Merge branch 'smv1999:master' into master

Author: ishikasinha-d

Arrays/Kth_smallest_element_in_an_array_using_heap.cpp

@@ -0,0 +1,41 @@
+/**************************************************************************
+Given an array arr[] and a number K where K is smaller than size of array, 
+the task is to find the Kth smallest element in the given array. 
+Given all Array elements are distinct.
+
+For Example: arr[] = {7, 8, 1, 4, 9, 3}
+             k = 3 ------> 3rd smallest element in the array
+        ANS: 4
+
+This can be solved using heap and priority queue.
+***************************************************************************/
+
+// SOLUTION (in C++):
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+int main()
+{
+   int n, k;
+   cin >> n >> k;
+   cout << "Enter the array elements" << endl;
+   int arr[n];
+   priority_queue<int> maxh;
+   //A priority queue keeps the elements in the order of their priority, i.e.,
+   //elements having greater values will be at the top of the queue and elements having smaller values will be kept at the bottom of the queue.
+   //The element popped out of this queue is the element with the maximum value.
+
+   for (int i = 0; i < n; i++)
+   {
+      maxh.push(arr[i]);
+      if (maxh.size() > k)
+      {
+         maxh.pop();
+      }
+   }
+
+   cout << "The " << k << "th smallest element is " << maxh.top();
+   return 0;
+}

Arrays/Max_XOR_of_Two_Array.cpp

@@ -0,0 +1,117 @@
+/* 
+Given an integer array nums, return the maximum result of nums[i] XOR nums[j], 
+where 0 ≤ i ≤ j < n.
+*/
+
+#include<iostream>
+#include<vector>
+using namespace std;
+
+// Constructing a trie
+struct trie {
+        trie *zero,*one;
+};
+
+//Building the trie
+void insert(int num,trie *root) {
+   // Store the head
+   trie *ptr=root;
+      for(int i=31;i>=0;i--) {
+        // Find the i-th bit
+         int h = (num>>i & 1);
+           if(h==0) {
+               // If ptr->zero is NULL
+                if(ptr->zero==NULL) {
+                    ptr->zero=new trie();
+                }
+                // Update ptr to ptr->zero
+                ptr=ptr->zero;
+            }
+            else {
+                // If ptr->onr is NULL
+                if(ptr->one==NULL) {
+                    ptr->one=new trie();
+                }
+                // Update ptr to ptr->one
+                ptr=ptr->one;
+            }
+        }
+}
+
+//Finding the maximum XOR for each element   
+int comp(int num,trie *root) {
+        trie *ptr = root;
+        int sum=0;
+        for(int i=31;i>=0;i--) {
+            sum=sum<<1;
+            // Finding ith bit
+           int h = (num>>i & 1);
+           // Check if the bit is 0
+            if(h==0) {
+                // If right node exists
+                if(ptr->one) {
+                   sum++;
+                    ptr=ptr->one;
+                }
+                else ptr=ptr->zero;
+                
+            }
+            else {
+                // Check if left node exists
+                  if(ptr->zero) {
+                   sum++;
+                    ptr=ptr->zero;
+                }
+                else ptr=ptr->one;
+            }
+        }
+        return sum;
+}
+   
+int findMaximumXOR(vector<int>& nums) {
+        // head Node of Trie
+        trie *root = new trie(); 
+        // Insert each element in trie
+        for(int i=0;i<nums.size();i++) {
+            insert(nums[i],root);
+        }
+        // Stores the maximum XOR value
+        int maxm=0;
+        // Traverse the given array
+        for(int i=0;i<nums.size();i++) {
+            maxm=max(comp(nums[i],root),maxm);
+        }
+        return maxm;
+}
+
+//Main Function
+int main() {
+
+   vector<int>nums;
+   int sz; 
+   
+   cout<<"Enter the vector size\n";
+   cin>>sz; // size of the vector
+ 
+   cout<<"Enter the elements in the vector\n";
+   for(int i=0;i<sz;i++) {
+   	 int x; 
+	 cin>>x;
+	 nums.push_back(x);
+   }
+  
+   int answer = findMaximumXOR(nums);
+   cout<<"The Maximum XOR of two numbers in the array/vector is : "<<answer<<endl;   
+
+        return 0;
+}
+
+/* Sample Text Case 
+ Enter the vector size
+ 6
+ Enter the elements in the vector
+ 3 10 5 25 2 8
+ The Maximum XOR of two numbers in the array/vector is : 28
+
+ Time Complexity : O(n) , where n is the number of elements in the vector.
+*/