Sync LeetCode submission Runtime - 561 ms (83.02%), Memory - 37.8 MB (91.51%)

Author: jimit105

2280-count-good-triplets-in-an-array/README.md

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+<p>You are given two <strong>0-indexed</strong> arrays <code>nums1</code> and <code>nums2</code> of length <code>n</code>, both of which are <strong>permutations</strong> of <code>[0, 1, ..., n - 1]</code>.</p>
+
+<p>A <strong>good triplet</strong> is a set of <code>3</code> <strong>distinct</strong> values which are present in <strong>increasing order</strong> by position both in <code>nums1</code> and <code>nums2</code>. In other words, if we consider <code>pos1<sub>v</sub></code> as the index of the value <code>v</code> in <code>nums1</code> and <code>pos2<sub>v</sub></code> as the index of the value <code>v</code> in <code>nums2</code>, then a good triplet will be a set <code>(x, y, z)</code> where <code>0 &lt;= x, y, z &lt;= n - 1</code>, such that <code>pos1<sub>x</sub> &lt; pos1<sub>y</sub> &lt; pos1<sub>z</sub></code> and <code>pos2<sub>x</sub> &lt; pos2<sub>y</sub> &lt; pos2<sub>z</sub></code>.</p>
+
+<p>Return <em>the <strong>total number</strong> of good triplets</em>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> nums1 = [2,0,1,3], nums2 = [0,1,2,3]
+<strong>Output:</strong> 1
+<strong>Explanation:</strong> 
+There are 4 triplets (x,y,z) such that pos1<sub>x</sub> &lt; pos1<sub>y</sub> &lt; pos1<sub>z</sub>. They are (2,0,1), (2,0,3), (2,1,3), and (0,1,3). 
+Out of those triplets, only the triplet (0,1,3) satisfies pos2<sub>x</sub> &lt; pos2<sub>y</sub> &lt; pos2<sub>z</sub>. Hence, there is only 1 good triplet.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> nums1 = [4,0,1,3,2], nums2 = [4,1,0,2,3]
+<strong>Output:</strong> 4
+<strong>Explanation:</strong> The 4 good triplets are (4,0,3), (4,0,2), (4,1,3), and (4,1,2).
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>n == nums1.length == nums2.length</code></li>
+	<li><code>3 &lt;= n &lt;= 10<sup>5</sup></code></li>
+	<li><code>0 &lt;= nums1[i], nums2[i] &lt;= n - 1</code></li>
+	<li><code>nums1</code> and <code>nums2</code> are permutations of <code>[0, 1, ..., n - 1]</code>.</li>
+</ul>

2280-count-good-triplets-in-an-array/solution.py

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+# Approach 1: Binary Indexed Tree
+
+# Time: O(n * log n)
+# Space: O(n)
+
+class FenwickTree:
+    def __init__(self, size):
+        self.tree = [0] * (size + 1)
+
+    def update(self, index, delta):
+        index += 1
+        while index <= len(self.tree) - 1:
+            self.tree[index] += delta
+            index += index & -index
+
+    def query(self, index):
+        index += 1
+        res = 0
+        while index > 0:
+            res += self.tree[index]
+            index -= index & -index
+        return res
+
+class Solution:
+    def goodTriplets(self, nums1: List[int], nums2: List[int]) -> int:
+        n = len(nums1)
+        pos2, reversed_index_mapping = [0] * n, [0] * n
+
+        for i, num2 in enumerate(nums2):
+            pos2[num2] = i
+
+        for i, num1 in enumerate(nums1):
+            reversed_index_mapping[pos2[num1]] = i
+
+        tree = FenwickTree(n)
+        res = 0
+
+        for value in range(n):
+            pos = reversed_index_mapping[value]
+            left = tree.query(pos)
+            tree.update(pos, 1)
+            right = (n - 1 - pos) - (value - left)
+            res += left * right
+
+        return res
+
+