Race To The End (RTTE)
Tags: Complete Search, Shortest path in DAG.
Problem:
practice
Author: Naman.
Tester: Shami.
There are two possible approaches for this problem.
Brute force
Since the limit on N is very small, we can try all possible combinations and find the result. We can store the minimum steps to reach each index in an array (arr).
Steps:
- Start from index 0. a[0] = 0
- For each index ‘i’, we update value of a[i] = min(a[i], a[i+1]+1)
we don’t need to check a[i-1] as it would already have been processed because we started from left.
- Find all indices j to the right such that a[j] == a[i]
a. For each j, update all left indices similar to step #2.
- Answer is stored in a[N-1].
Graph
Let’s consider each index ‘i’ as a node and all possible moves as directed edges. So the edges from A[i] will be
1. A[i-1]
2. A[i+1]
3. All A[j] such that A[j] == A[i]
Complexity to generate graph: O(N^2)
Notice that the directed graph may have back edges, but it does not matter in our case. Now we can apply BFS starting from index 0 and count the minimum number of levels to reach N. The number of levels is the answer.
asked
12 Jan, 15:14
0★mmmreddy
12●1
accept rate:
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