In: Computer Science

Find a **loop invariant (I)** for the following
while loop with the post-condition

**{Q: S=1}**, where S is an integer and the
operator **/** represents an integer division.

Show your work step by step to receive full credit.

while (S > 1) do S = S / 2; }

Loop invariant can be defined as a condition which will always be true. This property must be satisfied throughout every iteration of the loop.

We have the post-condition:

Q: S = 1

The given loop checks if the value of 'S' is greater than 1 or not. If it is true, then it divides 'S' by 2 and this process is repeated in every iteration. The while loop condition will fail when the value of 'S" is one or less. At that case, the value of 'S' will never be less than one as it is integer in nature. Loop invariant does not depend on the state of the iterative condition. It always remains true irrespective of the iterative condition which can be true or false.

The post-condition must be true after the execution of the while loop condition.

So, one loop invariant we can determine from the given relation is:

**S > 1 [the while loop will be executed only when 'S'
is greater than one, not equal to one]**

**Please comment in case of any doubt.
Please upvote if this helps.**

According to the loop invariant theorem, a valid loop invariant
?(?)I(n) must have the property that
Select one:
a. ?(?)=0I(n)=0 after a finite number of steps.
b. After the loop, ?ā?(?)PāI(N) where ?P is the
postcondition.
c. ?(0)ā?I(0)āQ, where ?Q is the precondition.
d. None of the other answers are correct

(C++)Change the following loop to a while loop:
int i;
for (i=0; i<10; i++)
{
cout<<i<<endl;
}

Why is an exit condition so important for a while loop?a.An exit condition is not vital. A while loop works
fine without one.b.So the programmer knows when it is okay to leave the room.c.If no exit condition is provided, while loops cannot continue
beyond one iterationd.It allows the loop to end instead of running indefinitely.e.While loops are unstable, and must know how to exi

I have to use a sentinel while loop to complete the following
task in a java program, I want to see how this is executed so I can
better understand how the sentinel while loop works. Thank you!
Convert Lab 10 from a counter controlled WHILE loop to a
sentinel WHILE loop. Do the following:
Prompts the user to enter a grade or a -1 to quit.
IF the user entered a -1 THEN
Display a message that the User...

Study the following code with a while-loop and convert it to a
for-loop (fill in the blanks).
int i=4, result=1; while(i>1) { result *= i; i--; }
The following for-loop performs the same functionality:
int result=1; for (__________ i=4; i _________1;____________) {
result *= i; }

Here is a traditional loop in C:
while (A{i} == 0)
A{i}
= A{5} + A{i+3};
(NOTE: please consider braces {} here as usual square brackets
for array index).
Assume that i is stored in register $s1, and the base address of
the array A is in $s2. Fill in the multiple blank spaces in the
following MIPS program that is supposed to be compiled from the
above C loop:
loop: sll $t0, $s1,
add
$t0, $t0,
lw
$t1, 20($s2)...

Consider the linear time invariant system described by the
transfer function G(s) given below. Find the steady-state response
of this system for two cases: G(s) = X(s)/F(s) =
(s+2)/(3(s^2)+6s+24) when the input is f(t) = 5sin(2t) and f(t) =
5sin(2t) + 3sin(2sqrt(3)t)

For each of the following answers, determine whether the answer
better describes a for loop or a while loop.It performs one iteration for every value in a sequence.It uses a loop variable.It continues the loop until the condition becomes
false.It continues the loop until reaching the end of the
sequence.It can easily cause infinite loops.The exact number of iterations are usally known when
starting the loop.

Condition 1 Scores
Condition 2 Scores
1
8
2
3
3
4
3
10
4
2
4
8
4
7
5
7
2
8
6
9
2
10
5
10
Column Mean
Column Median
Column Mode
Standard Deviation
Column Range
1. The correct mean for Condition One is _______ while the
correct mean for Condition Two is ______:
A. 3.50 and 8.00
B. 3.42 and 7.17
C. 4.00 and 8.00
D. 1.51 and 2.76
E. 7.17 and 3.42
2. The...

Given the following pre-condition and program segment, what is
the post-condition for y?
// Pre-condition: -2 <= x < 4
y = 2*x*x - x +3

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