You are given an array colors, in which there are three colors: 1, 2 and 3.
You are also given some queries. Each query consists of two integers i and c, return the shortest distance between the given index i and the target color c. If there is no solution return -1.
Example 1:
Input: colors = [1,1,2,1,3,2,2,3,3], queries = [[1,3],[2,2],[6,1]]
Output: [3,0,3]
Explanation:
The nearest 3 from index 1 is at index 4 (3 steps away).
The nearest 2 from index 2 is at index 2 itself (0 steps away).
The nearest 1 from index 6 is at index 3 (3 steps away).
Example 2:
Input: colors = [1,2], queries = [[0,3]]
Output: [-1]
Explanation: There is no 3 in the array.
Constraints:
1 <= colors.length <= 5*10^4
1 <= colors[i] <= 3
1 <= queries.length <= 5*10^4
queries[i].length == 2
0 <= queries[i][0] < colors.length
1 <= queries[i][1] <= 3
Solutions
Solution 1: Preprocessing
We can preprocess the distance from each position to the nearest color $1$, $2$, $3$ on the left, and the distance from each position to the nearest color $1$, $2$, $3$ on the right, and record them in the arrays $left$ and $right$. Initially, $left[0][0] = left[0][1] = left[0][2] = -\infty$, and $right[n][0] = right[n][1] = right[n][2] = \infty$, where $n$ is the length of the array colors.
Then for each query $(i, c)$, the minimum distance is $d = \min(i - left[i + 1][c - 1], right[i][c - 1] - i)$. If $d > n$, there is no solution, and the answer to this query is $-1$.
The time complexity is $O(n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array colors.