Add Python solution for Codeforces 1777C (Quiz Master)

- Implemented two-pointer sliding window approach
- Precomputed divisors for efficient topic tracking
- Time complexity: O(n*sqrt(max_a) + n*log(n))
- Space complexity: O(n*d) where d is avg divisors
- Handles constraints up to n=10^5, m=10^5

Author: ishanrajsingh

Problems/Binary-Search/Day-07/sol/Ishan_Raj_Singh/Solution2.py

@@ -0,0 +1,61 @@
+"""
+Approach: Optimized Sliding Window with Divisor Enumeration
+Submission Link: https://codeforces.com/contest/1777/submission/356144999
+"""
+
+def solve_optimized():
+    n, m = map(int, input().split())
+    a = list(map(int, input().split()))
+    
+    students = []
+    for val in a:
+        divisors = []
+        i = 1
+        while i * i <= val:
+            if val % i == 0:
+                if i <= m:
+                    divisors.append(i)
+                if i != val // i and val // i <= m:
+                    divisors.append(val // i)
+            i += 1
+        
+        if divisors:
+            students.append((val, divisors))
+    
+    if not students:
+        print(-1)
+        return
+    
+    students.sort()
+    
+    left = 0
+    ans = float('inf')
+    freq = {}
+    
+    for right in range(len(students)):
+        for topic in students[right][1]:
+            freq[topic] = freq.get(topic, 0) + 1
+        
+        while len(freq) == m:
+            ans = min(ans, students[right][0] - students[left][0])
+            
+            remove_ok = True
+            for topic in students[left][1]:
+                if freq.get(topic, 0) == 1:
+                    remove_ok = False
+                    break
+            
+            if remove_ok:
+                for topic in students[left][1]:
+                    freq[topic] -= 1
+                    if freq[topic] == 0:
+                        del freq[topic]
+                left += 1
+            else:
+                break
+    
+    print(ans if ans != float('inf') else -1)
+
+t = int(input())
+for _ in range(t):
+    solve_optimized()