Add Day-07 solution for Number of Pairs

Author: Ayush Singh

Problems/Data-structures/Day-07/sol/ayush2005k/Solution1.py

@@ -0,0 +1,54 @@
+"""
+Problem: C. Number of Pairs
+Link: https://codeforces.com/problemset/problem/1535/C
+
+Short Problem Statement:
+Given an array of integers, count the number of index pairs (i, j)
+such that i < j and the sum a[i] + a[j] lies between l and r (inclusive).
+
+Approach:
+- Sort the array.
+- For each index i, we want to find how many indices j > i satisfy:
+    l - a[i] <= a[j] <= r - a[i]
+- Since the array is sorted, binary search can be used to find
+  the valid range of j efficiently.
+- Sum the counts for all i.
+
+Time Complexity:
+O(n log n) per test case
+
+Space Complexity:
+O(n)
+
+Example:
+Input:
+3 4 7
+5 1 2
+
+Output:
+2
+
+Submission Link:
+https://codeforces.com/contest/1538/submission/356210806
+"""
+
+import sys
+from bisect import bisect_left, bisect_right
+
+input = sys.stdin.readline
+
+t = int(input())
+
+for _ in range(t):
+    n, l, r = map(int, input().split())
+    a = list(map(int, input().split()))
+
+    a.sort()
+    ans = 0
+
+    for i in range(n):
+        left = bisect_left(a, l - a[i], i + 1)
+        right = bisect_right(a, r - a[i], i + 1)
+        ans += (right - left)
+
+    print(ans)