Arrays

Problem

Thirty grades

A teacher writes a program for the test scores. For five students they make five variables:

int score1 = 62;
int score2 = 85;
int score3 = 47;
int score4 = 91;
int score5 = 78;
int sum = score1 + score2 + score3 + score4 + score5;
System.out.println(sum);

Output

363

But the class has thirty students. Thirty variables, thirty terms to add. And the highest score needs twenty-nine more comparisons. The loop from the last lesson does not help: it cannot go through score1, score2, score3, because those are separate names. We need many values under one name.

The idea

An array: a row of boxes

An array is a row of values of one type under one name. Each value, an element of the array, has a number: its index. Indexes start at 0.

int[] scores = { 62, 85, 47, 91, 78 };
System.out.println(scores[0]);
System.out.println(scores[4]);
System.out.println(scores.length);
scores[2] = 50;
System.out.println(scores[2]);

Output

62
78
5
50

• int[] is the type: "an array of int". The values go in { }.

• scores[0] is the first element, scores[4] the fifth. The last index is always 1 less than the count.
• scores.length is the number of elements. Here it is 5.
• scores[2] = 50; changes one element. The others stay the same.

If you don't know the values yet, you create the array with just a size. Then all the elements are 0:

int[] booked = new int[3];
booked[1] = 2;
System.out.println(booked[0] + " " + booked[1] + " " + booked[2]);

Output

0 2 0

The size is set when the array is created, and it does not change after that.

More precisely, if you are curious

• Indexes go only from 0 to the count minus 1. A negative index is outside the array.

Try it

Which is which?

What will the program print?

int[] prices = { 12, 7, 30, 5 };
System.out.println(prices[1] + prices[3]);

Answer

42

19

12

Check

The idea

A loop through the array

Now the loop does help. The counter i becomes the index: it goes from 0 to the last one and on every round takes scores[i].

int[] scores = { 62, 85, 47, 91, 78 };
int sum = 0;
for (int i = 0; i < scores.length; i++) {
    sum += scores[i];
}
System.out.println("Sum: " + sum);
System.out.println("Average: " + (double) sum / scores.length);

Output

Sum: 363
Average: 72.6

The condition is i < scores.length, not a number. If you add all thirty grades in { }, the loop does not change. This is called traversing the array.

(double) is needed because of integer division: 363 / 5 is 72, and we need 72.6.

See it

The highest score

How do you find the biggest number? You remember the biggest one so far and replace it as soon as you see a bigger one.

int[] scores = { 62, 85, 47, 91, 78 };
int max = scores[0];
for (int i = 1; i < scores.length; i++) {
    if (scores[i] > max) {
        max = scores[i];
    }
}
System.out.println(max);  // 91

Step by step, in words

1. Five scores, side by side. The numbers below are the indexes: from 0 to 4.
2. max starts from the first one: scores[0] is 62.
3. i = 1: 85 > 62, so max becomes 85.
4. i = 2: 47 is not bigger than 85. Nothing changes.
5. i = 3: 91 > 85, so max becomes 91.
6. i = 4: 78 < 91. Then i becomes 5, 5 < scores.length is false, and the loop stops.
7. The highest score is 91.

max starts from the first element, not from 0. If all the scores were negative, 0 would "win" without being in the array. That is also why the loop starts from i = 1: the first one is already in max.

Try it

Find the bug

The program should print the sum 363. Instead it stops with an error:

Error

Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: Index 5 out of bounds for length 5

Which line has the bug?

Pick the line with the bug.

1int[] scores = { 62, 85, 47, 91, 78 };2int sum = 0;3for (int i = 0; i <= scores.length; i++) {4 sum += scores[i];5}6System.out.println(sum);

Check

The idea

for-each: for every element

When you need only the values and not the indexes, there is a shorter loop. How many students passed the exam (60 points or more)?

int[] scores = { 62, 85, 47, 91, 78 };
int passed = 0;
for (int score : scores) {
    if (score >= 60) {
        passed++;
    }
}
System.out.println("Passed the exam: " + passed);

Output

Passed the exam: 4

It reads "for each score of scores". It is called for-each. There is no counter and no index, so you cannot go outside the array.

There is a limit too: you don't know which index you are at, and you cannot change the element.

