From c6510d2e0c6a68a8a7ba0e252e302e809efe56f4 Mon Sep 17 00:00:00 2001
From: AkshatAggEm <akshat.agg1506@gmail.com>
Date: Sat, 12 Oct 2019 00:09:45 +0530
Subject: [PATCH] made some changes to the mathematical problems/algorithms.

---
 Mathematical Algorithms/DecToOctal.cpp        | 25 ++++++++
 Mathematical Algorithms/PythaTriplets.cpp     | 44 ++++++++++++++
 Mathematical Algorithms/isArmstrong.cpp       | 30 ++++++++++
 Mathematical Algorithms/isFibonaccian.cpp     | 27 +++++++++
 .../K-Combinations.cpp                        | 54 ++++++++++++++++++
 Recursion, Backtracking etc/Permutations.cpp  | 57 +++++++++++++++++++
 Recursion, Backtracking etc/Power Set.cpp     | 51 +++++++++++++++++
 7 files changed, 288 insertions(+)
 create mode 100644 Mathematical Algorithms/DecToOctal.cpp
 create mode 100644 Mathematical Algorithms/PythaTriplets.cpp
 create mode 100644 Mathematical Algorithms/isArmstrong.cpp
 create mode 100644 Mathematical Algorithms/isFibonaccian.cpp
 create mode 100644 Recursion, Backtracking etc/K-Combinations.cpp
 create mode 100644 Recursion, Backtracking etc/Permutations.cpp
 create mode 100644 Recursion, Backtracking etc/Power Set.cpp

diff --git a/Mathematical Algorithms/DecToOctal.cpp b/Mathematical Algorithms/DecToOctal.cpp
new file mode 100644
index 0000000..f4b80f4
--- /dev/null
+++ b/Mathematical Algorithms/DecToOctal.cpp	
@@ -0,0 +1,25 @@
+#include<iostream>
+using namespace std;
+
+void decToOct(int num) 
+{	int arr[50], i = 0; 
+    
+	while (num != 0) { 
+        arr[i] = num % 8; 
+        num /= 8; 
+        i++; 
+    } 
+	
+    for (int j = i - 1; j >= 0; j--) 
+        cout << arr[j]; 
+} 
+
+int main() 
+{ 
+    int n;
+	cin >>n; 
+
+    decToOct(n);
+  
+    return 0; 
+} 
\ No newline at end of file
diff --git a/Mathematical Algorithms/PythaTriplets.cpp b/Mathematical Algorithms/PythaTriplets.cpp
new file mode 100644
index 0000000..f33a799
--- /dev/null
+++ b/Mathematical Algorithms/PythaTriplets.cpp	
@@ -0,0 +1,44 @@
+#include <iostream>
+using namespace std;
+
+int main() {
+	int num;
+	cin>>num;
+	
+	if(num == 1 || num == 2){
+	    cout<<"-1";
+	}
+	
+	/*
+        for pythagorean triplets, 
+        
+        if n is even, 
+            the triplets could be given by, 
+             n^2/4-1, n and n^2/4+1
+             so if a variable say, var = n^2/4-1, then
+             
+             a = var
+             b = n
+             c = var + 2
+            
+        if n is odd, 
+            the triplets could be given by, 
+             (n^2-1)/2, n and (n^2+1)/2
+             so if a variable say, var = (n^2-1)/2, then
+             
+             a = var
+             b = n
+             c = var + 1
+	*/
+	
+	else if(num%2==0){
+            long m=num/2;
+            long n=1;
+            cout<<(m*m-n*n)<<" "<<(m*m+n*n);
+        }else{
+            long m=(num + 1)/2;
+            long n=(num - 1)/2;
+            cout<<(2*m*n)<<" "<<(m*m+n*n);
+        }
+	return 0;
+}
\ No newline at end of file
diff --git a/Mathematical Algorithms/isArmstrong.cpp b/Mathematical Algorithms/isArmstrong.cpp
new file mode 100644
index 0000000..e9eaeb1
--- /dev/null
+++ b/Mathematical Algorithms/isArmstrong.cpp	
@@ -0,0 +1,30 @@
+#include<iostream>
+#include<math.h>
+using namespace std;
+
+bool isArmstrong(int num){
+    int temp = num,
+        sum = 0,
+        power;
+
+    power = std::to_string(temp).length();
+    /*
+        std::to_string(integer) coverts our number into a string so as to operate upon it various string
+        functionalities
+    */
+    // cout<<power;
+
+    while(num>=1){
+        sum = sum + pow((num%10), power);
+        num = num/10;
+    }
+    return(sum == temp);
+}
+
+int main(){
+    int n;
+    cin>>n;
+
+    isArmstrong(n)?cout<<"true":cout<<"false";
+    return 0;
+}
diff --git a/Mathematical Algorithms/isFibonaccian.cpp b/Mathematical Algorithms/isFibonaccian.cpp
new file mode 100644
index 0000000..b0e227f
--- /dev/null
+++ b/Mathematical Algorithms/isFibonaccian.cpp	
@@ -0,0 +1,27 @@
+#include<iostream>
+#include<math.h>
+using namespace std;
+
+//checks if it is perfect square or not
+bool isSqrt(int num){
+    int s = sqrt(num);
+    return(s*s == num);
+}
+
+//checks if it the two terms 5n^2 + 4 are perfect squares or not
+bool isFibonacci(int n){
+    return isSqrt(5*n*n + 4) || isSqrt(5*n*n - 4);
+}
+
+int main(){
+    //the main principle behind whether a number is a fibonacci series element or not is,
+    // say the number is n, it is in fibonacci, if and only if, one or both, (5n^2 + 4) and (5n^2 - 4) are perfect squares.
