I want to know that how to find the complexity of an algorithm in programming languages.

## 2 Replies - 15526 Views - Last Post: 07 January 2009 - 06:22 AM

### #1

# how to find complexity of an algorithm using programming

Posted 07 January 2009 - 05:25 AM

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**Replies To:** how to find complexity of an algorithm using programming

### #2

## Re: how to find complexity of an algorithm using programming

Posted 07 January 2009 - 05:43 AM

It depends on what algorithm it is and if it's iterative or recursive. It can also depend on the input size (pseudo-polynomials).

### #11

## Re: how to find complexity of an algorithm using programming

Posted 07 January 2009 - 06:22 AM

Time Complexity : The time complexity of a problem is the number of steps that it takes to solve an instance of the problem as a function of the size of the input (usually measured in bits), using the most efficient algorithm.

So we denote it in form of o(n) notation. [There are different notations for best , average, worst case (symboled by theta, omega and bit O)]. Generally a time complexity will be the time required for the most time consuming activity of algorithm.

e.g.

This will have time complexity of O(n^2) and the nested for loop will be the time consuming activity in any case.

In general calculation of time complexity of algorithms can be done using following calculations...

return 0; - statement like this executes in defined time [say 1 unit] so it's time complexity will be constant.

for ( i = 0; i < N; i++ ) printf("a"); - this for loop will take n iterations to finish, so total statement executions will be 3N+1, as this is directly proportional to N the time complexity here will be O(n).

you already have one example of O(n^2) above.

This code uses divide and conquer strategy, which makes it logarithmic i.e. The running time of the algorithm is proportional to the number of times N can be divided by 2. so it's complexity will be O(log n).

There are complexities like O(n^3), O(n*log n) etc. You can explore about them by yourself.

This and this can be a good resource on it.

Space Complexity : The space complexity of a problem is a related concept that measures the amount of space or memory required by the algorithm. An informal analogy would be the amount of scratch paper needed while working out a problem with pen and paper.

So similar to time complexity, this also considers the highest memory consuming part of the code as the decider of space complexity.

This can be a good resource on it.

So we denote it in form of o(n) notation. [There are different notations for best , average, worst case (symboled by theta, omega and bit O)]. Generally a time complexity will be the time required for the most time consuming activity of algorithm.

e.g.

void print() { for(int i=0;i<n,i++) { printf("%d ",i); } for(int j=0;j<n,j++) { for(int i=0;i<n,i++) { printf("%d ",i*j); } } }

This will have time complexity of O(n^2) and the nested for loop will be the time consuming activity in any case.

In general calculation of time complexity of algorithms can be done using following calculations...

return 0; - statement like this executes in defined time [say 1 unit] so it's time complexity will be constant.

for ( i = 0; i < N; i++ ) printf("a"); - this for loop will take n iterations to finish, so total statement executions will be 3N+1, as this is directly proportional to N the time complexity here will be O(n).

you already have one example of O(n^2) above.

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 code uses divide and conquer strategy, which makes it logarithmic i.e. The running time of the algorithm is proportional to the number of times N can be divided by 2. so it's complexity will be O(log n).

There are complexities like O(n^3), O(n*log n) etc. You can explore about them by yourself.

This and this can be a good resource on it.

Space Complexity : The space complexity of a problem is a related concept that measures the amount of space or memory required by the algorithm. An informal analogy would be the amount of scratch paper needed while working out a problem with pen and paper.

So similar to time complexity, this also considers the highest memory consuming part of the code as the decider of space complexity.

This can be a good resource on it.

This post has been edited by **AmitTheInfinity**: 07 January 2009 - 06:23 AM

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