Question

What is the run-time of this recursive code:

int maximum(int array[], int index, int len); //define maximum function.
int minimum(int array[], int index, int len);//define minimum function.

int main()
{
//Main method
int array[MAX_SIZE], N, max, min; //Defining all the variable.
int i;
printf("Enter size of the array: ");//Taking input from user as a array size
scanf("%d", &N);
printf("Enter %d elements in array: ", N);//Taking input from user
for(i=0; i<N; i++)
{
scanf("%d", &array[i]);//storing all the element in array.
}

max = maximum(array, 0, N);//calling maximum function which will return max element.
min = minimum(array, 0, N);//calling minimum function which will return min element.

printf("Minimum element in array = %d\n", min);//Displaying Min element.
printf("Maximum element in array = %d\n", max);//Displaying Max element.

return 0;
}

int maximum(int array[], int index, int len)
{ //maximum function will return maximum element from array.
int max;
  
if(index >= len-2)
{
if(array[index] > array[index + 1])
//If element array[index] is greater than array[index + 1] then return array[index]
return array[index];
else
return array[index + 1];
//Otherwise return array[index + 1]
}

max = maximum(array, index + 1, len); //Recursively calling maximum function.

if(array[index] > max)
//If array[index] is greater than max then return array[index]
return array[index];
else
return max;
//otherwise return max
}

int minimum(int array[], int index, int len)
{ //minimum function which will return min value from the array
int min;

if(index >= len-2)
{
if(array[index] < array[index + 1])
//If element array[index] is smaller than array[index + 1] then return array[index]
return array[index];
else
return array[index + 1];
//Otherwise return array[index + 1]
}

min = minimum(array, index + 1, len); //Recursively calling minimum function.

if(array[index] < min)
//if array[index] is smaller than min then return array[index]
return array[index];
else
return min;
//return min
}

Answer 1

The time complexity of recursive maximum() method is O(n) where n is the number of elements in the array.

The time complexity of recursive minimum() method is O(n) where n is the number of elements in the array.