Topic: An algorithm to find max (or min) of any three numbers Problem statement:
ID: 3591421 • Letter: T
Question
Topic: An algorithm to find max (or min) of any three numbers
Problem statement:
Given three input values (in double variables x,y,z for example), find max (or min) of the three values.
Approach 1:
We can compare each variable to see if it is larger than each of the other two variables is. If so, its value is given to max.
// if x is larger than y and x is larger than z – max is assigned x
if( (x > y) && (x > z) ) max = x;
We can proceed this way to see if y and z are max.
Code Segment 1 in the attached program implements this algorithm
Analysis: Does it work? – Check with values for x,y,z as: 12.5, 35.8, -43.1 (or any three numbers which differ from each other – Perhaps the results will convince that you will get correct answer.
Is there any catch? – What if, two or more input numbers are same? – Try inputs: 12.5, 12.5. 34.9 or 1.0, 1.0, 1.0 as inputs – Do you get a correct answer? – perhaps not!
Fix: use >= instead of > for comparison – that will take care of situations when two or more numbers are equal.
Approach 2
Apply the fix suggested – and Code Segment 2 does just that!
Try different inputs and see if the program works
Add additional code to computer min value of the three numbers – and check the results.
Approach 3
Here we assign the first value to max ( max = x; )
Each time max value is compared to other variables, one at a time and it is updated when necessary.
max =x;
if( y > max ) max = y;
if (z > max) max = z; // and so on
Now at the end of this program segment, max contains the largest value of the three.
Analysis: Approach 3 keeps one variable named max to keep track of the largest number it has encountered so far – It uses simple comparison operation, once per each variable to get updated when necessary – it can also be extended to deal with more than three variables along the same lines. This property is known as “Scalability”.
Approach 2 is simpler idea, but it involves comparing each variable with each of the other variables from input.
Approach 3 is a more elegant problem-solving approach – it can be used with several values of inputs also, as we will notice in future chapters.
Explanation / Answer
Hi,
here is the copyable code for all 3 approaches, i have added comments to help you understand.
double approach1(double x,double y,double z)
{
if(x>y && x>z)//comparing each element with other two
return x;
else if(y>x && y>z)
return y;
else
return z;
}
double approach2(double x,double y,double z)
{
if(x>=y && x>=z)//this handles if inputs are equal
return x;
else if(y>=x && y>=z)
return y;
else
return z;
}
double approach3(double x,double y,double z)
{
double max =x;//elegant way to find by keeping track of max till now
if( y > max ) max = y;
if (z > max) max = z;
return max;
}
Thumbs up if this was helpful otherwise let me know in comments