Add Solution2.py

Author: ishanrajsingh

Problems/Data-structures/Day-09/sol/ishanrajsingh/Solution2.py

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+#Submission Link - https://codeforces.com/contest/61/submission/356379545
+#Approach - Count triplets i < j < k where a[i] > a[j] > a[k] using two Fenwick Trees implicitly
+#Time Complexity - O(n log n)
+import sys
+sys.setrecursionlimit(10**6)
+input = sys.stdin.read
+data = input().split()
+
+n = int(data[0])
+a = list(map(int, data[1:]))
+pos = [0] * (n + 1)
+
+for i in range(n):
+    pos[a[i]] = i + 1
+
+N = n + 10
+ft = [0] * (N + 1)
+
+def update(idx, val):
+    while idx <= N:
+        ft[idx] += val
+        idx += idx & -idx
+
+def query(idx):
+    res = 0
+    while idx > 0:
+        res += ft[idx]
+        idx -= idx & -idx
+    return res
+
+ans = 0
+for i in range(n - 1, -1, -1):
+    r = pos[a[i]]
+    smaller_right = query(r - 1)
+    ans += smaller_right * query(a[i] - 1)
+    update(r, 1)
+
+print(ans)