Step-Count Method in Algorithm

[Anil2447]

Hi...!

In Design of Algorithm.
I think it is used to calculate the time complexity....

What is meant by STEP-COUNT METHOD?
What is the procedure in that to calculate?

I want brief explination. ....

[Narue]

What is meant by STEP-COUNT METHOD?

You define what a "step" means for the algorithm (usually statements), then the total of those steps using variables such as N can be calculated.What is the procedure in that to calculate?First define steps:

int mean(int a[], size_t n)
{
    int sum = 0;                 // 1 step
    for (int i = 0; i < n; i++)  // 1 step
        sum += a[i];             // 1 step
    return sum;                  // 1 step
}

Next determine the frequency of the steps based on N: int mean(int a[], size_t n) { int sum = 0; // 1 step * 1 for (int i = 0; i < n; i++) // 1 step * (N+1) sum += a[i]; // 1 step * N return sum; // 1 step * 1 } Add up the steps:1 + (N+1) + N + 1 Reduce: 2N + 3 Throw away factors that don't grow with N and you're done: O(N)

[Anil2447]

Thank You......!

How can we say that

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

is "N+1" times. Is it is the case that the loop itarates for "N+1" Number of times?

In the same manner how can we say

sum += a[i];

is it runs for "N" times?

[Narue]

Is it is the case that the loop itarates for "N+1" Number of times?

The loop iterates N times, but the statement is executed N+1 times. For example, if N is 0, the loop doesn't iterate but the condition must still be tested. Thus the statement is executed 0+1 times.In the same manner how can we say
The loop body runs N times. That should be obvious.

[Anil2447]

Thank You very Much.....!