文章目錄

• • 1. 題目
  • 2. 解題

1. 題目

We have n cities and m bi-directional roads where roads[i] = [ai, bi] connects city ai with city bi. Each city has a name consisting of exactly 3 upper-case English letters given in the string array names. Starting at any city x, you can reach any city y where y != x (i.e. the cities and the roads are forming an undirected connected graph).

You will be given a string array targetPath. You should find a path in the graph of the same length and with the minimum edit distance to targetPath.

You need to return the order of the nodes in the path with the minimum edit distance, The path should be of the same length of targetPath and should be valid (i.e. there should be a direct road between ans[i] and ans[i + 1]). If there are multiple answers return any one of them.

The edit distance is defined as follows:

Follow-up: If each node can be visited only once in the path, What should you change in your solution?

Example 1:

Input: n = 5, roads = [[0,2],[0,3],[1,2],[1,3],[1,4],[2,4]], names = ["ATL","PEK","LAX","DXB","HND"], targetPath = ["ATL","DXB","HND","LAX"] Output: [0,2,4,2] Explanation: [0,2,4,2], [0,3,0,2] and [0,3,1,2] are accepted answers. [0,2,4,2] is equivalent to ["ATL","LAX","HND","LAX"] which has edit distance = 1 with targetPath. [0,3,0,2] is equivalent to ["ATL","DXB","ATL","LAX"] which has edit distance = 1 with targetPath. [0,3,1,2] is equivalent to ["ATL","DXB","PEK","LAX"] which has edit distance = 1 with targetPath.

Example 2:

Input: n = 4, roads = [[1,0],[2,0],[3,0],[2,1],[3,1],[3,2]], names = ["ATL","PEK","LAX","DXB"], targetPath = ["ABC","DEF","GHI","JKL","MNO","PQR","STU","VWX"] Output: [0,1,0,1,0,1,0,1] Explanation: Any path in this graph has edit distance = 8 with targetPath.

Example 3:

Input: n = 6, roads = [[0,1],[1,2],[2,3],[3,4],[4,5]], names = ["ATL","PEK","LAX","ATL","DXB","HND"], targetPath = ["ATL","DXB","HND","DXB","ATL","LAX","PEK"] Output: [3,4,5,4,3,2,1] Explanation: [3,4,5,4,3,2,1] is the only path with edit distance = 0 with targetPath. It's equivalent to ["ATL","DXB","HND","DXB","ATL","LAX","PEK"]Constraints: 2 <= n <= 100 m == roads.length n - 1 <= m <= (n * (n - 1) / 2) 0 <= ai, bi <= n - 1 ai != bi The graph is guaranteed to be connected and each pair of nodes may have at most one direct road. names.length == n names[i].length == 3 names[i] consists of upper-case English letters. 1 <= targetPath.length <= 100 targetPath[i].length == 3 targetPath[i] consists of upper-case English letters.

來源：力扣（LeetCode）
鏈接：https://leetcode-cn.com/problems/the-most-similar-path-in-a-graph
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2. 解題

class Solution { public:vector<int> mostSimilar(int n, vector<vector<int>>& roads, vector<string>& names, vector<string>& targetPath) {vector<vector<int>> g(n);for(auto& r : roads){g[r[0]].push_back(r[1]);g[r[1]].push_back(r[0]);}//建圖int len = targetPath.size();vector<vector<int>> dp(len, vector<int>(n, INT_MAX));//走完 ？target后的 在城市 ni 的最小編輯距離vector<vector<int>> path1(n);//n個城市作為結(jié)束的最佳路線vector<vector<int>> path2(n);//存儲下一個狀態(tài)的路徑for(int i = 0; i < n; ++i)//初始化{dp[0][i] = (names[i] != targetPath[0]);path1[i].push_back(i);}int mindis = INT_MAX, minidx = -1;for(int k = 1; k < len; ++k){ //樣本維度for(int i = 0; i < n; ++i){ //前一個城市if(dp[k-1][i] == INT_MAX)continue;for(int j : g[i]){ //下一個相連的城市if(dp[k][j] > dp[k-1][i]+(names[j]!=targetPath[k])){dp[k][j] = dp[k-1][i]+(names[j]!=targetPath[k]);path2[j] = path1[i];path2[j].push_back(j);}}}swap(path1, path2);//滾動數(shù)組，更新當(dāng)前的最佳路徑至path1}for(int i = 0; i < n; i++) {if(mindis > dp[len-1][i]){mindis = dp[len-1][i];minidx = i;}}//取編輯距離最小的城市編號return path1[minidx];//返回路徑} };

1260 ms 109.6 MB

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