3244 - Shortest Distance After Road Addition Queries II.

Hard

You are given an integer n and a 2D integer array queries.

There are n cities numbered from 0 to n - 1. Initially, there is a unidirectional road from city i to city i + 1 for all 0 <= i < n - 1.

<code>queriesi = u_i, v_i</code> represents the addition of a new unidirectional road from city <code>u_i</code> to city <code>v_i</code>. After each query, you need to find the length of the shortest path from city 0 to city n - 1.

There are no two queries such that queries[i][0] < queries[j][0] < queries[i][1] < queries[j][1].

Return an array answer where for each i in the range [0, queries.length - 1], answer[i] is the length of the shortest path from city 0 to city n - 1 after processing the first i + 1 queries.

Example 1:

Input: n = 5, queries = \[\[2,4],0,2,0,4]

Output: 3,2,1

Explanation:

After the addition of the road from 2 to 4, the length of the shortest path from 0 to 4 is 3.

After the addition of the road from 0 to 2, the length of the shortest path from 0 to 4 is 2.

After the addition of the road from 0 to 4, the length of the shortest path from 0 to 4 is 1.

Example 2:

Input: n = 4, queries = \[\[0,3],0,2]

Output: 1,1

Explanation:

After the addition of the road from 0 to 3, the length of the shortest path from 0 to 3 is 1.

After the addition of the road from 0 to 2, the length of the shortest path remains 1.

Constraints:

• <code>3 <= n <= 10⁵</code>

• <code>1 <= queries.length <= 10⁵</code>

• queries[i].length == 2

• 0 <= queries[i][0] < queries[i][1] < n

• 1 < queries[i][1] - queries[i][0]

• There are no repeated roads among the queries.

• There are no two queries such that i != j and queries[i][0] < queries[j][0] < queries[i][1] < queries[j][1].