+
+     int number;
+
+     cout<<"Enter the number which you want to search inside the series: ";
+     cin>>number;
+
+     isFibonacci(number)? cout<<"Yes the number is present in series." :
+                          cout<<"No, it is not present in the list.";
+}
diff --git a/Recursion, Backtracking etc/K-Combinations.cpp b/Recursion, Backtracking etc/K-Combinations.cpp
new file mode 100644
index 0000000..8038234
--- /dev/null
+++ b/Recursion, Backtracking etc/K-Combinations.cpp	
@@ -0,0 +1,54 @@
+/*
+ Petar 'PetarV' Velickovic
+ Algorithm: K-Combinations
+*/
+
+#include <stdio.h>
+#include <math.h>
+#include <string.h>
+#include <iostream>
+#include <vector>
+#include <list>
+#include <string>
+#include <algorithm>
+#include <queue>
+#include <stack>
+#include <set>
+#include <map>
+#include <complex>
+using namespace std;
+typedef long long lld;
+
+int n, k;
+int skup[100];
+bool inSet[100];
+
+//Program koji generise sve kombinacije od po K elemenata datog skupa
+//Slozenost: O((n choose k))
+
+void kCombinations(int pos, int amt)
+{
+    if (n-pos<k-amt) return;
+    if (amt==k)
+    {
+        for (int i=0;i<n;i++) if (inSet[i]) printf("%d ",skup[i]);
+        printf("\n");
+        return;
+    }
+    inSet[pos] = true;
+    kCombinations(pos+1,amt+1);
+    inSet[pos] = false;
+    kCombinations(pos+1,amt);
+}
+
+int main()
+{
+    n = 5, k = 2;
+    skup[0] = 1;
+    skup[1] = 2;
+    skup[2] = 3;
+    skup[3] = 4;
+    skup[4] = 5;
+    kCombinations(0, 0);
+    return 0;
+}
diff --git a/Recursion, Backtracking etc/Permutations.cpp b/Recursion, Backtracking etc/Permutations.cpp
new file mode 100644
index 0000000..4173ab1
--- /dev/null
+++ b/Recursion, Backtracking etc/Permutations.cpp	
@@ -0,0 +1,57 @@
+/*
+ Petar 'PetarV' Velickovic
+ Algorithm: Permutations
+*/
+
+#include <stdio.h>
+#include <math.h>
+#include <string.h>
+#include <iostream>
+#include <vector>
+#include <list>
+#include <string>
+#include <algorithm>
+#include <queue>
+#include <stack>
+#include <set>
+#include <map>
+#include <complex>
+using namespace std;
+typedef long long lld;
+
+int n;
+int niz[100];
+bool inPerm[100];
+int currPerm[100];
+
+//Algoritam koji generise sve permutacije datog niza
+//Slozenost: O(n!)
+
+void generatePermutations(int pos)
+{ 
+    if (pos == n)
+    {
+        for (int i=0;i<n;i++) printf("%d ",currPerm[i]);
+        printf("\n");
+    }
+    for (int i=0;i<n;i++)
+    {
+        if (!inPerm[i])
+        {
+            currPerm[pos] = niz[i];
+            inPerm[i] = true;
+            generatePermutations(pos+1);
+            inPerm[i] = false;
+        }
+    }
+}
+
+int main()
+{
+    n = 3;
+    niz[0] = 1;
+    niz[1] = 2;
+    niz[2] = 3;
+    generatePermutations(0);
+    return 0;
+}
diff --git a/Recursion, Backtracking etc/Power Set.cpp b/Recursion, Backtracking etc/Power Set.cpp
new file mode 100644
index 0000000..f38ad5d
--- /dev/null
+++ b/Recursion, Backtracking etc/Power Set.cpp	
@@ -0,0 +1,51 @@
+/*
+ Petar 'PetarV' Velickovic
+ Algorithm: Power Set
+*/
+
+#include <stdio.h>
+#include <math.h>
+#include <string.h>
+#include <iostream>
+#include <vector>
+#include <list>
+#include <string>
+#include <algorithm>
+#include <queue>
+#include <stack>
+#include <set>
+#include <map>
+#include <complex>
+using namespace std;
+typedef long long lld;
+
+//Metoda koja generise partitivni skup nekog skupa
+//Slozenost: O(2^n)
+
+int n;
+int skup[100];
+bool inSet[100];
+
+void powerSet(int pos)
+{
+    if (pos==n)
+    {
+        for (int i=0;i<n;i++) if (inSet[i]) printf("%d ",skup[i]);
+        printf("\n");
+        return;
+    }
+    inSet[pos] = false;
+    powerSet(pos+1);
+    inSet[pos] = true;
+    powerSet(pos+1);
+}
+
+int main()
+{
+    n = 3;
+    skup[0] = 1;
+    skup[1] = 2;
+    skup[2] = 3;
+    powerSet(0);
+    return 0;
+}