(chapter 2) A Concise and Practical Introduction to Programming Algorithms in Java

1A Concise and Practical Introduction to Programming Algorithms in Java © 2009 Frank Nielsen
1
Frank NIELSEN
nielsen@lix.polytechnique.fr
A Concise and
Practical
Introduction to
Programming
Algorithms in Java
Chapter 2: Conditional structures and loops

Upper case versus Lower case
Java distinguishes between
uppercases (A..Z) and lowercases (a..z)
Unix differentiates upper/lower case filenames
class UpperLowerCase
{
public static void main (String arguments[])
{
int MyVar;
// this variable is different from MyVar
int myvar;
// Generate a syntax error at compile time:
// cannot find symbol variable myVar
System.out.println(myVar);
}
}

Reserved keywords
Reserved keywords in Java:
You cannot choose reserved keywordsreserved keywords for variable names:
class ReservedKeyword
{public static void main (String arg[]){
double x,y;
// Generate a syntax error:
// "not a statement"
int import;
}
}

Displaying versus Computing
●
You need to display if you'd like to see the result of
evaluating an expression
●
System.out.println displays on the console with a return carriage
●
System.out.print displays on the console without a return carriage
Java is not Maple nor SciLab!
Confusing in Maple:
Interpreter: compute:display

Output: Displaying values & messages
● System.out.println(stringname): displays a string with a return carriage
● System.out.print(stringname): displays a string without return line
● System.out.println(value): converts (cast) numerical value into a string
and displays it
● System.out.println(''The value of x is ''+x):
Converts the numerical value of x into a string and concatenate that string
with the constant string '' The value of x is ''
Display=write to console or to text file if it is redirected (as in java toto > result.txt )

More on System.out.print[ln]
Equivalences of stream output:
System.out.print(''n'') = System.out.println('''');
System.out.print(''Hello INF311 n'') = System.out.println(''INF311'');
Priority order+casting operations...

Display: String concatenations...
Cumbersome to type several
System.out.println and System.out.print
Shortcut: String concatenations « + »...
int a=1, b=-2;
System.out.print("a="); System.out.print(a);
System.out.print(" b="); System.out.println(b);
System.out.println("a="+a+" b="+b);
String s1="Lecture in", s2=" Java";
String s=s1+s2;// string concatenation
System.out.println(s);
Operator (expression)

/* Declare a constant (not a variable)
to bypass using Math.PI */
final double PI = 3.14; // constant
Declaring constants
Numeric bug in predicate !// Constant
final double PI = 3.14;
int a=1;
double b=a+PI;
if (b==4.14) // Equality test are dangerous!!!
System.out.println("Correct result");
else
{System.out.println("Incorrect result");
System.out.println("a="+a+" b="+b+" PI="+PI);
}
}

Syntax and compilation
Syntax errors are easy program bugs (mistyping?)
...But syntaxically correct program may be difficult to understand
Protecting Java Source with Code obsfucation
Avoid reverse engineering of applications
int i=3;
// syntax below is valid!
int var=i+++i;
What is the value of var?

Program: Data,computations + workflow
The control structures define the set of instructions being executed
(aiguillage des trains)
For example, a branching condition:
if (a<b) [then]
c=a; // Do-something-1
else
c=b; // Do-something-2
There are two potential instructions paths depending on the predicate:
● a<b, -> c=a;
or
● a>=b, -> c=b;
c is selected as
the minimum
of a and b
In Java, we do not use the word then

ControlingControling program workflow
Two kinds:
● Branching tests: (if else, switch)
● Repeat structure: Loop (while, for)
Predicate: true or false
if there is a numerical error at
that stage we take the wrong
flow and this yields a bug, with
potential desastrous effects.
Key difference with maths.

Annotating programs: comments!
Writing comments is good for (1) yourself and
for (2) others to proofread and debug your code
In fact, there are some paradigms to write in a single file both
● the clean documentations, and
● the code.
Exempla gratia (e.g.) cweb, Literate programming, etc.
http://www.literateprogramming.com/
In INF311, we rather write short programs, so we consider the standard comments:
// This is a single line comment
/* I can also write comments on
several lines
by using these delimiters */
D. Knuth

Comments: single versus multiple lines
(Jcreator IDE)

Comments...
with errors!
The compiler is verbose: Try to fix the first error first (greedy approach)

Comments...
repaired... = Syntaxically correct program
Do not forget:
Writing good comments is as important as writing source code
You will thank yourself for doing this once you look back at your programs months later

Structures of Java programs
● Comments // or /* */
● Constants (Math.PI, etc.)
● Variables (typed) with valid identifiers (not reserved keyword)
● Operators +,-,/,%, etc. for expressions
● Reserved language keywords: if, for, while, etc.
A set of instructions is called a block
Blocks can be delimited by parenthesis {Block}
{ // This is a block
// (non control structure inside it)
var1=Expression1;
var2=Expression2;
var3=Expression3;
...
}

