Write an algorithm that read three integers and then determines and prints the largest and the smallest integers in the group.

read x,y,z

min = max = x
if y<min then min=y
if y>max then max=y
if z<min then min=z
if z>max then max=z
print min,max

Algorithm:

1. Start
2. Read the first integer and store it in a variable called "number1"
3. Read the second integer and store it in a variable called "number2"
4. Read the third integer and store it in a variable called "number3"
5. Initialize a variable called "smallest" with the value of "number1"
6. Initialize a variable called "largest" with the value of "number1"
7. Check if "number2" is smaller than "smallest". If true, assign "number2" to "smallest".
8. Check if "number2" is larger than "largest". If true, assign "number2" to "largest".
9. Check if "number3" is smaller than "smallest". If true, assign "number3" to "smallest".
10. Check if "number3" is larger than "largest". If true, assign "number3" to "largest".
11. Print the value of "smallest" as the smallest integer.
12. Print the value of "largest" as the largest integer.
13. Stop.

Note: In case there are multiple integers with the same largest or smallest values, this algorithm will only consider the first occurrence.

To find the largest and smallest integers among three given numbers, you can follow this algorithm:

1. Start by defining three variables to store the three integers. Let's name them `num1`, `num2`, and `num3`.

2. Read the three integers from the user or any other input source and assign them to the respective variables.

3. Initialize two additional variables `largest` and `smallest` with initial values equal to the first inputted number, `num1`.

4. Compare `num2` with `largest`. If `num2` is greater than `largest`, update the value of `largest` to `num2`. Otherwise, if `num2` is smaller than `smallest`, update the value of `smallest` to `num2`.

5. Repeat the same comparison and update step for `num3`.

6. After comparing `num3` with `largest` and `smallest`, you should have updated values of `largest` and `smallest` if either `num3` is greater than `largest` or smaller than `smallest`, respectively.

7. Finally, print the values of `largest` and `smallest` to obtain the largest and smallest integers among the three.

Here's a sample implementation of the algorithm in Python:

```python
num1 = int(input("Enter the first integer: "))
num2 = int(input("Enter the second integer: "))
num3 = int(input("Enter the third integer: "))

largest = num1
smallest = num1

if num2 > largest:
largest = num2
elif num2 < smallest:
smallest = num2

if num3 > largest:
largest = num3
elif num3 < smallest:
smallest = num3

print("The largest integer is:", largest)
print("The smallest integer is:", smallest)
```

By following this algorithm, you can find and print the largest and smallest integers among the three inputted numbers.