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Problem solution · Python

Count Stepping Numbers in Range

Count Stepping Numbers in Range: a Python solution using dynamic programming. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Dynamic programming
Source
walkccc LeetCode Solutions
Length
41 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Dynamic programming

For Count Stepping Numbers in Range, the implementation records answers for smaller states and reuses them to build the requested result without repeating work.

  1. Define precisely what one DP state represents.
  2. Establish the base cases before transitions are evaluated.
  3. Process states in dependency order and combine only already-known values.

Code notes

  • 41 lines of Python from the credited upstream file 2801.py.
  • The implementation visibly relies on cached states.
  • No explicit loop blocks detected.

Complexity

Multiply the number of reachable states by the work performed for each transition, then include the stored state table in memory usage.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeCount Stepping Numbers in Range · PythonPython
Use this to learn the idea, then write your own version.
class Solution:  def countSteppingNumbers(self, low: str, high: str) -> int:    MOD = 1_000_000_007    low = '0' * (len(high) - len(low)) + low     @functools.lru_cache(None)    def dp(        i: int,        prevDigit: int,        isLeadingZero: bool,        tight1: bool,        tight2: bool,    ) -> int:      """      Returns the number of valid integers, considering the i-th digit, where      `prevDigit` is the previous digit, `tight1` indicates if the current      digit is tightly bound for `low`, and `tight2` indicates if the current      digit is tightly bound for `high`.      """      if i == len(high):        return 1       res = 0      minDigit = int(low[i]) if tight1 else 0      maxDigit = int(high[i]) if tight2 else 9       for d in range(minDigit, maxDigit + 1):        nextTight1 = tight1 and (d == minDigit)        nextTight2 = tight2 and (d == maxDigit)        if isLeadingZero:          # Can place any digit in [minDigit, maxDigit].          res += dp(i + 1, d, isLeadingZero and d ==                    0, nextTight1, nextTight2)        elif abs(d - prevDigit) == 1:          res += dp(i + 1, d, False, nextTight1, nextTight2)        res %= MOD       return res     return dp(0, -1, True, True, True)

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