Add this linear time selection algorithm

This is selection algorithm which finds kth smallest/largest element in a array with linear time complexity.

Author: souravmondaldev

Lineartimeselectionalgorithm/kthsmallestelement.py

@@ -0,0 +1,87 @@
+#----Median Of Median finding algorithm implimentation in python----
+
+
+#used to avoid overflow
+INT_MAX=2**32
+
+#finding the kth element from the list
+def kthS(a,k) :
+    a.sort()
+    return a[k-1]
+
+#finding median from the fixed length of array( median of arr[] from index l to l+n )
+def findmedian(a,l,n):
+    a=a[l:l+n]
+    a.sort()
+    return a[n//2]
+
+#This funrions uses median of median algo to find kthsmallest number in linear time
+def kthSmallest(a,l,r,k):
+    if k>0 and k<=r-l+1:
+        n=r-l+1
+        median=[0]*((n+4)//5)
+        i=0
+        #divide the array into smaller array of size 5 and find median of each small array
+        while(i<n//5):
+            median[i]=findmedian(a,l+i*5,5)
+            i+=1
+        # For last group with less than 5 elements 
+        if i*5<n:
+            median[i] = findmedian(a,l+i*5, n%5)  
+            i+=1
+        # Find median of all medians using recursive call.  
+        # If median[] has only one element, then no need  
+        # of recursive call
+        if(i == 1):
+            medOfMed = median[i-1]
+        else:    
+            kthSmallest(median, 0, i-1, i//2)
+        # Partition the array around a medOfMed 
+        # element and get position of pivot  
+        # element in sorted array 
+        pos = partition(a, l, r, medOfMed)
+        if pos-l == k-1: 
+            return a[pos]
+        if (pos-l > k-1):
+            return kthSmallest(a, l, pos-1, k)
+        return kthSmallest(a, pos+1, r, k-pos+l-1) 
+    return INT_MAX
+#for swapping two array elements
+def swap(arr, a, b): 
+    temp = arr[a] 
+    arr[a] = arr[b] 
+    arr[b] = temp 
+
+# It searches for x in arr[l..r],   
+# and partitions the array around x
+def partition(a,l,r,x):  
+    for i in range(l,r):
+        if (a[i] == x):
+           break
+    swap(a,i,r)
+    i = l 
+    for j in range(l,r):
+        if (a[j] <= x):
+            swap(a,i,j)
+            i+=1
+    swap(a,i,r); 
+    return i;
+#driver code
+def main():
+    #Total number of elements in the list is n
+    n=int(input("Enter value of n:"))
+    k=(n+1)//2
+    a=[]
+    #entering n elements to the lsit
+    for i in range(n):
+        x=int(input())
+        a.append(x)
+    #if total number of elements is even just print the kth elements
+    if(n%2==0):
+        print("result is: %d"%kthS(a,k))
+        return
+    #if total number of elements is odd the use median of median algo to find kth smallest
+    print("result %d"%kthSmallest(a, 0, n-1, k))
+#Calling the main funtion
+if __name__ == '__main__':
+    main()