Kth Smallest Instructions — LeetCode 1643 Python Solution

The problem

Bob is standing at cell (0, 0), and he wants to reach destination: (row, column). He can only travel right and down.

Example

Input

destination = [2,3], k = 1

Output

"HHHVV"

Explanation

All the instructions that reach (2, 3) in lexicographic order are as follows:

Python solution

class Solution:
    def kthSmallestPath(self, destination: List[int], k: int) -> str:
        v, h = destination
        ans = []
        for _ in range(h + v):
            if h == 0:
                ans.append("V")
            else:
                x = comb(h + v - 1, h - 1)
                if k > x:
                    ans.append("V")
                    v -= 1
                    k -= x
                else:
                    ans.append("H")
                    h -= 1
        return "".join(ans)

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1643. Kth Smallest Instructions is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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