How calculate time complexity step by step of given two program program

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Program-1:

C++

for (i = 0; i < m, i + +){
    for (j = 0; j < n, j + +){
      if (a = b){
        arr[i][j] = 1;
      }
      else{
        arr[i][j] = 2;
      }
    }
}

for (i = 0; i < m, i + +){
    for (j = 0; j < n, j + +){
      arr[i] += arr[i][j];
    }
}

for (i = 0; i < m, i + +){
  if (a = b){
    p[i] = i
    q [i] = i
  }
}

Program-2:

C++

for (i = 0; i < m, i + +){
  sum = 0;
    for (j = 0; j < n, j + +){
      if (a = b){
        arr[i][j] = 1
        sum += 1;
      }
      else{
         arr[i][j] = 2
      }
    }
    if (c = d){
      arr[i] = sum;
      p[i] = i
      q [i] = i
    }   
}

What I have tried:

I tried to make a time complexity equation step by step for both program. and which one is better and how much? Could you please help on that?

for program-1:
m*n*c1 + m*n*c2 + m*c3

for program-2
m*n*c1 + m*c2

Posted 23-Sep-20 0:19am

Member 11512486

Updated 23-Sep-20 1:00am

CPallini

v2

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Comments

Richard Deeming 23-Sep-20 7:24am

REPOST
This is now your THIRD copy of exactly the same question:
How can I calculate time complexity and compare between given two algorithms? - Algorithms Discussion Boards[^]
Calculate time complexity step by step of given two program program - Algorithms Discussion Boards[^]

3 solutions

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CPallini · Answer 1 · 2020-09-23T00:54:00

Solution 3

Time complexity of both programs is O(m x n), so, why worry?

Posted 23-Sep-20 0:54am

CPallini

OriginalGriff · Answer 2 · 2020-09-23T00:52:00

Which do you think is faster? Look at the complexities you have calculated, and compare them.
O(1) has a fixed time: no matter how many data samples are used, it will always execute in the same time.
O(N) directly compares the number of data samples to the execution time in a linear fashion: if you increase N from 10 to 20, execution time will double.
O(2N) is also linear, if you increase N from 10 to 20, execution time will also double. The complexity is equivalent, but slower than O(2N)
O(N²) is exponential - a small increase in N results in a big increase in execution time.

Look at your two complexities and it's pretty obvious which is faster if you think about it.

This is your homework, not ours: your tutor is looking for you thoughts, not mine. So give it a try!

Patrice T · Answer 3 · 2020-09-23T00:49:00

Solution 1

Not your question, but your programs are wrong:

C++

if (a = b){ // this store value of b in a

must be replaced by:

C++

if (a == b){ // this compare a and b for equality

Posted 23-Sep-20 0:49am

Patrice T