From 6ac73f8451ec07c1ecd5013a026e48b399adf2c5 Mon Sep 17 00:00:00 2001
From: firoz Syed <syedfiroz2010@gmail.com>
Date: Sat, 26 Oct 2024 21:44:41 -0700
Subject: [PATCH] Binary-Search-2 Completed

---
 FindMinInSortedArray.java | 52 ++++++++++++++++++++++++++++++++++++++
 FindPeakElement.java      | 22 ++++++++++++++++
 FirstAndLastElement.java  | 53 +++++++++++++++++++++++++++++++++++++++
 3 files changed, 127 insertions(+)
 create mode 100644 FindMinInSortedArray.java
 create mode 100644 FindPeakElement.java
 create mode 100644 FirstAndLastElement.java

diff --git a/FindMinInSortedArray.java b/FindMinInSortedArray.java
new file mode 100644
index 00000000..de33c500
--- /dev/null
+++ b/FindMinInSortedArray.java
@@ -0,0 +1,52 @@
+// Time Complexity: O(logn)
+// Space Complexity : O(1)
+// Approach : Apply Binary Search to reduce the search range by moving the pointer towards unsorted portion as chances of min on the sorted portion is less.
+class Solution {
+    public int findMin(int[] nums) {
+        int n = nums.length;
+        int low = 0;
+        int high = n-1;
+        while(low<=high){
+            int mid = low + (high-low)/2;
+            // array rotated n times then it becomes sorted array
+            if(nums[low]<=nums[high]){
+                return nums[low];
+            }
+            // mid happen to be the pivot where the rotation happened
+            if((mid == 0 || (nums[mid-1] > nums[mid])) && (mid==high || (nums[mid+1] > nums[mid]))){
+                return nums[mid];
+            // right Array is sorted
+            }else if(nums[mid]<nums[high]){
+                high=mid-1;
+            // left Array is sorted
+            }else{
+                low=mid+1;
+            }
+        }
+        return -1;
+    }
+}
+class Solution {
+    // Time complexity: O(logn)
+    // Space Complexity: O(1)
+    // Approach : Binary Search and divide the search space by eliminating the sorted portion because min wont be present.
+    public int findMin(int[] nums) {
+        int n = nums.length;
+        int low =0;
+        int high=n-1;
+        while(low<=high){
+            int mid = low + (high-low)/2;
+            if((mid==0 || nums[mid-1]>nums[mid]) && (mid == high || nums[mid+1]>nums[mid])){
+                    return nums[mid] ;// on the pivot - rotation happend
+            }
+            // sorted portion is on right
+            if(nums[mid]<nums[high]){
+                high=mid-1;
+            }else{
+                low=mid+1;
+            }
+            
+        }
+        return -1;
+    }
+}
\ No newline at end of file
diff --git a/FindPeakElement.java b/FindPeakElement.java
new file mode 100644
index 00000000..b64a5e0e
--- /dev/null
+++ b/FindPeakElement.java
@@ -0,0 +1,22 @@
+// Time Complexity:
+// Space Complexity:
+// Approach : Binary Search and move the pointers towards right or left
+class Solution {
+    public int findPeakElement(int[] nums) {
+        int n = nums.length;
+        int low = 0;
+        int high = n-1;
+        while(low <= high){
+            int mid = low + (high-low)/2;
+            if((mid==0 || nums[mid-1]<nums[mid])&&(mid == n-1 || nums[mid+1]<nums[mid])){
+                return mid;
+            }
+            else if(mid>0 && nums[mid]<nums[mid-1]){
+                high=mid-1;
+            } else{
+                low=mid+1;
+            }
+        }
+        return -1;
+    }
+}
\ No newline at end of file
diff --git a/FirstAndLastElement.java b/FirstAndLastElement.java
new file mode 100644
index 00000000..38474524
--- /dev/null
+++ b/FirstAndLastElement.java
@@ -0,0 +1,53 @@
+// Time Complexity : logn + log n = O(logn)
+// Space Complexity : O(1)
+// Approach : Using Binary Search calculate first index of target which elements second half of arrya and using another binary search calculate second index which eliminates first half of array.
+class Solution {
+    public int[] searchRange(int[] nums, int target) {
+        int n =nums.length;
+        if(n==0) return new int []{-1,-1};
+        int low = 0;
+        int high = nums.length -1;
+
+        int firstPosition = firstBinarySearch(nums,low,high,target);
+        if (firstPosition == -1){
+            return new int[]{-1,-1};
+        }
+
+        int lastPosition = secondBinarySearch(nums,firstPosition,high,target);
+        return new int []{firstPosition,lastPosition};
+    }
+    public int firstBinarySearch(int[] nums , int low, int high, int target){
+        while(low<=high){
+            int mid = low + (high-low)/2;
+            if(nums[mid]==target){
+                if(mid ==0 || nums[mid-1]<nums[mid]){
+                    return mid;
+                } else {
+                    high = mid-1;
+                }
+            } else if(nums[mid]<target){
+                low = mid+1;
+            } else{
+                high = mid-1;
+            }
+        }
+        return -1;
+    }
+    public int secondBinarySearch(int[] nums , int low, int high, int target){
+        while(low<=high){
+            int mid = low + (high-low)/2;
+            if(nums[mid]==target){
+                if(mid == nums.length-1 || nums[mid+1]>nums[mid]){
+                    return mid;
+                } else {
+                    low = mid+1;
+                }
+            } else if(nums[mid]>target){
+                high = mid-1;
+            } else{
+                low = mid+1;
+            }
+        }
+        return -1;
+    }
+}
\ No newline at end of file