Determine the Big O for the following segments of code. Provide comments for all code that effects Complexity. Be sure to explain your rationale for your decision.

1.

int m=0;

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

m=m+1;

}

Complexity:

Rationale:

2.

int m=0;

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

m=m+1;

}

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

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

m=m+1;

}

}

Complexity:

Rationale:

3.

int m=0;

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

for(int j = n/2; j < n; j++)

for(int k=0;k*k < n; k++ )

m=m+1;

}

Complexity:

Rationale:

4.

int m=0;

for (int i = n/2; i < n; i++) {

for(int j = n/2; j < n; j++)

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

m=m+1;

}

m=m+1;

}

Complexity:

Rationale: