Advalgo

Labs/Lab01/Randomized_QuickSort.cpp → Labs/Lab01/1_Randomized_QuickSort.cpp

@@ -1,25 +1,28 @@
 #include <bits/stdc++.h>
 
-
 using namespace std;
 
-int c = 0, sw = 0;
-int getRandom(int p, int r) {    
+int getRandom(int p, int r)
+{
     srand(time(0));
     return (rand() % (r - p + 1)) + p;
 }
+
+int c = 0, sw = 0;
+int partition(vector<int> &v, int l, int h)
+{
 
-int partition(vector <int> &v, int l, int h){
-
-    // Take last element as pivot 
+    // Take last element as pivot
     int pivot = v[h];
 
     int i = l;
-    for(int j = l; j < h;j++){
+    for (int j = l; j < h; j++)
+    {
 
         c++;
-        // 
-        if(v[j] <= pivot){
+        //
+        if (v[j] <= pivot)
+        {
             sw++;
             swap(v[i], v[j]);
             i++;
@@ -30,10 +33,12 @@ int partition(vector <int> &v, int l, int h){
 
     return i;
 }
-void quickSort(vector <int> &v, int l, int h){
 
+void quickSort(vector<int> &v, int l, int h)
+{
 
-    if(l < h){
+    if (l < h)
+    {
         int random = getRandom(l, h);
         swap(v[random], v[h]);
 
@@ -42,35 +47,34 @@ void quickSort(vector <int> &v, int l, int h){
         quickSort(v, q + 1, h);
     }
 
-
     return;
 }
 
+int main()
+{
 
-int main(){
-
     // vector <int> v = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
     // vector <int> v = {10, 9, 8, 7, 6, 5, 4, 3, 2, 1};
     // vector <int> v = {7, 5, 6, 10, 9, 2, 1, 8, 4, 3};
     // vector <int> v = {4, 3, 6, 8, 5, 9, 20, 50, 12, 30, 432, 12, 69, 29, 40, 50, 10, 4, 23, 34, 45, 45, 24,  89, 799, 45, 80, 50, 10, 30, 43,54,65,76,87, 98, 21, 32, 43, 78, 98, 57, 29, 91, 34,  54, 64, 19, 82, 87, 65};
 
-    // vector <int> v = {1, 2, 3, 4, 5, 6}; 
+    // vector <int> v = {1, 2, 3, 4, 5, 6};
 
     int n;
     cin >> n;
-    vector <int> v(n);
+    vector<int> v(n);
     for (int i = 0; i < n; i++)
     {
         v[i] = i;
     }
-    
+
     quickSort(v, 0, n - 1);
     cout << "Sorted : ";
-    for(auto k : v) cout << k << " ";
+    for (auto k : v)
+        cout << k << " ";
 
     cout << "\nComparisions : " << c << "\n";
     cout << "Swaps : " << sw << "\n";
-   
+
     return 0;
 }
-

Labs/Lab01/2_Kth_Smallest_Element.cpp

@@ -0,0 +1,73 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+
+int getRandom(int p, int r) {    
+    srand(time(0));
+    return (rand() % (r - p + 1)) + p;
+}
+
+
+int partition(vector <int> &v, int l, int h){
+
+
+    // Take last element as pivot
+    int pivot = v[h];
+
+
+    int i = l;
+    for(int j = l; j < h;j++){
+
+
+        if(v[j] <= pivot){
+
+            swap(v[i], v[j]);
+            i++;
+        }
+    }
+
+    swap(v[i], v[h]);
+
+
+    return i;
+}
+
+
+int  find(vector <int> &v, int l, int h, int k){
+
+
+    if(l < h){
+        int random = getRandom(l, h);
+        swap(v[random], v[h]);
+        int q = partition(v, l, h);
+
+
+        if(k - 1 == q) return v[q];
+
+
+        if(k - 1 < q){
+            return find(v, l, q - 1, k);
+        }
+        else{
+            return find(v, q + 1, h, k - q - 1); //
+        }
+    }
+    return 0;
+}
+
+
+
+
+int main(){
+
+
+
+    vector <int> v = {10, 9, 1, 2, 6, 99, 11};
+
+    int k = 4;
+    int n = v.size();
+
+    cout << find(v, 0, n - 1, k);
+
+    return 0;
+}

Labs/Lab01/Readme.md

@@ -1 +1,58 @@
-### Randomized Quick Sort
+## Randomized Quick Sort
+---
+>### Randomizer
+```c++
+// Generate Random number in between p and r :
+
+int getRandom(int l, int h) {    
+    srand(time(0));
+    return (rand() % (h - l + 1)) + l;
+}
+```
+>### Partition Function : last element as pivot
+```c++
+int partition(vector <int> &v, int l, int h){
+
+    // Take last element as pivot 
+    int pivot = v[h];
+
+    int i = l;
+    for(int j = l; j < h;j++){
+
+        if(v[j] <= pivot){
+            swap(v[i], v[j]);
+            i++;
+        }
+    }
+    swap(v[i], v[h]);
+
+    return i;
+}
+```
+>### Randomized Quick Sort
+```c++
+void quickSort(vector <int> &v, int l, int h){
+
+    if(l < h){
+        // Swap last element of array with any other element of array 
+        int random = getRandom(l, h);
+        swap(v[random], v[h]);
+
+        int q = partition(v, l, h);
+        quickSort(v, l, q - 1);
+        quickSort(v, q + 1, h);
+    }
+
+    return;
+}
+```
+
+>### Output : 
+For n = 10000
+|Run|Output|
+|---|---|
+|1.|![Alt text](images/image-0.png) |
+|2.|![Alt text](images/image-1.png)|
+
+|Simple Quick Sort|Randomized Quick Sort|
+|---|---|

Labs/Lab02/1_Primality_Testing.cpp

@@ -0,0 +1,91 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+using USLLI = unsigned long long int;
+
+// Generate Random number in between p and r :
+USLLI getRandom(USLLI p, USLLI r)
+{
+    srand(time(0));
+    return (rand() % (r - p + 1)) + p;
+}
+
+USLLI gcd(USLLI a, USLLI b)
+{
+
+    while (b != 0)
+    {
+        USLLI res = a % b;
+        a = b;
+        b = res;
+    }
+
+    return a;
+}
+
+USLLI power(USLLI a, USLLI x, USLLI n)
+{
+    USLLI res = 1;
+
+    while (x > 0)
+    {
+
+        // Odd
+
+        if (x % 2 == 1)
+        {
+            res = (res * a) % n;
+        }
+
+        x = x / 2;
+
+        a = (a * a) % n;
+    }
+
+    return res;
+}
+
+// as k increases, probability of correct ans increases
+int k = 100;
+
+bool isPrime(USLLI n)
+{
+
+    if (n <= 1 || n == 4)
+        return false;
+
+    if (n <= 3)
+        return true;
+
+    while (k > 0)
+    {
+
+        USLLI a = getRandom(2, n - 2);
+
+        if (gcd(n, a) != 1)
+            return false;
+
+        if (power(a, n - 1, n) != 1)
+            return false;
+
+        k--;
+    }
+
+    return true;
+}
+int main()
+{
+
+    USLLI n;
+    cout << "Enter Number for Primality Testing : ";
+    cin >> n;
+    // 1000000007
+
+    if (isPrime(n))
+        cout << n << " is Prime";
+    else
+        cout << n << " is Composite";
+
+    return 0;
+}

Labs/Lab02/2_Probability_Of_liars.cpp

@@ -0,0 +1,50 @@
+#include <bits/stdc++.h>
+using namespace std;
+using USLLI = unsigned long long int;
+
+USLLI power(USLLI a, USLLI x, USLLI n)
+{
+    USLLI res = 1;
+
+    while (x > 0)
+    {
+
+        // Odd
+
+        if (x % 2 == 1)
+        {
+            res = (res * a) % n;
+        }
+
+        x = x / 2;
+
+        a = (a * a) % n;
+    }
+
+    return res;
+}
+
+int main()
+{
+
+    USLLI n;
+    cout << "Enter Number : ";
+    cin >> n;
+
+    USLLI count = 0;
+
+    for (USLLI i = 2; i <= n - 2; i++)
+    {
+        if (power(i, n - 1, n) == 1)
+        {
+            count++;
+        }
+    }
+
+    cout << "Fermate's Liars : " << count << "\n";
+    cout << "Fermate's Witnesses : " << n - 3 - count << "\n";
+
+    cout << "Probability of Fermate's Liars: " << (double)count / (n - 3);
+
+    return 0;
+}