Arrays - ETH Z · 2019. 3. 4. · Dennis Komm Programming and Problem Solving Arrays, Strings, and...

Dennis Komm

Programming and Problem SolvingArrays, Strings, and Methods

Spring 2019 – March 4, 2019

Arrays

Arrays

Declare array variables: int[] z; z

Create an array: z = new int[5];

z[1] z[2] z[3] z[4]z[0]

z is a reference to the array data,but only after the assignment to the created dataotherwise it points to nowhere: nullElements are indexedthe first index is 0 and the last index is array size− 1Element access: name[index]

Programming and Problem Solving – Arrays, Strings, and Methods Spring 2019 Dennis Komm 1 / 50

Arrays

int[] b;int b[];

ï b is array variable, but array does not exist yet

b = new int[10];

ï With new memory is assigned to b

int[] b = new int[10];

ï Both can be combined

int[] b = {9,6,3,6,2,1,6,8,3};

ï Values can be given immediatelyProgramming and Problem Solving – Arrays, Strings, and Methods Spring 2019 Dennis Komm 2 / 50

Arrays are Dynamic Objects

Arrays are always created dynamically

int[] b;b = new int[10]; // 10 elements with index 0,...,9...b = new int[20]; // can be reassigned

Size of an array can be set at runtime

But an array does not grow automatically


Arrays are Dynamic Objects

int sq = new int[7];for (int i = 0; i < sq.length; ++i) {

sq[i] = i * i;}sq[8] = 64; java.lang.ArrayIndexOutOfBoundsException

// output array:for (int i = 0; i < a.length; ++i) {

Out.println("a[" + i + "]=" + a[i]);}


Array Assignments

When assigning arrays, references are being copied, not data

int[] z = new int[5];

for (int i=0; i < z.length; ++i) {z[i] = i*i;

}

int[] x = z;

int j = x[2];

x[1] = 99;

z

0 1 4 9 16

x

4

j

99


Idea – Counting Digits

6 5 4 2 4 5 7 8 9 1 1 3 2 4 5

0

0

0

1

0

2

0

3

0

4

0

5

0

6

0

7

0

8

0

9

1111 2 2 1 1 112 12 3 3


Exercise – Counting Digits

Write an algorithm that

takes an (unsorted) array xcontaining numbers from the range[0, . . . , 9]outputs for each number, how manytimes it occurs in x


Counting Digits

public class CountNumbers {public static void main(String[] args) {

int[] numbers = {6, 5, 4, 2, 4, 5, 7, 8, 9, 1, 1, 3, 2, 4, 5};int[] index = new int[10];

for (int i = 0; i < numbers.length ; i++) {index[numbers[i]]++;

}

for (int i = 0; i < index.length ; i++) {Out.println("Count (" + i + ")=" + index[i]);

}}

}Programming and Problem Solving – Arrays, Strings, and Methods Spring 2019 Dennis Komm 8 / 50

ArraysMultidimensional Arrays

Multidimensional Arrays

double[][] matrix = new double[4][4];

m


Multidimensional Arrays

double[][] matrix = new double[4][4];

// Identity matrixfor (int r=0; r < matrix.length; ++r) {

for (int c=0; c < matrix[r].length; ++c) {if (r==c) {

matrix[r][c] = 1;} else {

matrix[r][c] = 0;}

}}


Multidimensional arrays

A two-dimensional array is an array of references to a one-dimensional array

double[][] matrix = ...;

for (int r = 0; r < matrix.length; ++r) {double[] vector = matrix[r];for (int c = 0; c < vector.length; ++c) {

Out.print(vector[c] + " ");}Out.println();

}


Multidimensional arrays

Even the following is possible

double[][] m = new double[5][];for (int r = 0; r < m.length; ++r) {

m[r] = new double[r+1];}

m


ArraysArray Comparisons

Array Comparisons

Arrays are references

double[] x = {1,2,3};double[] y = x;double[] z = {1,2,3};

if (y == x) {...} // y==x is trueif (z == x) {...} // z==x is false

if (z.equals(x)) {...} // z.equals(x) is also falseif (Arrays.equals(x,z)) {...} // Arrays.equals(x,z) is true

Attention when using Arrays.equals on multidimensional arrays


Strings

Strings

Strings are objects that store character arrays

String name = "Informatics";String university = "ETH";String lecture = name + " at " + university;int x = 3;int y = 5;String coordinates = "(" + x + "," + y + ")"; // "(3,5)"


Strings

Evaluation order

int x = 3;int y = 5;String s1 = x + y + "X"; // s1 = "8X"String s2 = "X" + x + y + ""; // s2 = "X35"


Characters

Elements of strings can be accessed by index (but not replaced)

String info = "Informatics";char c = info.charAt(3); // c = ’o’

