diff --git a/Problem1.java b/Problem1.java
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+++ b/Problem1.java
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+// I perform binary search twice: once to find the first occurrence and once to find the last occurrence.
+// For each direction, I continue searching even after finding the target to ensure I locate the boundary index.
+// This approach keeps the runtime O(log n) while accurately returning both start and end positions.
+class Solution {
+    public int[] searchRange(int[] nums, int target) {
+        return new int[]{findFirst(nums, target), findLast(nums, target)};
+    }
+
+    private int findFirst(int[] nums, int target) {
+        int left = 0, right = nums.length - 1, index = -1;
+
+        while (left <= right) {
+            int mid = left + (right - left) / 2;
+
+            if (nums[mid] == target) {
+                index = mid;
+                right = mid - 1; // keep searching left
+            } else if (nums[mid] < target) {
+                left = mid + 1;
+            } else {
+                right = mid - 1;
+            }
+        }
+
+        return index;
+    }
+
+    private int findLast(int[] nums, int target) {
+        int left = 0, right = nums.length - 1, index = -1;
+
+        while (left <= right) {
+            int mid = left + (right - left) / 2;
+
+            if (nums[mid] == target) {
+                index = mid;
+                left = mid + 1; // keep searching right
+            } else if (nums[mid] < target) {
+                left = mid + 1;
+            } else {
+                right = mid - 1;
+            }
+        }
+
+        return index;
+    }
+}
diff --git a/Problem2.java b/Problem2.java
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+++ b/Problem2.java
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+// I use binary search to determine which side of the array is sorted and then discard the sorted side
+// because the minimum cannot lie there unless nums[mid] is the smallest element.
+// By repeatedly narrowing the range toward the unsorted half, I can find the minimum in O(log n).
+
+class Solution {
+    public int findMin(int[] nums) {
+        int left = 0, right = nums.length - 1;
+
+        while (left < right) {
+            int mid = left + (right - left) / 2;
+
+            if (nums[mid] > nums[right]) {
+                left = mid + 1;   // min must be to the right
+            } else {
+                right = mid;      // mid might be the minimum
+            }
+        }
+
+        return nums[left];
+    }
+}
+
diff --git a/Problem3.java b/Problem3.java
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index 00000000..4573e386
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+++ b/Problem3.java
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+// I apply binary search and compare mid with its next element to determine the direction of increasing slope.
+// If nums[mid] < nums[mid+1], I move right because a peak must exist on that rising slope.
+// Otherwise, I move left because the peak is on the left side or at mid itself.
+
+class Solution {
+    public int findPeakElement(int[] nums) {
+        int left = 0, right = nums.length - 1;
+
+        while (left < right) {
+            int mid = left + (right - left) / 2;
+
+            if (nums[mid] < nums[mid + 1]) {
+                left = mid + 1;   // go right
+            } else {
+                right = mid;      // go left or stay
+            }
+        }
+
+        return left; // or right (same position)
+    }
+}
+