Merge pull request div-bargali#797 from rachitmanas/main

Added algorithm to Search kth smallest in O(n) time

Author: div-bargali

C++/Algorithms/Searching-Algorithms/KthSmallestSearch.cpp

@@ -0,0 +1,112 @@
+// C++ implementation of worst case linear time algorithm 
+// to find k'th smallest element 
+#include<iostream> 
+#include<algorithm> 
+#include<climits> 
+ 
+using namespace std; 
+ 
+int partition(int arr[], int l, int r, int k); 
+ 
+// A simple function to find median of arr[]. This is called 
+// only for an array of size 5 in this program. 
+int findMedian(int arr[], int n) 
+{ 
+ sort(arr, arr+n); // Sort the array 
+ return arr[n/2]; // Return middle element 
+} 
+ 
+// Returns k'th smallest element in arr[l..r] in worst case 
+// linear time. ASSUMPTION: ALL ELEMENTS IN ARR[] ARE DISTINCT 
+int kthSmallest(int arr[], int l, int r, int k) 
+{ 
+ // If k is smaller than number of elements in array 
+ if (k > 0 && k <= r - l + 1) 
+ { 
+ int n = r-l+1; // Number of elements in arr[l..r] 
+ 
+ // Divide arr[] in groups of size 5, calculate median 
+ // of every group and store it in median[] array. 
+ int i, median[(n+4)/5]; // There will be floor((n+4)/5) groups; 
+ for (i=0; i<n/5; i++) 
+ median[i] = findMedian(arr+l+i*5, 5); 
+ if (i*5 < n) //For last group with less than 5 elements 
+ { 
+ median[i] = findMedian(arr+l+i*5, n%5); 
+ i++; 
+ } 
+ 
+ // Find median of all medians using recursive call. 
+ // If median[] has only one element, then no need 
+ // of recursive call 
+ int medOfMed = (i == 1)? median[i-1]: 
+ kthSmallest(median, 0, i-1, i/2); 
+ 
+ // Partition the array around a random element and 
+ // get position of pivot element in sorted array 
+ int pos = partition(arr, l, r, medOfMed); 
+ 
+ // If position is same as k 
+ if (pos-l == k-1) 
+ return arr[pos]; 
+ if (pos-l > k-1) // If position is more, recur for left 
+ return kthSmallest(arr, l, pos-1, k); 
+ 
+ // Else recur for right subarray 
+ return kthSmallest(arr, pos+1, r, k-pos+l-1); 
+ } 
+ 
+ // If k is more than number of elements in array 
+ return INT_MAX; 
+} 
+ 
+void swap(int *a, int *b) 
+{ 
+ int temp = *a; 
+ *a = *b; 
+ *b = temp; 
+} 
+ 
+// It searches for x in arr[l..r], and partitions the array 
+// around x. 
+int partition(int arr[], int l, int r, int x) 
+{ 
+ // Search for x in arr[l..r] and move it to end 
+ int i; 
+ for (i=l; i<r; i++) 
+ if (arr[i] == x) 
+ break; 
+ swap(&arr[i], &arr[r]); 
+ 
+ // Standard partition algorithm 
+ i = l; 
+ for (int j = l; j <= r - 1; j++) 
+ { 
+ if (arr[j] <= x) 
+ { 
+ swap(&arr[i], &arr[j]); 
+ i++; 
+ } 
+ } 
+ swap(&arr[i], &arr[r]); 
+ return i; 
+} 
+ 
+// Driver program to test above methods 
+int main() 
+{ 
+ int n,k;
+ cout<<"Enter size of the array: ";
+ cin>>n;
+ cout<<"Enter The elements of array\n";
+ int arr[n];
+ for (int i = 0; i < n; i++)
+ {
+ cin>>arr[i];
+ }
+ cout<<"Enter k: ";//Program will find kth smallest value in array without sorting
+ cin>>k;
+ cout << "K'th smallest element is "
+ << kthSmallest(arr, 0, n-1, k); 
+ return 0; 
+}