Merge pull request #213 from abhisheks008/main

Job Sequencing Problem using Greedy Approach

Author: prathimacode-hub

Greedy/Job Sequencing Problem/Images/jsp-1.png

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+# Job Sequencing Problem using Greedy Approach
+🔴 Language used : **Python 3**
+
+## 🎯 Aim
+The aim of this script is to find the maximum profit earned by executing the tasks within the specified deadlines.
+
+## 👉 Purpose
+The main purpose of this script is to show the implementation of Greedy Approach to find the maximum profit earned by executing the tasks within the specified deadlines.
+
+## 📄 Description
+Given an array of jobs where every job has a deadline and associated profit if the job is finished before the deadline. It is also given that every job takes a single unit of time, so the minimum possible deadline for any job is 1. Maximize the total profit if only one job can be scheduled at a time.
+
+🔴 Examples: 
+
+```
+Constraints:
+arr[] -> Set of datapoints including JobID, Deadline and Profit into a single array.
+t -> No. of jobs to be scheduled.
+
+Input:  
+Five Jobs with following deadlines and profits
+
+JobID   Deadline  Profit
+  a        2       100
+  b        1       19
+  c        2       27
+  d        1       25
+  e        3       15
+
+Output: 
+Following is maximum profit sequence of jobs: 
+c, a, e
+```
+
+
+## 🧮 Algorithm
+Greedily choose the jobs with maximum profit first, by sorting the jobs in decreasing order of their profit. This would help to maximize the total profit as choosing the job with maximum profit for every time slot will eventually maximize the total profit.
+- This problem is basically solved using the `printJobScheduling(arr, t)` funtion, which is basically the main function. `arr` signifies the job array and `t` signifies the number of jobs to be scheduled.
+- Sort all jobs in decreasing order of profit. 
+- Iterate on jobs in decreasing order of profit.For each job , do the following :
+  - Find a time slot `i`, such that slot is empty and `i < deadline` and `i` is greatest. Put the job in this slot and mark this slot filled. 
+  - If no such `i` exists, then ignore the job. 
+- This whole process will be repeated until and unless the funtion got the `-1` value. Once it got the `-1` value it will stop the program and provide the output.
+
+## 💻 Input and Output 
+- **Test Case 1 :**
+```
+Input Given :
+arr = [['a', 2, 100],
+       ['b', 1, 19],
+       ['c', 2, 27],
+       ['d', 1, 25],
+       ['e', 3, 15]]
+```
+
+![](https://github.com/abhisheks008/PyAlgo-Tree/blob/main/Greedy/Job%20Sequencing%20Problem/Images/jsp-1.png)
+
+- **Test Case 2 :**
+```
+Input Given :
+arr = [['a', 4, 20], 
+       ['b', 1, 10],
+       ['c', 1, 40],
+       ['d', 1, 30]]
+```
+![](https://github.com/abhisheks008/PyAlgo-Tree/blob/main/Greedy/Job%20Sequencing%20Problem/Images/jsp-2.png)
+
+## ⏰ Time and Space complexity
+- **Time Complexity :** `O(n^2)`.
+- **Space Complexity :** `O(n)`.
+
+---------------------------------------------------------------
+## 🖋️ 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/Job Sequencing Problem/Images/jsp-2.png

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+# Problem Name: Job Sequencing Problem
+# Approach used: Greedy Method
+# Language used: Python
+
+# Problem Statement: Given an array of jobs where every job has a deadline 
+#                    and associated profit if the job is finished before the
+#                    deadline. It is also given that every job takes a single
+#                    unit of time, so the minimum possible deadline for any 
+#                    job is 1. Maximize the total profit if only one job can
+#                    be scheduled at a time.
+
+# -----------------------------------------------------------------------------
+
+# Constraints:
+# arr[] -> Set of datapoints including JobID, Deadline and Profit into a single array.
+# t -> No. of jobs to be scheduled.
+
+# -----------------------------------------------------------------------------
+
+
+def printJobScheduling(arr, t):
+# This is the main funtion for determining the final result
+# function to schedule the jobs take 2 arguments array and no of jobs to schedule
+ 
+    # length of array
+    n = len(arr)
+ 
+    # Sort all jobs according to
+    # decreasing order of profit
+    for i in range(n):
+        for j in range(n - 1 - i):
+            if arr[j][2] < arr[j + 1][2]:
+                arr[j], arr[j + 1] = arr[j + 1], arr[j]
+ 
+    # To keep track of free time slots
+    result = [False] * t
+ 
+    # To store result (Sequence of jobs)
+    job = ['-1'] * t
+ 
+    # Iterate through all given jobs
+    for i in range(len(arr)):
+ 
+        # Find a free slot for this job
+        # (Note that we start from the
+        # last possible slot)
+        for j in range(min(t - 1, arr[i][1] - 1), -1, -1):
+ 
+            # Free slot found
+            if result[j] is False:
+                result[j] = True
+                job[j] = arr[i][0]
+                break
+ 
+    # print the sequence
+    print(job)
+ 
+ 
+# Driver's Code
+if __name__ == '__main__':
+    arr = [['a', 2, 100],  # Job Array
+           ['b', 1, 19],
+           ['c', 2, 27],
+           ['d', 1, 25],
+           ['e', 3, 15]]
+
+    print ("-- Job Sequencing Problem using Greedy Approach --")
+    print ()
+    print ("Job ID    Deadline     Profit")
+    for i in range(0, len(arr)):
+      for j in range (0, 3):
+        print (arr[i][j], end = "           ")
+      print()
+
+    print ("\nOutput --")
+    print("Following is maximum profit sequence of jobs")
+ 
+    # Function Call
+    printJobScheduling(arr, 3)
+
+    
+# -------------------------------------------------------------------------
+   
+# Output  
+# -- Job Sequencing Problem using Greedy Approach --
+
+# Job ID    Deadline     Profit
+# a           2           100           
+# b           1           19           
+# c           2           27           
+# d           1           25           
+# e           3           15           
+
+# Output --
+# Following is maximum profit sequence of jobs
+# c a e
+
+# -------------------------------------------------------------------------
+
+# Code contributed by, Abhishek Sharma, 2022
+
+# -------------------------------------------------------------------------

Greedy/Job Sequencing Problem/README.md

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+## Implementations of Greedy Algorithms :computer:
 
+- [**Activity Selection Problem**](https://github.com/abhisheks008/PyAlgo-Tree/tree/main/Greedy/Activity%20Selection%20Problem)
+- [**Job Sequencing Problem**](https://github.com/abhisheks008/PyAlgo-Tree/tree/main/Greedy/Job%20Sequencing%20Problem)