1. Explain how time complexity is calculated. Give an example.
Answers
Answer:
Explanation:
Now lets tap onto the next big topic related to Time complexity, which is How to Calculate Time Complexity. It becomes very confusing some times, but we will try to explain it in the simplest way.
Now the most common metric for calculating time complexity is Big O notation. This removes all constant factors so that the running time can be estimated in relation to N, as N approaches infinity. In general you can think of it like this :
statement;
Above we have a single statement. Its Time Complexity will be Constant. The running time of the statement will not change in relation to N.
for(i=0; i < N; i++)
{
statement;
}
The time complexity for the above algorithm will be Linear. The running time of the loop is directly proportional to N. When N doubles, so does the running time.
for(i=0; i < N; i++)
{
for(j=0; j < N;j++)
{
statement;
}
}
This time, the time complexity for the above code will be Quadratic. The running time of the two loops is proportional to the square of N. When N doubles, the running time increases by N * N.
while(low <= high)
{
mid = (low + high) / 2;
if (target < list[mid])
high = mid - 1;
else if (target > list[mid])
low = mid + 1;
else break;
}
This is an algorithm to break a set of numbers into halves, to search a particular field(we will study this in detail later). Now, this algorithm will have a Logarithmic Time Complexity. The running time of the algorithm is proportional to the number of times N can be divided by 2(N is high-low here). This is because the algorithm divides the working area in half with each iteration.
void quicksort(int list[], int left, int right)
{
int pivot = partition(list, left, right);
quicksort(list, left, pivot - 1);
quicksort(list, pivot + 1, right);
}
Taking the previous algorithm forward, above we have a small logic of Quick Sort(we will study this in detail later). Now in Quick Sort, we divide the list into halves every time, but we repeat the iteration N times(where N is the size of list). Hence time complexity will be N*log( N ). The running time consists of N loops (iterative or recursive) that are logarithmic, thus the algorithm is a combination of linear and logarithmic.
Answer:
Explanation:
Now lets tap onto the next big topic related to Time complexity, which is How to Calculate Time Complexity. It becomes very confusing some times, but we will try to explain it in the simplest way.
Now the most common metric for calculating time complexity is Big O notation. This removes all constant factors so that the running time can be estimated in relation to N, as N approaches infinity. In general you can think of it like this :
statement;
Above we have a single statement. Its Time Complexity will be Constant. The running time of the statement will not change in relation to N.
for(i=0; i < N; i++)
{
statement;
}
The time complexity for the above algorithm will be Linear. The running time of the loop is directly proportional to N. When N doubles, so does the running time.
for(i=0; i < N; i++)
{
for(j=0; j < N;j++)
{
statement;
}
}
This time, the time complexity for the above code will be Quadratic. The running time of the two loops is proportional to the square of N. When N doubles, the running time increases by N * N.
while(low <= high)
{
mid = (low + high) / 2;
if (target < list[mid])
high = mid - 1;
else if (target > list[mid])
low = mid + 1;
else break;
}
This is an algorithm to break a set of numbers into halves, to search a particular field(we will study this in detail later). Now, this algorithm will have a Logarithmic Time Complexity. The running time of the algorithm is proportional to the number of times N can be divided by 2(N is high-low here). This is because the algorithm divides the working area in half with each iteration.
void quicksort(int list[], int left, int right)
{
int pivot = partition(list, left, right);
quicksort(list, left, pivot - 1);
quicksort(list, pivot + 1, right);
}
Taking the previous algorithm forward, above we have a small logic of Quick Sort(we will study this in detail later). Now in Quick Sort, we divide the list into halves every time, but we repeat the iteration N times(where N is the size of list). Hence time complexity will be N*log( N ). The running time consists of N loops (iterative or recursive) that are logarithmic, thus the algorithm is a combination of linear and logarithmic.
