbol table is searched for line number 15 (which is not found). The line number is inserted as type L and assigned the next location in the array, 01 (remember that rem statements do not produce code, so the instruction counter is not incremented).

The statement

20 if y == x goto 60  

is tokenized next. Line number 20 is inserted in the symbol table and given type L with the next location in the SML array 01. The command if indicates that a condition is to be evaluated. The variable y is not found in the symbol table, so it is inserted and given the type V and the SML location 98. Next, SML instructions are generated to evaluate the condition. Since there is no direct equivalent in SML for the if...goto, it must be simulated by performing a calculation using x and y and branching based on the result. If y is equal to x, the result of subtracting x from y is zero, so the branch zero instruction can be used with the result of the calculation to simulate the if...goto statement. The first step requires that y be loaded (from SML location 98) into the accumulator. This produces the instruction 01 +2098. Next, x is subtracted from the accumulator. This produces the instruction 02 +3199. The value in the accumulator may be zero, positive or negative. Since the operator is ==, we want to branch zero. First, the symbol table is searched for the branch location (60 in this case), which is not found. So 60 is placed in the flags array at location 03, and the instruction 03 +4200 is generated (we cannot add the branch location, because we have not assigned a location to line 60 in the SML array yet). The instruction counter is incremented to 04.

The compiler proceeds to the statement

25 rem increment y  

The line number 25 is inserted in the symbol table as type L and assigned SML location 04. The instruction counter is not incremented.

When the statement

30 let y = y + 1  

is tokenized, the line number 30 is inserted in the symbol table as type L and assigned SML location 04. Command let indicates that the line is an assignment statement. First, all the symbols on the line are inserted in the symbol table (if they are not already there). The integer 1 is added to the symbol table as type C and assigned SML location 97. Next, the right side of the assignment is converted from infix to postfix notation. Then the postfix expression (y 1 +) is evaluated. Symbol y is located in the symbol table, and its corresponding memory location is pushed onto the stack. Symbol 1 is also located in the symbol table, and its corresponding memory location is pushed onto the stack. When the operator + is encountered, the postfix evaluator pops the stack into the right operand of the operator, pops the stack again into the left operand of the operator and produces the SML instructions

The result of the expression is stored in a temporary location in memory (96) with instruction

and the temporary location is pushed on the stack. Now that the expression has been evaluated, the result must be stored in y (i.e., the variable on the left side of =). So the temporary location is loaded into the accumulator, and the accumulator is stored in y with the instructions

The reader will immediately notice that SML instructions appear to be redundant. We will discuss this issue shortly.

When the statement

35 rem add y to total  

is tokenized, line number 35 is inserted in the symbol table as type L and assigned location 09.

The statement

40 let t = t + y  

is similar to line 30. The variable t is inserted in the symbol table as type V and assigned SML location 95. The instructions follow the same logic and format as line 30, and the instructions 09 +2095, 10 +3098, 11 +2194, 12 +2094 and 13 +2195 are generated. Note that the result of t + y is assigned to temporary location 94 before being assigned to t (95). Once again, the reader will note that the instructions in memory locations 11 and 12 appear to be redundant. Again, we will discuss this shortly.

The statement

45 rem loop y  

is a remark, so line 45 is added to the symbol table as type L and assigned SML location 14.

The statement

50 goto 20  

transfers control to line 20. Line number 50 is inserted in the symbol table as type L and assigned SML location 14. The equivalent of goto in SML is the unconditional branch (40) instruction that transfers control to a specific SML location. The compiler searches the symbol table for line 20 and finds that it corresponds to SML location 01. The operation code (40) is multiplied by 100, and location 01 is added to it to produce the instruction 14 +4001.

The statement

55 rem output result  

is a remark, so line 55 is inserted in the symbol table as type L and assigned SML location 15.

The statement

60 print t  

is an output statement. Line number 60 is inserted in the symbol table as type L and assigned SML location 15. The equivalent of print in SML is operation code 11 (write). The location of t is determined from the symbol table and added to the result of the operation code multiplied by 100.

The statement

99 end  

is the final line of the program. Line number 99 is stored in the symbol table as type L and assigned SML location 16. The end command produces the SML instruction +4300 (43 is halt in SML), which is written as the final instruction in the SML memory array.

