Count Pairs Of Nodes — LeetCode 1782 Python Solution

The problem

You are given an undirected graph defined by an integer n, the number of nodes, and a 2D integer array edges, the edges in the graph, where edges[i] = [ui, vi] indicates that there is an undirected edge between ui and vi. You are also given an integer array queries.

Example

Input

n = 4, edges = [[1,2],[2,4],[1,3],[2,3],[2,1]], queries = [2,3]

Output

[6,5]

Explanation

The calculations for incident(a, b) are shown in the table above.

Python solution

class Solution:
    def countPairs(
        self, n: int, edges: List[List[int]], queries: List[int]
    ) -> List[int]:
        cnt = [0] * n
        g = defaultdict(int)
        for a, b in edges:
            a, b = a - 1, b - 1
            a, b = min(a, b), max(a, b)
            cnt[a] += 1
            cnt[b] += 1
            g[(a, b)] += 1

        s = sorted(cnt)
        ans = [0] * len(queries)
        for i, t in enumerate(queries):
            for j, x in enumerate(s):
                k = bisect_right(s, t - x, lo=j + 1)
                ans[i] += n - k
            for (a, b), v in g.items():
                if cnt[a] + cnt[b] > t and cnt[a] + cnt[b] - v <= t:
                    ans[i] -= 1
        return ans

Complexity

Pattern: Two Pointers

Use the order already in the input to discard half the search space at every step. LeetCode 1782. Count Pairs Of Nodes is filed here because LeetCode tags it Two Pointers, which is the vocabulary this hub collects.

The two pointers guide has the Python template for the pattern and the 201 LeetCode problems that use it.

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