README FOR FORD FULKERSON METHOD (jainaman224#2589)

Ford_Fulkerson_Method/README.md

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+# Ford-Fulkerson Algorithm
+
+The Ford-Fulkerson algorithm is an algorithm that tackles the max-flow min-cut problem. That is, given a network with vertices and edges between those vertices that have certain weights, how much "flow" can the network process at a time? Flow can mean anything, but typically it means data through a computer network.
+
+It was discovered in 1956 by Ford and Fulkerson. This algorithm is sometimes referred to as a method because parts of its protocol are not fully specified and can vary from implementation to implementation. An algorithm typically refers to a specific protocol for solving a problem, whereas a method is a more general approach to a problem.
+
+The Ford-Fulkerson algorithm assumes that the input will be a graph, GG, along with a source vertex, ss, and a sink vertex, tt. The graph is any representation of a weighted graph where vertices are connected by edges of specified weights. There must also be a source vertex and sink vertex to understand the beginning and end of the flow network.
+
+Ford-Fulkerson has a complexity of O\big(|E| \cdot f^{*}\big),O(∣E∣⋅f 
+∗
+ ), where f^{*}f 
+∗
+  is the maximum flow of the network. The Ford-Fulkerson algorithm was eventually improved upon by the Edmonds-Karp algorithm, which does the same thing in O\big(V^2 \cdot E\big)O(V 
+2
+ ⋅E) time, independent of the maximum flow value.
+
+## ALGORITHM
+Follow 3 basic steps:
+1. Find augmented path
+2. Complete the bottle neck capacity
+3. Augment each edge and total flow
+Repeat these steps until the augmented path is reached
+
+### Example:
+![step1](https://github.com/syedareehaquasar/hello-world/blob/master/e.PNG)
+here only 2 spaces are there in DT so taking 2
+![step2](https://github.com/syedareehaquasar/hello-world/blob/master/ee.PNG)
+Similarly another path
+![step3](https://github.com/syedareehaquasar/hello-world/blob/master/eee.PNG)
+Similarly another path
+![step5](https://github.com/syedareehaquasar/hello-world/blob/master/eeeee.PNG)
+Similarly another path
+![step6](https://github.com/syedareehaquasar/hello-world/blob/master/eeeeeeeeeee.PNG)
+Here paths SA and CD are full but we require 2 in AC but place of only 1 in CD so we have reached our answer ->19
+![final answer](https://github.com/syedareehaquasar/hello-world/blob/master/eeeeeeeeeeeeeee.PNG)
+
+## PSEUDOCODE
+
+The pseudo-code for this method is quite short; however, there are some functions that bear further discussion. The simple pseudo-code is below.
+This pseudo-code is not written in any specific computer language. Instead, it is an informal, high-level description of the algorithm.
+
+Ford-Fulkerson Algorithm ((Graph GG, source ss, sink t):t):
+```
+initialize flow to 0
+path = findAugmentingPath(G, s, t)
+while path exists:
+    augment flow along path                 #This is purposefully ambiguous for now
+    G_f = createResidualGraph()
+    path = findAugmentingPath(G_f, s, t)
+return flow
+```
+
+# Time Complexity
+O(max_flow * E)
+Time complexity of the above algorithm is O(max_flow * E). We run a loop while there is an augmenting path. In worst case, we may add 1 unit flow in every iteration. Therefore the time complexity becomes O(max_flow * E)
+![tc](https://github.com/syedareehaquasar/hello-world/blob/master/h.PNG)
+
+# Implementation
+
+ - [c code](https://github.com/jainaman224/Algo_Ds_Notes/blob/master/Ford_Fulkerson_Method/Ford_Fulkerson_Method.c)
+ - [coffee code]
+ - [cpp code](https://github.com/jainaman224/Algo_Ds_Notes/blob/master/Ford_Fulkerson_Method/Ford-Fulkerson.cpp)
+ - [c# code]
+ - [go code]
+ - [java code](https://github.com/jainaman224/Algo_Ds_Notes/blob/master/Ford_Fulkerson_Method/Ford_Fulkerson_Method.java)
+ - [javaScript code]
+ - [kotlin code]
+ - [python code](https://github.com/jainaman224/Algo_Ds_Notes/blob/master/Ford_Fulkerson_Method/Ford_Fulkerson_Method.py)
+ - [ruby code]
+ - [dart code]