You are given an undirected tree with n nodes, numbered from 0 to n - 1. It is represented by a 2D integer array edges of length n - 1, where edges[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the tree.
You are also given two binary strings start and target of length n. For each node x, start[x] is its initial color and target[x] is its desired color.
In one operation, you may pick an edge with index i and toggle both of its endpoints. That is, if the edge is [u, v], then the colors of nodes u and v each flip from '0' to '1' or from '1' to '0'.
Return an array of edge indices whose operations transform start into target. Among all valid sequences with minimum possible length, return the edge indices in increasing order.
If it is impossible to transform start into target, return an array containing a single element equal to -1.
Example 1:
Input: n = 3, edges = [[0,1],[1,2]], start = "010", target = "100"
Output: [0]
Explanation:
Toggle edge with index 0, which flips nodes 0 and 1.
The string changes from "010" to "100", matching the target.
Example 2:
Input: n = 7, edges = [[0,1],[1,2],[2,3],[3,4],[3,5],[1,6]], start = "0011000", target = "0010001"
Output: [1,2,5]
Explanation:
After these operations, the resulting string becomes "0010001", which matches the target.
Example 3:
Input: n = 2, edges = [[0,1]], start = "00", target = "01"
Output: [-1]
Explanation:
There is no sequence of edge toggles that transforms "00" into "01". Therefore, we return [-1].
Constraints:
2 <= n == start.length == target.length <= 105edges.length == n - 1edges[i] = [ai, bi]0 <= ai, bi < nstart[i] is either '0' or '1'.target[i] is either '0' or '1'.edges represents a valid tree.Solutions for this problem are being prepared.
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