From efb3ce0e0ababa1807fdd32b1b6dea829ef6c9cf Mon Sep 17 00:00:00 2001
From: Brijesh Kumar <brijeshsos66@.com>
Date: Thu, 1 Oct 2020 14:49:35 +0530
Subject: [PATCH] added backtracking algorithm named all permutations

---
 .../backtracking/all_permutations.hpp         | 51 +++++++++++++++++++
 .../backtracking/all_permutations.cpp         | 29 +++++++++++
 2 files changed, 80 insertions(+)
 create mode 100644 cpp/include/algorithm/backtracking/all_permutations.hpp
 create mode 100644 cpp/test/algorithm/backtracking/all_permutations.cpp

diff --git a/cpp/include/algorithm/backtracking/all_permutations.hpp b/cpp/include/algorithm/backtracking/all_permutations.hpp
new file mode 100644
index 00000000..b4b3e96e
--- /dev/null
+++ b/cpp/include/algorithm/backtracking/all_permutations.hpp
@@ -0,0 +1,51 @@
+/*
+    Printing all the permutations of a string/array
+    --------------------
+    A permutation, also called an “arrangement number” or “order,” is a rearrangement 
+    of the elements of an ordered list S into a one-to-one correspondence with S itself.
+    A string of length n has n! permutation. Generate all the permutations of the string.
+    
+    Time complexity
+    ---------------
+    O(N*N!), where N is the length of the string.
+    
+    Space complexity
+    ----------------
+    O(N!), where N is the length of the string.
+    
+    Author
+    ------
+    Brijesh Kumar (@brijeshsos66)
+*/
+
+#ifndef ALL_PERMUTATIONS_HPP
+#define ALL_PERMUTATIONS_HPP
+
+#include <algorithm>
+
+/*
+Below is the program for printing the permutations of a string. Inorder to perform the same on a array/vector
+then convert the array elements into string(using to_string() function) and perform the same.
+Here start is the starting point of a string intially equals to 0 and end is initially equals to length of the 
+string minus 1 (N - 1) as indices are starting from 0.
+*/
+void permutations(string str, int start, int end){ 
+    //BASE case
+    if(start == end)
+        cout<<str<<endl;
+    else{
+        for(int i=start;i<=end;i++){
+            //SWAP
+            swap(a[start],a[i]);
+            
+            //RECURSION
+            permutations(str,start+1,end);
+            
+            //BACKTRACKING
+            swap(a[start],a[i]);
+        }
+    }
+}
+
+
+#endif // ALL_PERMUTATIONS_HPP
diff --git a/cpp/test/algorithm/backtracking/all_permutations.cpp b/cpp/test/algorithm/backtracking/all_permutations.cpp
new file mode 100644
index 00000000..f60f722c
--- /dev/null
+++ b/cpp/test/algorithm/backtracking/all_permutations.cpp
@@ -0,0 +1,29 @@
+#include "third_party/catch.hpp"
+#include "algorithm/backtracking/all_permutations.hpp"
+
+TEST_CASE("Base cases","[backtracking][all_permutations]"){
+ string s =""; // empty string
+ vector<string> permutations = {""};
+ REQUIRE(all_permutations(s,0,s.length()-1) == permutations);
+
+ s = "a";
+ permutations = {"a"};
+ REQUIRE(all_permutations(s,0,s.length()-1) == permutations); 
+ 
+ s = " ";
+ permutations = {" "};
+ REQUIRE(all_permutations(s,0,s.length()-1) == permutations); 
+}
+
+ TEST_CASE("Normal cases",[backtracking][all_permutations]"){
+ string s = "abc";
+ vector<string> permutations = {"abc","acb","bac","bca","cab","cba"};
+ REQUIRE(all_permutations(s,0,s.length()-1) == permutations);
+
+ s = "abcd";
+ permutations ={"abcd","abdc","acbd","acdb","adcb","adbc",
+                "bacd","badc","bcad","bcda","bdca","bdac",
+                "cbad","cbda","cabd","cadb","cdab","cdba",
+                "dbca","dbac","dcba","dcab","dacb","dabc" };
+ REQUIRE(all_permutations(s,0,s.length()-1) == permutations);
+}
\ No newline at end of file