@@ -70,4 +70,67 @@ public static double medianUsingCountingSort(int[] array) {
7070 return median ;
7171 }
7272
73+ 74+ 75+ // partition function similar to quick sort
76+ // Considers last element as pivot and adds
77+ // elements with less value to the left and
78+ // high value to the right and also changes
79+ // the pivot position to its respective position
80+ // in the final array.
81+ public static int partition (int [] arr , int low ,
82+ int high )
83+ {
84+ int pivot = arr [high ], pivotloc = low ;
85+ for (int i = low ; i <= high ; i ++) {
86+ // inserting elements of less value
87+ // to the left of the pivot location
88+ if (arr [i ] < pivot ) {
89+ int temp = arr [i ];
90+ arr [i ] = arr [pivotloc ];
91+ arr [pivotloc ] = temp ;
92+ pivotloc ++;
93+ }
94+ }
95+ 96+ // swapping pivot to the final pivot location
97+ int temp = arr [high ];
98+ arr [high ] = arr [pivotloc ];
99+ arr [pivotloc ] = temp ;
100+ 101+ return pivotloc ;
102+ }
103+ 104+ /**
105+ * QuickSelect is a selection algorithm to find the k-th smallest element in an unordered list.
106+ * It is related to the quick sort sorting algorithm.
107+ */
108+ // finds the kth position (of the sorted array)
109+ // in a given unsorted array i.e this function
110+ // can be used to find both kth largest and
111+ // kth smallest element in the array.
112+ // ASSUMPTION: all elements in arr[] are distinct
113+ @ TimeComplexity ("O(n)" )
114+ public static int kthSmallestWithQuickSelect (int [] arr , int low ,
115+ int high , int k )
116+ {
117+ // find the partition
118+ int partition = partition (arr , low , high );
119+ 120+ // if partition value is equal to the kth position,
121+ // return value at k.
122+ if (partition == k - 1 )
123+ return arr [partition ];
124+ 125+ // if partition value is less than kth position,
126+ // search right side of the array.
127+ else if (partition < k - 1 )
128+ return kthSmallestWithQuickSelect (arr , partition + 1 , high , k );
129+ 130+ // if partition value is more than kth position,
131+ // search left side of the array.
132+ else
133+ return kthSmallestWithQuickSelect (arr , low , partition - 1 , k );
134+ }
135+ 73136}
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