Apply color-coding for path of length k in O(2^k n^{O(1)})
Analyze the apply color-coding for path of length k in o(2^k n^{o(1)}).
Examples
Input:"test_input_1"
Output:"output_1"
Input:"test_input_2"
Output:"output_2"
Hints
Consider using the color-coding technique where each vertex is assigned a color independently and uniformly at random from a set of colors of size proportional to k.
Explore the use of dynamic programming to track paths of length k, where the state includes the current vertex and the set of colors encountered so far.
Investigate the application of the Lovász Local Lemma to bound the probability that no valid path of length k exists with the desired color-coding, ensuring the algorithm runs in the desired time complexity.
Apply color-coding for path of length k in O(2^k n^{O(1)})
Analyze the apply color-coding for path of length k in o(2^k n^{o(1)}).