Longest Common Subpath

arraybinary searchrolling hash

Problem Statement

There is a country of n cities numbered from 0 to n - 1 . In this country, there is a road connecting every pair of cities.

There are m friends numbered from 0 to m - 1 who are traveling through the country. Each one of them will take a path consisting of some cities. Each path is represented by an integer array that contains the visited cities in order. The path may contain a city more than once , but the same city will not be listed consecutively.

Given an integer n and a 2D integer array paths where paths[i] is an integer array representing the path of the i ^th friend, return the length of the longest common subpath that is shared by every friend's path, or 0 if there is no common subpath at all .

A subpath of a path is a contiguous sequence of cities within that path.

Examples

Example 1

Input: n = 5, paths = [[0,1, 2,3 ,4],
 [ 2,3 ,4],
 [4,0,1, 2,3 ]]
Output: 2
The longest common subpath is [2,3].

Example 2

Input: n = 3, paths = [[0],[1],[2]]
Output: 0
There is no common subpath shared by the three paths.

Example 3

Input: n = 5, paths = [[ 0 ,1,2,3,4],
 [4,3,2,1, 0 ]]
Output: 1
The possible longest common subpaths are [0], [1], [2], [3], and [4]. All have a length of 1.

Constraints

1 <= n <= 10 ^5

m == paths.length

2 <= m <= 10 ^5

sum(paths[i].length) <= 10 ^5

0 <= paths[i][j] < n

The same city is not listed multiple times consecutively in paths[i] .

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicBinary Search