Structures of java programs: Blocks
Block 2
Block 1
Principal block

Conditional structures:
if (predicate) Block1 else Block2
Essential control structure for executing a (block of) operations if a condition is true
(or false for the else-Block)
if (condition) Instruction
if (condition) {
Instruction1;
Instruction2;
Instruction3;
... ;
}
if (condition)
BlockForTrueCase
else
BlockForFalseCase
Block=sequence of instructions
predicate

Conditional structures: Compact form
if (predicate) Inst1 else Inst2
Conditional instruction for singe instruction block can be called
using the ternary operator (3 operands) « ? : »
BoolOperand1 ? TypeOperandTrue2 : TypeOperandFalse3
2.718281828459045 difference with max=0.423310825130748
double x1=Math.PI;
double x2=Math.E;
double min=(x1>x2)? x2 : x1; // min value
double diff= (x1>x2)? x1-x2 : x2-x1; // absolute val.
System.out.println(min+" difference with max="+diff);

Instructions and conditions
Instructions always terminate with a semi colon ;
(except potentially the last one in a block)
A set of instructions encapsulated in { } is a block
The block has the same syntax as an instruction
Variables can be declared in a block
A condition is a boolean expression
that returns either true or false :
= A predicate

Variables and blocks
Very different from C++!
(Java better controls the syntax of programs, better semantic)
We cannot declare twice a same variable in encapsulated block

Variables and blocks: Scopes
Error!!! Variable l is not defined in the block it here

Boolean operators for comparisons
a==b Test of equality (for basic types)
a!=b Test for difference [ equivalent to ! (a==b) ]
Inequalities:
a<b True if and only if (iff.) a<b
a<=b True iff. a<b or a=b
a>b True iff. a>b
a>=b True iff. a>b or a=b
Beware: a=b is assignment not test (test of equality is ==)
Typing helps you avoid this mistake:
int a=3;
if (a=3) System.out.println("THEN-PART");
else System.out.println("ELSE-PART");
incompatible types found : int
required: boolean

(6-2) == 4 evalutes to true but 22/7 == 3+1.0/7 evaluates to false
Boolean comparisons are of type boolean
class Boolean{
public static void main(String[] args)
{
boolean b1 = (6-2) == 4;
boolean b2 = 22/7 == 3+1/7.0 ;
boolean b3 = 22/7 == 3+ 1/7;
System.out.println(b1); // true
System.out.println(b2); // false
System.out.println(b3); // true
}
}

More on boolean operators: Tables
Unary operator:Unary operator:
NOT !
BinaryBinary connector operatorsconnector operators::
AND &&
OR ||

Priority order for boolean expressions
Lazy evaluation of boolean binary operators:
● If a is false we do not need to evaluate b in a && b
● If a is true we do not need either to evaluate b in a || b

Few remarks
Key difference between assignment (=) and logical test ==
Do not forget the semi-colon at the end of Instructions;
Indent your code and structure it into blocks for clarity
Think of nested if control structures
if (condition1)
{BlockT1;}
else
{
if (condition2)
{BlockT2;}
else{BlockF2;}
}
Nested if

Nested conditionals (nested if)
Set curly brackets { } to increase code readibility

Loops: While/do for iterations
Structure for iterating
● Process a single instruction or a block until the given boolean expression is true
(thus may loop forever... and program may not terminate)
● Boolean expression is re-evaluated at each round
● We can exit the loop at any time using the keyword break;
while (boolean_expression)
single_instruction;
while (boolean_expression)
{ block_instruction;}
do
while (boolean_expression);
At least, the loop
is executed once.

Loops: Euclid' GCD algorithm
While
Do
Greatest common divisor of two integers a and b

Loops: Newton's method
Converge to a root of the function f
Setting
y=f'(xprev)(x-xprev)+f(xprev)=0
give new value for x
Use to calculate the square root function
f(x)=x*x-a
double a = 2.0, x, xold;
x = a;
do{
xold = x;
// compute one iteration
x = (xold+a/xold)/2;
System.out.println(x);
} while(Math.abs(x-xold) > 1e-10);
1.5
1.4166666666666665
1.4142156862745097
1.4142135623746899
1.4142135623730949

Loops:
Syracuse and termination conjecture
do
while (boolean_expression);
Nobody knows whether this programs stops for any given input (open problem)
No counter example from simulation so far but no termination proof too!
Replace x by x/2 (for x odd) and x by 3x+1 (for x even)
Start from any given x, does the replacing alway terminate (x=1)
do{
if ((n%2)==0)
n/=2;// divide by 2
else
n=3*n+1;
} while (n>1);

Loops: Perpetual movements...
Always ensure that loops terminate when programming
int i=0;
while (true)
i++;
for(i=0;i>=0;i++)
; // common mistyping error
for(i=0;i>=0;i++)
{ }
Easy to do when programming.... ESC key or Control-C to escape!

