Number of Pairs Satisfying Inequality — LeetCode 2426 Python Solution

The problem

You are given two 0-indexed integer arrays nums1 and nums2, each of size n, and an integer diff. Find the number of pairs (i, j) such that: 0 <= i < j <= n - 1 and nums1[i] - nums1[j] <= nums2[i] - nums2[j] + diff.

Example

Input

nums1 = [3,2,5], nums2 = [2,2,1], diff = 1

Output

3

Explanation

There are 3 pairs that satisfy the conditions:

Python solution

class BinaryIndexedTree:
    def __init__(self, n):
        self.n = n
        self.c = [0] * (n + 1)

    @staticmethod
    def lowbit(x):
        return x & -x

    def update(self, x, delta):
        while x <= self.n:
            self.c[x] += delta
            x += BinaryIndexedTree.lowbit(x)

    def query(self, x):
        s = 0
        while x:
            s += self.c[x]
            x -= BinaryIndexedTree.lowbit(x)
        return s


class Solution:
    def numberOfPairs(self, nums1: List[int], nums2: List[int], diff: int) -> int:
        tree = BinaryIndexedTree(10**5)
        ans = 0
        for a, b in zip(nums1, nums2):
            v = a - b
            ans += tree.query(v + diff + 40000)
            tree.update(v + 40000, 1)
        return ans

Complexity

Pattern: Monotonic Stack

Answer "what is the next greater element" for every position in one pass. LeetCode 2426. Number of Pairs Satisfying Inequality is filed here because the reference solution below belongs to the algorithm family this hub collects, even though its LeetCode tags point elsewhere.

The monotonic stack guide has the Python template for the pattern and the 225 LeetCode problems that use it.

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