add(coding/1742): maximum-number-of-balls-in-a-box

source/coding/1742-maximum-number-of-balls-in-a-box.md

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+---
+title: 1742. Maximum Number of Balls in a Box
+notebook: coding
+tags:
+- easy
+date: 2025-02-13 10:07:26
+updated: 2025-02-13 10:07:26
+---
+## Problem
+
+You are working in a ball factory where you have `n` balls numbered from `lowLimit` up to `highLimit` **inclusive** (i.e., `n == highLimit - lowLimit + 1`), and an infinite number of boxes numbered from `1` to `infinity`.
+
+Your job at this factory is to put each ball in the box with a number equal to the sum of digits of the ball's number. For example, the ball number `321` will be put in the box number `3 + 2 + 1 = 6` and the ball number `10` will be put in the box number `1 + 0 = 1`.
+
+Given two integers `lowLimit` and `highLimit`, return _the number of balls in the box with the most balls._
+
+<https://leetcode.cn/problems/maximum-number-of-balls-in-a-box/>
+
+**Example 1:**
+
+> Input: `lowLimit = 1, highLimit = 10`
+> Output: `2`
+> Explanation:
+>
+> ``` text
+> Box Number:  1 2 3 4 5 6 7 8 9 10 11 ...
+> Ball Count:  2 1 1 1 1 1 1 1 1 0  0  ...
+> ```
+>
+> Box 1 has the most number of balls with 2 balls.
+
+**Example 2:**
+
+> Input: lowLimit = 5, highLimit = 15
+> Output: 2
+> Explanation:
+>
+> ``` text
+> Box Number:  1 2 3 4 5 6 7 8 9 10 11 ...
+> Ball Count:  1 1 1 1 2 2 1 1 1 0  0  ...
+> ```
+>
+> Boxes 5 and 6 have the most number of balls with 2 balls in each.
+
+**Example 3:**
+
+> Input: lowLimit = 19, highLimit = 28
+> Output: 2
+> Explanation:
+>
+> ``` text
+> Box Number:  1 2 3 4 5 6 7 8 9 10 11 12 ...
+> Ball Count:  0 1 1 1 1 1 1 1 1 2  0  0  ...
+> ```
+>
+> Box 10 has the most number of balls with 2 balls.
+
+**Constraints:**
+
+- `1 <= lowLimit <= highLimit <= 10⁵`
+
+## Test Cases
+
+``` python
+class Solution:
+    def countBalls(self, lowLimit: int, highLimit: int) -> int:
+```
+
+{% asset_code coding/1742-maximum-number-of-balls-in-a-box/solution_test.py %}
+
+## Thoughts
+
+跟 [2342. Max Sum of a Pair With Equal Sum of Digits](2342-max-sum-of-a-pair-with-equal-sum-of-digits) 类似，按 “sum of digits of the number” 把 `[lowLimit, highLimit]` 区间的所有数字分组，记录每组的数字个数，然后取最大即可。
+
+一个小的优化是，对于连续的正整数，如果个位是从 0 到 9，则对应的 “sum of digits of the number” 也是连续递增的。利用这个规则可以节省 90% 左右的计算量。
+
+时间复杂度 `O(n)`，空间复杂度 `O(n)`。
+
+## Code
+
+{% asset_code coding/1742-maximum-number-of-balls-in-a-box/solution.py %}

source/coding/1742-maximum-number-of-balls-in-a-box/solution.py

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+from collections import defaultdict
+
+
+class Solution:
+    def countBalls(self, lowLimit: int, highLimit: int) -> int:
+        def sum_digits(num: int) -> int:
+            s = 0
+            while num > 0:
+                s += num % 10
+                num //= 10
+            return s
+
+        boxes: dict[int, int] = defaultdict(int) # box number -> number of balls
+        box_num = sum_digits(lowLimit - 1)
+        for num in range(lowLimit, highLimit + 1):
+            if num % 10 == 0:
+                box_num = sum_digits(num)
+            else:
+                box_num += 1
+
+            boxes[box_num] += 1
+
+        return max(boxes.values())

source/coding/1742-maximum-number-of-balls-in-a-box/solution_test.py

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+import pytest
+
+from solution import Solution
+
+
+@pytest.mark.parametrize('lowLimit, highLimit, expected', [
+    (1, 10, 2),
+    (5, 15, 2),
+    (19, 28, 2),
+])
+@pytest.mark.parametrize('sol', [Solution()])
+def test_solution(sol, lowLimit, highLimit, expected):
+    assert sol.countBalls(lowLimit, highLimit) == expected