Loops: Breaking the loop with break
Read a sequence of non-negative natural integers and
compute the cumulative sum of the sequence.
Observe the shortcut:
sum+=n; that is equivalent to assignment sum=sum+n;

Loops: For... iterations
● Allows one to execute a block of instructions, and
● Increment the counter at each round
● Semantically equivalent to a while loop
● Often used for program readibility (e.g., for a range of integers)
for(instruction1; boolean_condition; instruction2)
block_instruction3;
instruction1;
while (boolean_condition)
{block_instruction3;
instruction2;}
Equivalence with While construction

Loops: For... iterations
for(instruction1; boolean_condition; instruction2)
block_instruction3;
class ForLoop
{
public static void main(String args[])
{
int i, n=10;
int cumulLoop=0;
for(i=0;i<n;i++) cumulLoop+=i;
int cumul=(n*(n-1))/2; // closed-form solution
System.out.println(cumulLoop+" closed-form:"+cumul);
}
} We get 45

int cumulLoop=0;
for(i=0;i<n;i++) cumulLoop+=i;
Loops: For... iterations (unlooping)
int cumulLoop=0;
i=0; // Initialization
cumulLoop+=i;
i++; // i=1 now
// i<n so we continue...
cumulLoop+=i;
i++; // i=2 now
// i<n so we continue...
cumulLoop+=i;
...
cumulLoop+=i; // i=n-1
i++; // i=n now
// i is not i<n so we stop...
Unlooping...

Examples of for loop: IsPrime
Program that determines whether a given integer is prime or not.
209=11x19

Multiple choices: switch
Avoid nested if-else structures for multiple choices
class ProgSwitch
{public static void main(String arg[]){
System.out.print("Input a digit in [0..9]:");
int n=TC.lireInt();
switch(n)
{
case 0: System.out.println("zero"); break;
case 1: System.out.println("one"); break;
case 2: System.out.println("two"); break;
case 3: System.out.println("three"); break;
default: System.out.println("Above three!");
break;
}}}

Natural integers and int
Difference between mathematics (infinite precision) and computing.
Computing: discrete algorithms working on finite representations
of numbers
Source of many bugs !!!
Typically, an algorithm can be correct but its implementation
buggy because of numerical errors.
int: maximum machine-representable int is 2^31-1
(in the old days, written as 2**31-1)
long: maximum machine-representable long is 2^63-1

Overflow problems...
A toy example
Computes 2^s, but at some point 2^64 cannot fit 64-bit, we get first
- negative number (leading bit set to 1 by the arithmetic logic unit - ALU)
- then zero!!!!

Overflow problems: revisited
Declaration
inside the For
Increment:
i++
or
++i
Multiplication is just
a bit shift << to the right

Floating points & numerical precisions
64-bit IEEE 754 floating point.
http://en.wikipedia.org/wiki/IEEE_floating-point_standard
● float (32-bit) or double (64-bit) have sign, exponent and matissa parts
● Examples: float a=0.3; float b=2e-8 (scientific engineering); float c=1.1f;
● Math class contains important ''constants'': Math.PI, Math.E, etc.
and transcendental functions: Math.log(), Math.exp(), Math.sin(), Math.cos()
32-bit IEEE 754 floating point.

Loosing numerical precision...
A bug
Usually, difficult to
test for the zero
(use threshold or better analysis)

Loosing associativity rule
Rounding & truncations to fit the standard yields the loss of associativity
Better to add numbers having already the same exponent decomposition...

Computing Euler-Mascheroni 's constant

Types and conversions: Cast operator
● All variables and constants are typed: Math.PI is a (static) double
● Variables should be declared according to their type: double x; int i; etc
● The type of variable determines the operator and meaning:
Exempla gratia, 3.0+2.1 (double) or ''Hello ''+'' INF311'' (String)
● The expression is also typed (by the compiler)
● For assignment =, the left-hand side (variable) and right-hand side (expression)
should have the same type.
Casting types
with parenthesis (type):
double x=3.14;
int i=(int)x;
double x=(double)i;

Converting strings to numbers...
Use Type.parseType(String stringtoparse)

Declaring functions in Java
class INF311{
public static typeF F(type1 arg1, ..., typeN argN)
{
// Description
Block of instructions;
}
}
● This kind of function is also called a static method
● Functions must be defined inside classes
● A function not returning a result has type void
(also known as a procedure)
A glimpse at functions

Defining the body of a function in Java
class INF311{
public static typeF F(type1 arg1, ..., typeN argN)
{
// Description
Block of instructions;
}
}
Body of a function
Body should contain an instruction return to indicate the result
If branching structures are used (if or switch) ,
then a return should be written for all different branches.
Otherwise we get a compiler error! (why? => not type safe!)

A few examples of basic functions
class FuncDecl{
public static int square(int x)
{return x*x;}
public static boolean isOdd(int p)
{if ((p%2)==0) return false; else return true;}
public static double distance(double x, double y)
{if (x>y) return x-y; else return y-x;}
public static void display(double x, double y)
{System.out.println("("+x+","+y+")");
return; // return void
}
public static void main (String[] args)
{
display(square(2),distance(5,9));
int p=123124345;
if (isOdd(p)) System.out.println("p is odd");
else System.out.println("p is even");
}
}

53

(chapter 2) A Concise and Practical Introduction to Programming Algorithms in Java

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(chapter 2) A Concise and Practical Introduction to Programming Algorithms in Java