Loop Analysis

Loop Analysis (a Mr. F is absent experience)

Analyzing Loops Includes

• Determining the execution count of different parts of a loop

  • An execution count is how many times a section of code is repeated.

• Determining when (and if) a loop terminates

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Why is the last answer 5?

for (int i = 3; i < 7; i++) {

++System.out.print("*");

}

The table outlines the order of commands in the loop.

1st:	Make i = 3​	​Is i < 7?	​Print *	​Increase i by 1
2nd:	​(i is now 4)	​is i < 7?	Print *​	Increase i by 1
3nd:	​​(i is now 5)	​is i < 7?	​Print *​	Increase i by 1
4th:	​​(i is now 6)	​is i < 7?	​Print *​	Increase i by 1
5th:	​(i is now 7)	is i < 7?	STOP!	​

Notice that the question "is i < 7" is asked one more time than the number of stars - that extra time is when it determines the loop should end.

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Multiple Choice

How many stars are printed by this code?

• 6

• 5

• 4

• 3

• An infinite number

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Multiple Choice

What does this code print?

• A rectangle of 8 rows with 5 stars per row.

• A rectangle of 8 rows with 4 stars per row.

• A rectangle of 6 rows with 5 stars per row.

• A rectangle of 6 rows with 4 stars per row.

Why?

A rectangle of 6 rows with 5 stars per row.

for (int i = 3; i <= 8; i++) {

++for (int y = 2; y < 7; y++) {

++++System.out.print("*");

++}

++System.out.println();

}

++

​Outside loop is the number of rows:
i goes through these values: 3-4-5-6-7-8, or a total of 6

​Inside loop is the number of stars per row:
y goes through these values: 2-3-4-5-6, or a total of 5

​*****
*****
*****
*****
*****

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Why 18?

for (int i = 3; i <= 6; i++) {

++for (int j = 9; j > i; j--) {

++++System.out.print("*");

++}

++System.out.println();

}++++

​When i is 3...	​Inside Loop: 9 to 4	​9-8-7-6-5-4 means 6 stars
​When i is 4...	​Inside Loop: 9 to 5	​9-8-7-6-5 means 5 stars
​​When i is 5...	​Inside Loop: 9 to 6	​9-8-7-6 means 4 stars
​​When i is 6...	​Inside Loop: 9 to 7	​9-8-7 means 3 stars

6 + 5 + 4 + 3 = 18

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Why 10?

int i = 0;

while (i <= 4) {

++for (int j = i+1; j < 5; j++) {

++++System.out.println("Hi!");

++}

++i++;

}

​When i is 0...	​Inside Loop: 1 to 4	​1-2-3-4 means 4 Hi!'s
​When i is 1...	​Inside Loop: 2 to 4	​​2-3-4 means 3 Hi!'s
​​When i is 2...	​Inside Loop: 3 to 4	​3-4 means 2 Hi!'s
​​When i is 3...	​Inside Loop: 4 to 4	​​4 means 1 Hi!'s
When i is 4...	Inside loop starts at 5 - loop condition is false immediately!	​

4 + 3 + 2 + 1 = 10

Multiple Choice

Which Java expression below will correctly represent the number of stars printed by the given code segment?

• (n+1)/2

• n/2

• (n-1)/2

• n

• n-1

Why (n+1)/2?

int n = ...; // n>=0

for(int i = 0; i < n; i++) {

++if(i % 2 == 0) {
+++System.out.print("*");

++}

}

​The code prints stars for all the even numbers from 0 to n (not including n). And abot half the values between 0 and n are even.
- if n is 5, it should print stars for the numbers 0, 2, and 4 (so 3 stars)
- if n is 6, it should also print stars for the numbers 0, 2 and 4 (so still 3 stars)

(5 + 1) / 2 evaluates to 3
(6 + 1) /2 also evaluates to 3 because of integer division!

For problems like this, it's a good idea to test values of n (especially even and odd values)

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