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 allA **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;
}
}
```