More precisely, if you are curious

• If you write score = 0; in the body, you change only the copy in score. The array stays the same. The compiler does not stop you.

• To change elements, or when you need the index (for example for the neighbor scores[i + 1]), use a regular for.

Try it

Two names, one array

What will the program print?

int[] prices = { 10, 20, 30 };
int[] sale = prices;
sale[0] = 5;
System.out.println(prices[0]);

Answer

5

0

10

Check

More precisely, if you are curious

You make a real copy with a new array and a loop:

int[] prices = { 10, 20, 30 };
int[] sale = new int[prices.length];
for (int i = 0; i < prices.length; i++) {
    sale[i] = prices[i];
}
sale[0] = 5;
System.out.println(prices[0] + " " + sale[0]);

Output

10 5

prices.clone() does the same.

Try it

Put the lines in order

The program should find the lowest price. Put its lines in order.

1. int[] prices = { 18, 7, 25, 12 };↑↓
2. for (int i = 1; i < prices.length; i++) {↑↓
3. }↑↓
4. if (prices[i] < min) {↑↓
5. min = prices[i];↑↓
6. int min = prices[0];↑↓
7. }↑↓
8. System.out.println(min);↑↓

Check

Exercise

Working with an array

Solve the exercises in your editor. Each program first reads how many numbers there are, then the numbers themselves, one per line:

Scanner in = new Scanner(System.in);
int n = in.nextInt();
int[] numbers = new int[n];
for (int i = 0; i < n; i++) {
    numbers[i] = in.nextInt();
}

1. Sum, even, odd. Print the sum of all the numbers, of the even ones and of the odd ones.

Input

3
1
2
3

Output

Sum: 6
Even: 2
Odd: 4

2. Reversed. Create a new array with the same numbers in reverse order and print it on one line.

Input

5
1
2
3
4
5

Output

5 4 3 2 1

3. Lowest, highest, average. In one pass through the array.

Input

5
4
9
2
7
4

Output

Lowest: 2
Highest: 9
Average: 5.2

Exercise

Sorting and counting

4. Sorting. Sort the numbers from the smallest to the biggest. Hint: go through the array, and if two neighbors are in the wrong order, swap them (swapping is from the lesson on variables). Repeat until there is nothing left to swap. This is called bubble sort: the big numbers "bubble up" to the end.

Input

5
42
7
19
3
25

Output

3 7 19 25 42

5. Longest run. Find the longest run of equal numbers one after another.

Input

8
2
2
5
5
5
1
5
5

Output

The number 5, 3 times in a row

6. Grade statistics. Read grades from 2 to 6 and print how many there are of each kind. Hint: an array counts with 7 elements, where the grade is the index: counts[grade]++.

Input

8
6
4
5
6
3
2
6
5

Output

Excellent (6): 3
Very good (5): 2
Good (4): 1
Fair (3): 1
Poor (2): 1

More exercises

• Median. The number in the middle of the sorted array. For 3, 1, 4, 1, 5 the median is 3. If there is an even count of numbers, the median is the average of the two in the middle: for 7, 1, 3, 9 it is (3 + 7) / 2 = 5.
• Symmetric array. Does it read the same from front to back and from back to front? 1 2 3 2 1 is symmetric, 1 2 3 1 is not.
• Roman numerals. Read a number from 1 to 3999 and print it in Roman numerals: 2024 is MMXXIV, 1994 is MCMXCIV. Hint: two arrays side by side, with the values 1000, 900, 500, 400, 100, …, 1 and with the symbols "M", "CM", "D", "CD", "C", …, "I". While the number is at least the current value, add the symbol and subtract the value.

Test

Check yourself

1. In the array { 62, 85, 47, 91, 78 }, at which index is 91?

9143

2. What is the index of the last element of the array scores?

scores.length - 10scores.length

3. What is in the array right after int[] booked = new int[3];?

The numbers 1, 2, 3Nothing, you have to fill it before you read itThree zeros

4. The loop is for (int i = 0; i <= scores.length; i++) and it reads scores[i]. What happens?

It goes through all the elementsThe program stops with ArrayIndexOutOfBoundsExceptionIt skips the last element

5. int[] sale = prices; sale[0] = 5; What happens to prices[0]?

The program does not compileIt does not changeIt becomes 5

Check

Start the lesson over