Strings are references as well

info

I

0

n

1

f

2

o

3

r

4

m

5

a

6

t

7

i

8

c

9

s

10


StringsString Comparisons

String Comparisons

The comparison with “==” again compares references, not content

String n1 = In.readWord();String n2 = In.readWord();if (n1 == n2) {

Out.println(n1 + "==" + n2);} else {

Out.println(n1 + "!=" + n2);}

Input: Info, Info

Output: Info != Info


String Comparisons

The comparison with “equals” compares the content (this does not apply toarrays)

String n1 = In.readWord();String n2 = In.readWord();if (n1.equals(n2)) {

Out.println(n1 + " equals " + n2);} else {

Out.println(n1 + " does not equal " + n2);}

Input: Info, Info

Output: Info equals Info


Methods

Methods

Code fragments can be assembled in methods

Advantages

Define once – use several times

Clearer, more readable code, easier to comprehend

Code in methods can be tested easier


Example – Cookie Calculator

public class Keksrechner {public static void main(String[] args) {

Out.print("Kinder: ");int kinder = In.readInt();

Out.print("Kekse: ");int kekse = In.readInt();

Out.println("Jedes Kind kriegt " + kekse / kinder + " Kekse");Out.println("Papa kriegt " + kekse % kinder + " Kekse");

}}

We want to make sure that kinder is positive and that each child gets atleast one cookie


Cookie Calculator – Check Input

From this . . .

Out.print("Kinder: ");int kinder = In.readInt();

. . . we go to this

int kinder;do {

Out.print("Kinder: ");kinder = In.readInt();if (kinder < 1) {

Out.println("Wert zu klein. Mindestens " + 1);}

} while (kinder < 1);

Analogously, we have to check that kekse >= kinderProgramming and Problem Solving – Arrays, Strings, and Methods Spring 2019 Dennis Komm 21 / 50

Cookie Calculator – Getting Complicated


int kinder;

do {Out.print("Kinder: ");kinder = In.readInt();if (kinder < 1) {

Out.println("Wert zu klein. Mindestens " + 1);}

} while (kinder < 1);

int kekse;

do {Out.print("Kekse: ");kekse = In.readInt();if (kekse < kinder) {

Out.println("Wert zu klein. Mindestens " + kinder);}

} while (kekse < kinder);

Out.println("Jedes Kind kriegt " + kekse / kinder + " Kekse");Out.println("Papa kriegt " + kekse % kinder + " Kekse");

}}

Read and check num-ber of children

Read and check num-ber of cookies


Cookie Calculator – Takeaway

The two code fragments are nearly identical

The following aspects are different:The prompt, i.e., "Kinder: " vs. "Kekse: "The minimum, i.e., “1” vs. “kinder”

We can outsource the code fragment into a method and thus feature reuse

We have to parameterize the different aspects


MethodsDeclaration of a Method

Declaration of a Method

private static int checkInt(String prompt, int min) {...}

modifiers

return type of the method

name of the method

parameter list

implementation


Declaration of a Method

Modifiers: Will be treated later

Return type: Data type of the return value; if the method does not return avalue, this type is void

Name: A valid name; should be starting with a lower letter

Parameter list: List of parameters surrounded by parentheses, declared bydata type and name; parameters are set when method is called; can be usedlike local variables

Implementation: The code that is executed when the method is called


Method Signature

private static int checkInt(String prompt, int min) { ...}

Signature of the method

Signature is unique within a class

It is thus possible to have several methods with the same name but differentnumbers or types of parameters. – not recommended

Return type is not part of the signature; it is not possible to have severalmethods that are only distinguishable by their return type


MethodsPass by Value

Method Call – Pass By Value

A method call is an expression with the return value of the method

In Java we always have pass by value semantics

Pass by value means that argument values are copied into theparameters upon method call

This corresponds to the same principle as the assignment to a variable


Method Call – Pass By Value

// Methodenaufrufint kekse = checkInt( "Kekse: " , kinder );

private static int checkInt( String prompt , int min ) {// ...

}

K e k s e :

prompt

copy of the reference

5

5

min

copy of the value


Back to the Example – Method checkInt

private static int checkInt(String prompt, int min) {int number;do {

Out.print(prompt);number = In.readInt();if (number < min) {

Out.println("Wert zu klein. Mindestens " + min);}

} while (number < min);return number;

}


MethodsReturn Values

Return Values of Methods

Return type = void: The evaluation of the method can be ended with thestatement return

Return type 6= void: The evaluation of the method must happen via“return value”. The value is passed back to the calling method.

Important

In the second case every possible finite execution path must contain areturn statement


Return Values on All Execution Paths

Correct

private static int checkInt(String prompt, int min) {int number;do {

Out.print(prompt);number = In.readInt();if (number < min) {

Out.println("Wert zu klein. Mindestens " + min);}

} while (number < min);

return number;}

Is reached always if the method termi-nates at all.



