Given a string S of length N consisting of lower case character, the task is to find the minimum cost to reach from index i to index j.
At any index k, the cost to jump to the index k+1 and k-1(without going out of bounds) is 1.
Additionally, the cost to jump to any index m such that S[m] = S[k] is 0.
Input : S = “abcde”, i = 0, j = 4
Output : 4
The shortest path will be:
Thus, the answer will be 4.
Input : S = “abcdefb”, i = 0, j = 5
Output : 2
0->1 edge weight is 1, 1->6 edge weight is 0, and 6->5 edge weight is 1.
Thus, the answer will be 2
- One approach to solve this problem is 0-1 BFS.
- The setup can be visualized as a graph with N nodes.
- All the the nodes will be connected to adjacent nodes with an edge of weight of ‘1’ and nodes with same characters with an edge with weight ‘0’.
- In this setup, 0-1 BFS can be run to find shortest path from index ‘i’ to index ‘j’.
Time complexity: O(N^2) – As number of vertices would be of O(N^2)
- For each character X, all the characters are found for which it is adjacent to.
- A graph is created with number of nodes as number of distinct characters in the string, each representing a character.
- Each node X, will have an edge of weight 1 with all the nodes representing characters adjacent to character X.
- Then BFS can be run from nodes representing S[i] to nodes representing S[j] in this new graph
Time complexity: O(N)
Below is the implementation of the above approach:
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