Add 1533_Kth_Missing_Positive_Number.java (qiyuangong#48)

* Add Kth_Missing_Positive_Number.java

Contributed by @dvlpsh

Author: dvlpsh

java/1533_Kth_Missing_Positive_Number.java

@@ -0,0 +1,47 @@
+class Solution {
+    public int findKthPositive(int[] a, int k) 
+    {
+        int B[] = new int[a.length];
+        
+        //equation (A)
+        //B[i]=a[i]-i-1
+        
+        
+        //B[i]=number of missing numbers BEFORE a[i]
+        for(int i=0;i<a.length;i++)
+            B[i]=a[i]-i-1; //-1 is done as here missing numbers start from 1 and not 0
+        
+        //binary search upper bound of k
+        //smallest value>=k
+        
+        int lo=0,hi=B.length-1;
+        
+        while(lo<=hi)
+        {
+            int mid = lo+(hi-lo)/2;
+            
+            if(B[mid]>=k)
+                hi=mid-1;
+            else
+                lo=mid+1;
+        }
+        
+        //lo is the answer
+        
+        /*now the number to return is a[lo]-(B[lo]-k+1) (EQUATION B)
+        //where (B[lo]-k+1) is the number of steps we need to go back 
+        //from lo to retrieve kth missing number, since we need to find 
+        //the kth missing number BEFORE a[lo], we do +1 here as 
+        //a[lo] is not a missing number when B[lo]==k
+        //putting lo in equation(A) above
+        //B[i]=a[i]-i-1
+        //B[lo]=a[lo]-lo-1
+        and using this value of B[lo] in equation B
+        //we return a[lo]-(a[lo]-lo-1-k+1)
+        we get lo+k as ans
+        so return it*/
+        
+        return lo+k;
+        
+    }
+}