Formatted question description: https://leetcode.ca/all/1923.html

1923. Longest Common Subpath

Level

Hard

Description

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.

Example 1:

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

Example 2:

Input: n = 3, paths = [[0],[1],[2]]
Output: 0
Explanation: 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
Explanation: 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].

Solution

Use binary search and rolling hash. The minimum possible length is 0 and the maximum possible length is the shortest length among all paths. Each time, check whether it is possible to have a common subpath of the selected length.

class Solution {
    static final long BASE = 100001, MODULO = 100000000007L;

    public int longestCommonSubpath(int n, int[][] paths) {
        int minLength = Integer.MAX_VALUE;
        for (int[] path : paths)
            minLength = Math.min(minLength, path.length);
        long[] pow = new long[minLength + 1];
        pow[0] = 1;
        for (int i = 1; i <= minLength; i++)
            pow[i] = pow[i - 1] * BASE % MODULO;
        int low = 0, high = minLength;
        while (low < high) {
            int mid = (high - low + 1) / 2 + low;
            if (check(paths, mid, pow))
                low = mid;
            else
                high = mid - 1;
        }
        return low;
    }

    public boolean check(int[][] paths, int mid, long[] pow) {
        int m = paths.length;
        Set<Long> set = rollingHash(paths[0], mid, pow);
        for (int i = 1; i < m; i++) {
            set.retainAll(rollingHash(paths[i], mid, pow));
            if (set.isEmpty())
                return false;
        }
        return true;
    }

    public Set<Long> rollingHash(int[] path, int mid, long[] pow) {
        Set<Long> set = new HashSet<Long>();
        long hash = 0;
        int length = path.length;
        for (int i = 0; i < mid; i++)
            hash = (hash * BASE + path[i]) % MODULO;
        set.add(hash);
        for (int prev = 0, curr = mid; curr < length; prev++, curr++) {
            hash = (hash * BASE % MODULO - path[prev] * pow[mid] % MODULO + path[curr]) % MODULO;
            if (hash < 0)
                hash += MODULO;
            set.add(hash);
        }
        return set;
    }
}

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