This completes the first pass of the compiler. We now consider the second pass. The flags array is searched for values other than -1. Location 03 contains 60, so the compiler knows that instruction 03 is incomplete. The compiler completes the instruction by searching the symbol table for 60, determining its location and adding the location to the incomplete instruction. In this case, the search determines that line 60 corresponds to SML location 15, so the completed instruction 03 +4215 is produced, replacing 03 +4200. The Simple program has now been compiled successfully.

To build the compiler, you will have to perform each of the following tasks:

1. Modify the Simpletron simulator program you wrote in Exercise 8.19 to take its input from a file specified by the user (see Chapter 17). The simulator should output its results to a disk file in the same format as the screen output. Convert the simulator to be an object-oriented program. In particular, make each part of the hardware an object. Arrange the instruction types into a class hierarchy using inheritance. Then execute the program polymorphically by telling each instruction to execute itself with an executeInstruction message.
2. Modify the infix-to-postfix conversion algorithm of Exercise 21.12 to process multidigit integer operands and single-letter variable name operands. [Hint: C++ Standard Library function strtok can be used to locate each constant and variable in an expression, and constants can be converted from strings to integers using standard library function atoi ().] [Note: The data representation of the postfix expression must be altered to support variable names and integer constants.]
3. Modify the postfix evaluation algorithm to process multidigit integer operands and variable name operands. Also, the algorithm should now implement the "hook" discussed previously so that SML instructions are produced rather than directly evaluating the expression. [Hint: Standard library function strtok can be used to locate each constant and variable in an expression, and constants can be converted from strings to integers using standard library function atoi.] [Note: The data representation of the postfix expression must be altered to support variable names and integer constants.]
4. Build the compiler. Incorporate parts (b) and (c) for evaluating expressions in let statements. Your program should contain a function that performs the first pass of the compiler and a function that performs the second pass of the compiler. Both functions can call other functions to accomplish their tasks. Make your compiler as object oriented as possible.

(Optimizing the Simple Compiler) When a program is compiled and converted into SML, a set of instructions is generated. Certain combinations of instructions often repeat themselves, usually in triplets called productions. A production normally consists of three instructions such as load, add, and store. For example, Fig. 21.32 illustrates five of the SML instructions that were produced in the compilation of the program in Fig. 21.30. The first three instructions are the production that adds 1 to y. Note that instructions 06 and 07 store the accumulator value in temporary location 96 and load the value back into the accumulator so instruction 08 can store the value in location 98. Often a production is followed by a load instruction for the same location that was just stored. This code can be optimized by eliminating the store instruction and the subsequent load instruction that operate on the same memory location, thus enabling the Simpletron to execute the program faster. Figure 21.33 illustrates the optimized SML for the program of Fig. 21.30. Note that there are four fewer instructions in the optimized codea memory-space savings of 25 percent.

Figure 21.32. Nonoptimized code from the program of Fig. 21.30.

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Modify the compiler to provide an option for optimizing the Simpletron Machine Language code it produces. Manually compare the nonoptimized code with the optimized code, and calculate the percentage reduction.

(Modifications to the Simple Compiler) Perform the following modifications to the Simple compiler. Some of these modifications may also require modifications to the Simpletron Simulator program written in Exercise 8.19.

1. Allow the modulus operator (%) to be used in let statements. Simpletron Machine Language must be modified to include a modulus instruction.
2. Allow exponentiation in a let statement using ^ as the exponentiation operator. Simpletron Machine Language must be modified to include an exponentiation instruction.
3. Allow the compiler to recognize uppercase and lowercase letters in Simple statements (e.g., 'A' is equivalent to 'a'). No modifications to the Simulator are required.
4. Allow input statements to read values for multiple variables such as input x, y. No modifications to the Simpletron Simulator are required.
5. Allow the compiler to output multiple values in a single print statement such as print a, b, c. No modifications to the Simpletron Simulator are required.
6. Add syntax-checking capabilities to the compiler so error messages are output when syntax errors are encountered in a Simple program. No modifications to the Simpletron Simulator are required.
7. Allow arrays of integers. No modifications to the Simpletron Simulator are required.
8. Allow subroutines specified by the Simple commands gosub and return. Command gosub passes program control to a subroutine, and command return passes control back to the statement after the gosub. This is similar to a function call in C++. The same subroutine can be called from many gosub commands distributed throughout a program. No modifications to the Simpletron Simulator are required.
9. Allow repetition statements of the form

   for x = 2 to 10 step 2

        Simple statements

   next

   This for statement loops from 2 to 10 with an increment of 2. The next line marks the end of the body of the for. No modifications to the Simpletron Simulator are required.

