Builds up a solution piece by piece, always choosing the next piece that offers the most obvious and immediate benefit. Greedy algorithms are used for optimization problems. An optimization problem can be solved using Greedy if the problem has the following property: At every step, we can make a choice that looks best at the moment, and we get the optimal solution of the complete problem.
You are given n activities with their start and finish times. Select the maximum number of activities that can be performed by a single person, assuming that a person can only work on a single activity at a time.
Example 1 : Consider the following 3 activities sorted by
by finish time.
start[] = {10, 12, 20};
finish[] = {20, 25, 30};
A person can perform at most two activities. The
maximum set of activities that can be executed
is {0, 2} [ These are indexes in start[] and
finish[] ]
Example 2 : Consider the following 6 activities
sorted by by finish time.
start[] = {1, 3, 0, 5, 8, 5};
finish[] = {2, 4, 6, 7, 9, 9};
A person can perform at most four activities. The
maximum set of activities that can be executed
is {0, 1, 3, 4} [ These are indexes in start[] and
finish[] ]
// Prints a maximum set of activities that can be done by a single
// person, one at a time.
// n --> Total number of activities
// s[] --> An array that contains start time of all activities
// f[] --> An array that contains finish time of all activities
void printMaxActivities(int s[], int f[], int n)
{
int i, j;
printf ("Following activities are selected n");
// The first activity always gets selected
i = 0;
printf("%d ", i);
for (j = 1; j < n; j++)
{
// If this activity has start time greater than or
// equal to the finish time of previously selected
// activity, then select it
if (s[j] >= f[i])
{
printf ("%d ", j);
i = j;
}
}
}Time Complexity : It takes O(n log n) time if input activities may not be sorted. It takes O(n) time when it is given that input activities are always sorted.