Question

1923. Longest Common Subpath

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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 ith 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 <= 105
• m == paths.length
• 2 <= m <= 105
• sum(paths[i].length) <= 105
• 0 <= paths[i][j] < n
• The same city is not listed multiple times consecutively in paths[i].

Solutions

Solution 1

class Solution:
  def longestCommonSubpath(self, n: int, paths: List[List[int]]) -> int:
    def check(k: int) -> bool:
      cnt = Counter()
      for h in hh:
        vis = set()
        for i in range(1, len(h) - k + 1):
          j = i + k - 1
          x = (h[j] - h[i - 1] * p[j - i + 1]) % mod
          if x not in vis:
            vis.add(x)
            cnt[x] += 1
      return max(cnt.values()) == m

    m = len(paths)
    mx = max(len(path) for path in paths)
    base = 133331
    mod = 2**64 + 1
    p = [0] * (mx + 1)
    p[0] = 1
    for i in range(1, len(p)):
      p[i] = p[i - 1] * base % mod
    hh = []
    for path in paths:
      k = len(path)
      h = [0] * (k + 1)
      for i, x in enumerate(path, 1):
        h[i] = h[i - 1] * base % mod + x
      hh.append(h)
    l, r = 0, min(len(path) for path in paths)
    while l < r:
      mid = (l + r + 1) >> 1
      if check(mid):
        l = mid
      else:
        r = mid - 1
    return l

class Solution {
  int N = 100010;
  long[] h = new long[N];
  long[] p = new long[N];
  private int[][] paths;
  Map<Long, Integer> cnt = new HashMap<>();
  Map<Long, Integer> inner = new HashMap<>();

  public int longestCommonSubpath(int n, int[][] paths) {
    int left = 0, right = N;
    for (int[] path : paths) {
      right = Math.min(right, path.length);
    }
    this.paths = paths;
    while (left < right) {
      int mid = (left + right + 1) >> 1;
      if (check(mid)) {
        left = mid;
      } else {
        right = mid - 1;
      }
    }
    return left;
  }

  private boolean check(int mid) {
    cnt.clear();
    inner.clear();
    p[0] = 1;
    for (int j = 0; j < paths.length; ++j) {
      int n = paths[j].length;
      for (int i = 1; i <= n; ++i) {
        p[i] = p[i - 1] * 133331;
        h[i] = h[i - 1] * 133331 + paths[j][i - 1];
      }
      for (int i = mid; i <= n; ++i) {
        long val = get(i - mid + 1, i);
        if (!inner.containsKey(val) || inner.get(val) != j) {
          inner.put(val, j);
          cnt.put(val, cnt.getOrDefault(val, 0) + 1);
        }
      }
    }
    int max = 0;
    for (int val : cnt.values()) {
      max = Math.max(max, val);
    }
    return max == paths.length;
  }

  private long get(int l, int r) {
    return h[r] - h[l - 1] * p[r - l + 1];
  }
}