10. Allow repetition statements of the form

    for x = 2 to 10

         Simple statements

    next

    This for statement loops from 2 to 10 with a default increment of 1. No modifications to the Simpletron Simulator are required.

11. Allow the compiler to process string input and output. This requires the Simpletron Simulator to be modified to process and store string values. [Hint: Each Simpletron word can be divided into two groups, each holding a two-digit integer. Each two-digit integer represents the ASCII decimal equivalent of a character. Add a machine-language instruction that will print a string beginning at a certain Simpletron memory location. The first half of the word at that location is a count of the number of characters in the string (i.e., the length of the string). Each succeeding half word contains one ASCII character expressed as two decimal digits. The machine-language instruction checks the length and prints the string by translating each two-digit number into its equivalent character.]
12. Allow the compiler to process floating-point values in addition to integers. The Simpletron Simulator must also be modified to process floating-point values.

(A Simple Interpreter) An interpreter is a program that reads a high-level language program statement, determines the operation to be performed by the statement and executes the operation immediately. The high-level language program is not converted into machine language first. Interpreters execute slowly because each statement encountered in the program must first be deciphered. If statements are contained in a loop, the statements are deciphered each time they are encountered in the loop. Early versions of the BASIC programming language were implemented as interpreters.

Write an interpreter for the Simple language discussed in Exercise 21.26. The program should use the infix-to-postfix converter developed in Exercise 21.12 and the postfix evaluator developed in Exercise 21.13 to evaluate expressions in a let statement. The same restrictions placed on the Simple language in Exercise 21.26 should be adhered to in this program. Test the interpreter with the Simple programs written in Exercise 21.26. Compare the results of running these programs in the interpreter with the results of compiling the Simple programs and running them in the Simpletron Simulator built in Exercise 8.19.

(Insert/Delete Anywhere in a Linked List) Our linked list class template allowed insertions and deletions at only the front and the back of the linked list. These capabilities were convenient for us when we used private inheritance and composition to produce a stack class template and a queue class template with a minimal amount of code by reusing the list class template. Actually, linked lists are more general than those we provided. Modify the linked list class template we developed in this chapter to handle insertions and deletions anywhere in the list.

(List and Queues without Tail Pointers) Our implementation of a linked list (Figs. 21.321.5) used both a firstPtr and a lastPtr. The lastPtr was useful for the insertAtBack and removeFromBack member functions of the List class. The insertAtBack function corresponds to the enqueue member function of the Queue class. Rewrite the List class so that it does not use a lastPtr. Thus, any operations on the tail of a list must begin searching the list from the front. Does this affect our implementation of the Queue class (Fig. 21.16)?

Use the composition version of the stack program (Fig. 21.15) to form a complete working stack program. Modify this program to inline the member functions. Compare the two approaches. Summarize the advantages and disadvantages of inlining member functions.

(Performance of Binary Tree Sorting and Searching) One problem with the binary tree sort is that the order in which the data is inserted affects the shape of the treefor the same collection of data, different orderings can yield binary trees of dramatically different shapes. The performance of the binary tree sorting and searching algorithms is sensitive to the shape of the binary tree. What shape would a binary tree have if its data was inserted in increasing order? in decreasing order? What shape should the tree have to achieve maximal searching performance?

(Indexed Lists) As presented in the text, linked lists must be searched sequentially. For large lists, this can result in poor performance. A common technique for improving list searching performance is to create and maintain an index to the list. An index is a set of pointers to various key places in the list. For example, an application that searches a large list of names could improve performance by creating an index with 26 entriesone for each letter of the alphabet. A search operation for a last name beginning with 'Y' would first search the index to determine where the 'Y' entries begin and "jump into" the list at that point and search linearly until the desired name is found. This would be much faster than searching the linked list from the beginning. Use the List class of Figs. 21.321.5 as the basis of an IndexedList class. Write a program that demonstrates the operation of indexed lists. Be sure to include member functions insertInIndexedList, searchIndexedList and deleteFromIndexedList.