solve Sequential Digits

Author: saubhik

problems/sequential_digits.py

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+from typing import List
+
+
+class Solution:
+    # Straight Forward Iterative.
+    #
+    # Time: O(1)
+    # Space: O(1)
+    #
+    # Examples:
+    # low = 100, high = 300
+    # [123, 234]
+    # low = 1000, high = 13000
+    # [1234, 2345, 3456, 4567, 5678, 6789, 12345]
+    # 10 <= low <= high <= 10^9
+    def sequentialDigits(self, low: int, high: int) -> List[int]:
+        def get_num_digits(num: int):
+            # O(1) time, O(1) space.
+            num_digits = 0
+            while num:
+                num //= 10
+                num_digits += 1
+            return num_digits
+
+        low_num_digits = get_num_digits(num=low)
+        high_num_digits = get_num_digits(num=high)
+
+        def get_sequential_numbers(num_digits: int):
+            # O(1) time, O(1) space
+            # 1 <= num_digits <= 9
+            for digit in range(1, 10 - num_digits + 1):
+                num = 0
+                for _ in range(num_digits):
+                    num = num * 10 + digit
+                    digit += 1
+                yield num
+
+        # O(1) time, O(1) additional space
+        ans = []
+        for num_digits in range(low_num_digits, high_num_digits + 1):
+            for num in get_sequential_numbers(num_digits=num_digits):
+                if low <= num <= high:
+                    ans.append(num)
+
+        return ans
+
+
+class SolutionTwo:
+    # Sliding Window.
+    #
+    # All sequential numbers are substrings of the string "123456789".
+    # We slide over the string, with window length = number of digits, which itself
+    # iterates from number of digits in low, and the number of digits in high.
+    #
+    # Time: O(1)
+    # Space: O(1)
+    def sequentialDigits(self, low: int, high: int):
+        sample = "123456789"
+        ans = []
+        for length in range(len(str(low)), len(str(high)) + 1):
+            for start in range(10 - length):
+                num = int(sample[start : start + length])
+                if low <= num <= high:
+                    ans.append(num)
+        return ans
+
+
+class SolutionThree:
+    # Pre-computation.
+    # Time: O(1)
+    # Space: O(1)
+    def sequentialDigits(self, low: int, high: int):
+        sequential_numbers = [
+            12,
+            23,
+            34,
+            45,
+            56,
+            67,
+            78,
+            89,
+            123,
+            234,
+            345,
+            456,
+            567,
+            678,
+            789,
+            1234,
+            2345,
+            3456,
+            4567,
+            5678,
+            6789,
+            12345,
+            23456,
+            34567,
+            45678,
+            56789,
+            123456,
+            234567,
+            345678,
+            456789,
+            1234567,
+            2345678,
+            3456789,
+            12345678,
+            23456789,
+            123456789,
+        ]
+
+        return [num for num in sequential_numbers if low <= num <= high]

tests/test_sequential_digits.py

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+import unittest
+
+from sequential_digits import Solution, SolutionTwo, SolutionThree
+
+
+class TestSequentialDigits(unittest.TestCase):
+    def test_example_1(self):
+        assert Solution().sequentialDigits(low=100, high=300) == [123, 234]
+        assert SolutionTwo().sequentialDigits(low=100, high=300) == [123, 234]
+        assert SolutionThree().sequentialDigits(low=100, high=300) == [123, 234]
+
+    def test_example_2(self):
+        assert Solution().sequentialDigits(low=1000, high=13000) == [
+            1234,
+            2345,
+            3456,
+            4567,
+            5678,
+            6789,
+            12345,
+        ]
+        assert SolutionTwo().sequentialDigits(low=1000, high=13000) == [
+            1234,
+            2345,
+            3456,
+            4567,
+            5678,
+            6789,
+            12345,
+        ]
+        assert SolutionThree().sequentialDigits(low=1000, high=13000) == [
+            1234,
+            2345,
+            3456,
+            4567,
+            5678,
+            6789,
+            12345,
+        ]