From 69ee8198b0d2bd21a4c21112220e3bf8e9791266 Mon Sep 17 00:00:00 2001
From: Samir Paul <77569653+SamirPaulb@users.noreply.github.com>
Date: Sun, 1 Dec 2024 11:40:42 +0530
Subject: [PATCH] Update 11. Kth Missing Positive Number.py

---
 .../11. Kth Missing Positive Number.py        | 39 +++++++++++++------
 1 file changed, 27 insertions(+), 12 deletions(-)

diff --git a/11_Binary-Search/11. Kth Missing Positive Number.py b/11_Binary-Search/11. Kth Missing Positive Number.py
index 95ca2f3c..a0c11727 100644
--- a/11_Binary-Search/11. Kth Missing Positive Number.py	
+++ b/11_Binary-Search/11. Kth Missing Positive Number.py	
@@ -1,18 +1,33 @@
 # https://leetcode.com/problems/kth-missing-positive-number/
-# https://youtu.be/88k8xa-pSrM
+# https://www.youtube.com/watch?v=uZ0N_hZpyps
 
+# Brute Force approach
+# If there were no elements in arr, then Kth element would be k.
+# But for every element of value less than equal to k, will make
+# Kth missing value shift to right 
 class Solution:
     def findKthPositive(self, arr: List[int], k: int) -> int:
-        l, r = 0, len(arr)-1
-        while l <= r:
-            mid = l + (r - l) // 2
-            if arr[mid] < mid+1 + k:
-                l = mid + 1
+        for i in arr:
+            if i <= k: k += 1 
+            else: break
+        return k
+# Time: O(N)
+# Space: O(1)
+
+
+# Binary Search approach => Most Optimised
+class Solution:
+    def findKthPositive(self, arr: List[int], k: int) -> int:
+        l,r = 0,len(arr)-1
+        while l<=r:
+            m = l+(r-l)//2
+            tmp = m
+            if arr[m] - m - 1 < k:
+                l = m+1
             else:
-                r = mid - 1
-        
-        return l + k
-    
-    
-# Time: O(log(n))
+                r = m-1
+        # Now r<l and arr[r] to arr[l]: Kth element is in this window
+        return arr[r] + (k - (arr[r]-r-1))
+
+# Time: O(log(N))
 # Space: O(1)