Solution identical with regards to content

private static int checkInt(String prompt, int min) {

int number;while (true) {

Out.print(prompt);

number = In.readInt();

if (number >= min) return number;

Out.println("Wert zu klein. Mindestens " + min);

};}

Compiler understands the infinite loop and accepts

that “return” can only occur here.



Solution identical with regards to content

private static int checkInt(String prompt, int min) {

int number;do {

Out.print(prompt);

number = In.readInt();

if (number >= min) return number;

Out.println("Wert zu klein. Mindestens " + min);

} while (number < min);return 0;

}

Fulfills the “return” on each path. Actually

that cannot be reached. (. . . Why not?)


Cookie Calculator – More Comprehensible


int kinder = checkInt("Kinder: ", 1);int kekse = checkInt("Kekse: ", kinder);

Out.println("Jedes Kind kriegt " + kekse/kinder + " Kekse");Out.println("Papa kriegt " + kekse % kinder + " Kekse");

}

private static int checkInt(String prompt, int min) {// ... see previous slidereturn number;

}}


MethodsPre- and Postconditions

Pre- and Postconditions

characterize (as complete as possible) what a Method does

document the method for users and programmers (we or other people)

make programs more readable: we do not have to understand how themethod works

are ignored by the compiler

Pre and postconditions render statements about the correctness of a programpossible – provided they are correct


pow

public static double pow(double b, int e) {double result = 1.0;if (e < 0) { // b^e = (1/b)^(-e)

b = 1.0/b;e = -e;

}for (int i = 0; i < e; ++i) {

result *= b;}return result;

}


Scope of Formal Arguments

public static double pow(double b, int e) {double r = 1.0;if (e

Preconditions

Precondition

What is required to hold when the method is called?

Defines the domain of the method

Examples

0e is undefined for e < 0

// PRE: e >= 0 || b != 0.0


Postconditions

Postcondition

What is guaranteed to hold after the method call?

Specifies value and effect of the method call

Example

Here only value, no effect

// POST: return value is b^e



should be correct

if the precondition holds when the method is called then also thepostcondition holds after the call

Example

Method pow works for all numbers b 6= 0



We do not make a statement about what happens if the precondition does nothold

Examples

Method pow: division by 0



Pre-condition should by as weak as possible (large domain of definition)

Post-condition should be as strong as possble (detailled statement)


Example – pow

// PRE: e >= 0 || b != 0.0// POST: return value is b^epublic static double pow(double b, int e) {

double result = 1.0;if (e < 0) { // b^e = (1/b)^(-e)

b = 1.0/b;e = -e;

}for (int i = 0; i < e; ++i) {

result *= b;}return result;

}


Example – xor

// post: returns l XOR rpublic static boolean xor(boolean l, boolean r) {

return l && !r || !l && r;}


Example – harmonic

// PRE: n >= 0// POST: returns nth harmonic number// computed with backward sumpublic static float harmonic(int n) {

float res = 0;for (int i = n; i >= 1; --i) {

res += 1.0f / i;}return res;

}


Example – min

// POST: returns the minimum of a and bpublic static int min(int a, int b) {

if (a= 0 || b != 0.0// POST: return value is bê

is formally incorrect

Overflow if e or b are too large

be potentially not representable as a double (holes in the domain)


White Lies. . . are Allowed

// PRE: e >= 0 || b != 0.0// POST: return value is bê

The exact pre- and postconditions are platform-dependent and oftencomplicated

We abstract away and provide the mathematical conditions

ï Compromise between formal correctness and lax practice


Checking Preconditions. . . with Asserts

Preconditions are only comments

How can we ensure that they hold when the method is called?

// PRE: e >= 0 || b != 0.0// POST: return value is bêpublic static double pow(double b, int e) {

assert e >= 0 || b != 0 : "division by zero";double result = 1.0;...

}


Postconditions with Asserts

The result of “complex” computations is often easy to check

Then the use of asserts for the postcondition is worthwhile

// PRE: the discriminant p*p/4 - q is nonnegative// POST: returns larger root of the polynomial x^2 + p x + qpublic static double root(double p, double q) {

assert(p*p/4 >= q); // preconditiondouble x1 = - p/2 + sqrt(p*p/4 - q);assert(equals(x1*x1+p*x1+q,0)); // postconditionreturn x1;

}


ArraysMultidimensional ArraysArray Comparisons

StringsString Comparisons

MethodsDeclaration of a MethodPass by ValueReturn ValuesPre- and Postconditions

Arrays - ETH Z · 2019. 3. 4. · Dennis Komm Programming and Problem Solving Arrays, Strings, and...

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