add(coding/2342): max-sum-of-a-pair-with-equal-sum-of-digits

source/coding/2342-max-sum-of-a-pair-with-equal-sum-of-digits.md

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+---
+title: 2342. Max Sum of a Pair With Equal Sum of Digits
+notebook: coding
+tags:
+- medium
+date: 2025-02-12 10:09:30
+updated: 2025-02-12 10:09:30
+---
+## Problem
+
+You are given a **0-indexed** array `nums` consisting of **positive** integers. You can choose two indices `i` and `j`, such that `i != j`, and the sum of digits of the number `nums[i]` is equal to that of `nums[j]`.
+
+Return _the **maximum** value of_ `nums[i] + nums[j]` _that you can obtain over all possible indices_ `i` _and_ `j` _that satisfy the conditions._
+
+<https://leetcode.com/problems/max-sum-of-a-pair-with-equal-sum-of-digits/>
+
+**Example 1:**
+
+> Input: `nums = [18,43,36,13,7]`
+> Output: `54`
+> Explanation: The pairs `(i, j)` that satisfy the conditions are:
+>
+> - `(0, 2)`, both numbers have a sum of digits equal to 9, and their sum is `18 + 36 = 54`.
+> - `(1, 4)`, both numbers have a sum of digits equal to 7, and their sum is `43 + 7 = 50`.
+>
+> So the maximum sum that we can obtain is 54.
+
+**Example 2:**
+
+> Input: `nums = [10,12,19,14]`
+> Output: `-1`
+> Explanation: There are no two numbers that satisfy the conditions, so we return -1.
+
+**Constraints:**
+
+- `1 <= nums.length <= 10⁵`
+- `1 <= nums[i] <= 10⁹`
+
+## Test Cases
+
+``` python
+class Solution:
+    def maximumSum(self, nums: List[int]) -> int:
+```
+
+{% asset_code coding/2342-max-sum-of-a-pair-with-equal-sum-of-digits/solution_test.py %}
+
+## Thoughts
+
+先按 "sum of digits of the number" 把 nums 分组，用一个字典记录分组结果。
+
+每组数字只需要保留最大的两个，以便得到这一组数字的最大和，所以字典的值可以用大小不超过 2 的最小堆。
+
+对所有的数字分组之后，遍历所有分组，如果一个分组里有至少两个数字，就可以计算这一组数字的最大和。所有组的最大和取最大即可。
+
+时间复杂度 `O(n)`，空间复杂度 `O(n)`。
+
+## Code
+
+{% asset_code coding/2342-max-sum-of-a-pair-with-equal-sum-of-digits/solution.py %}

source/coding/2342-max-sum-of-a-pair-with-equal-sum-of-digits/solution.py

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+from collections import defaultdict
+from heapq import heappush, heappushpop
+
+
+class Solution:
+    def maximumSum(self, nums: list[int]) -> int:
+        max2 = lambda a, b: a if a >= b else b
+        groups: dict[int, list[int]] = defaultdict(list)
+        for num in nums:
+            sd = 0
+            val = num
+            while val > 0:
+                sd += val % 10
+                val //= 10
+
+            group = groups[sd]
+            if not group:
+                group.append(num)
+            elif len(group) == 1:
+                heappush(group, num)
+            else:
+                heappushpop(group, num)
+
+        max_sum = -1
+        for group in groups.values():
+            if len(group) > 1:
+                max_sum = max2(max_sum, group[0] + group[1])
+
+        return max_sum

source/coding/2342-max-sum-of-a-pair-with-equal-sum-of-digits/solution_test.py

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+import pytest
+
+from solution import Solution
+
+
+@pytest.mark.parametrize('nums, expected', [
+    ([18,43,36,13,7], 54),
+    ([10,12,19,14], -1),
+
+    ([279,169,463,252,94,455,423,315,288,64,494,337,409,283,283,477,248,8,89,166,188,186,128], 872),
+])
+@pytest.mark.parametrize('sol', [Solution()])
+def test_solution(sol, nums, expected):
+    assert sol.maximumSum(nums) == expected