Merge pull request #206 from abhisheks008/main

Activity Selection Problem using Greedy Approach

Author: prathimacode-hub

Greedy/Activity Selection Problem/Images/asp-1.png

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+# Activity Selection Problem using Greedy Approach
+🔴 Language used : **Python 3**
+
+## 🎯 Aim
+The aim of this script is to find out the maximum number of activities to be performed by a single person in between the start and finish time given in the problem.
+
+## 👉 Purpose
+The main purpose of this script is to show the implementation of Greedy Approach to find out the maximum number of activities to be performed by a single person in between the start and finish time given in the problem.
+
+## 📄 Description
+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. 
+
+Suppose `S = {1, 2....n}` is the set of n proposed activities. The activities share resources which can be used by only one activity at a time, e.g., Tennis Court, Lecture Hall, etc. Each Activity `i` has start time si and a finish time `fi`, where `si ≤fi`. If selected activity `i` take place meanwhile the half-open time interval `[si,fi)`. Activities `i` and `j` are compatible if the intervals `(si, fi)` and `[si, fi)` do not overlap (i.e. `i` and `j` are compatible if `si≥fi` or `si≥fi)`. The activity-selection problem chosen the maximum-size set of mutually consistent activities.
+
+🔴 Examples: 
+
+```
+Constraints:
+start[] -> an array of start time for the activities.
+finish[] -> an array of finish time for the activities.
+output[] -> an array of maximum set of activities to be done by a person.
+
+Input:
+Consider the following 6 activities  sorted by finish time.
+
+start[]  =  {1, 3, 0, 5, 8, 5};
+finish[] =  {2, 4, 6, 7, 9, 9};
+
+Output:
+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[]]
+```
+
+## 📊 Flowchart
+```
+printMaxActivities(s, f)
+1. n ← length [s]
+2. A ← {1}
+3. j ← 1.
+4. for i ← 2 to n
+5. do if si ≥ fi
+6. then A ← A ∪ {i}
+7. j ← i
+8. return A
+```
+
+## 🧮 Algorithm
+- This algorithm is called Greedy-Iterative-Activity-Selector, because it is first of all a greedy algorithm, and then it is iterative. There's also a recursive version of this greedy algorithm.
+- Sorts in increasing order of finish times the array of activities `A` by using the finish times stored in the array `f`. This operation can be done in `O(n log n)` time, using for example merge sort, heap sort, or quick sort algorithms.
+- Creates a set `S` to store the selected activities, and initialises it with the activity that has the earliest finish time.
+- Creates a variable `k` that keeps track of the index of the last selected activity.
+- Starts iterating from the second element of that array `A` up to its last element.
+- If the start time `s[i]` of the `ith` activity `A[i]` is greater or equal to the finish time `f[k]` of the last selected activity `A[k]`, then `A[i]` is compatible to the selected activities in the set `S`, and thus it can be added to `S`.
+- The index of the last selected activity is updated to the just added activity `A[i]`.
+
+
+## 💻 Input and Output 
+- **Test Case 1 :**
+```
+Input Given :
+s = [1 , 3 , 0 , 5 , 8 , 5]
+f = [2 , 4 , 6 , 7 , 9 , 9]
+```
+
+![](https://github.com/abhisheks008/PyAlgo-Tree/blob/main/Greedy/Activity%20Selection%20Problem/Images/asp-1.png)
+
+- **Test Case 2 :**
+```
+Input Given :
+s = [1, 2, 3, 4, 7, 8, 9, 9, 11, 12]
+f = [3, 5, 4, 7, 10, 9, 11, 13, 12, 14]
+```
+![](https://github.com/abhisheks008/PyAlgo-Tree/blob/main/Greedy/Activity%20Selection%20Problem/Images/asp-2.png)
+
+## ⏰ Time and Space complexity
+- **Time Complexity :** `O(n)`.
+- **Space Complexity :** `O(1)`.
+
+---------------------------------------------------------------
+## 🖋️ Author
+**Code contributed by, _Abhishek Sharma_, 2022 [@abhisheks008](github.com/abhisheks008)**
+
+[![forthebadge made-with-python](http://ForTheBadge.com/images/badges/made-with-python.svg)](https://www.python.org/)

Greedy/Activity Selection Problem/Images/asp-2.png

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+# Problem Name: Activity Selection Problem
+# Method used: Greedy Approach
+
+# -------------------------------------------------------------------------
+
+# Problem Statement: 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. 
+
+# -------------------------------------------------------------------------
+
+# Constraints:
+# 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
+
+
+# Let's solve the problem.
+
+# This is the actual function, which is going to find out the result for this problem.
+# The function printMaxActivities takes two parameters, s and f
+# s[] denotes all the start time activities.
+# f[] denotes all the finish time activities.
+def printMaxActivities(s, f ):
+    n = len(f)
+    print ("The following activities are selected")
+ 
+    # The first activity is always selected
+    i = 0
+    print (i,end=' ')
+ 
+    # Consider rest of the activities
+    for j in range(1, n):
+ 
+        # 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]:
+            print (j,end=' ')
+            i = j
+ 
+# Driver program to test above function
+print ("-- Activity Selection Problem using Greedy Approach --\n")
+s = [1 , 3 , 0 , 5 , 8 , 5]
+f = [2 , 4 , 6 , 7 , 9 , 9]
+print ("** Activities during start time **")
+print (s)
+print ("** Activities during finish time **")
+print (f)
+print ()
+printMaxActivities(s , f)
+
+
+# -------------------------------------------------------------------------
+
+# Output:
+# -- Activity Selection Problem using Greedy Approach --
+
+# ** Activities during start time **
+# [1, 3, 0, 5, 8, 5]
+# ** Activities during finish time **
+# [2, 4, 6, 7, 9, 9]
+
+# The following activities are selected
+# 0 1 3 4 
+
+# -------------------------------------------------------------------------
+
+# Code contributed by, Abhishek Sharma, 2022
+
+# -------------------------------------------------------------------------