2342. Max Sum of a Pair With Equal Sum of Digits

Description

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.

 

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

Solutions

Solution 1: Hash Table

We can use a hash table $d$ to record the maximum value corresponding to each digit sum, and initialize an answer variable $ans = -1$.

Next, we traverse the array $nums$. For each number $v$, we calculate its digit sum $x$. If $x$ exists in the hash table $d$, then we update the answer $ans = \max(ans, d[x] + v)$. Then update the hash table $d[x] = \max(d[x], v)$.

Finally, return the answer $ans$.

Since the maximum element in $nums$ is $10^9$, the maximum digit sum is $9 \times 9 = 81$. We can directly define an array $d$ of length $100$ to replace the hash table.

The time complexity is $O(n \times \log M)$, and the space complexity is $O(D)$. Here, $n$ is the length of the array $nums$, and $M$ and $D$ are the maximum value of the elements in the array $nums$ and the maximum value of the digit sum, respectively. In this problem, $M \leq 10^9$, $D \leq 81$.

Python Code
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class Solution:
    def maximumSum(self, nums: List[int]) -> int:
        d = defaultdict(int)
        ans = -1
        for v in nums:
            x, y = 0, v
            while y:
                x += y % 10
                y //= 10
            if x in d:
                ans = max(ans, d[x] + v)
            d[x] = max(d[x], v)
        return ans

Java Code
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class Solution {
    public int maximumSum(int[] nums) {
        int[] d = new int[100];
        int ans = -1;
        for (int v : nums) {
            int x = 0;
            for (int y = v; y > 0; y /= 10) {
                x += y % 10;
            }
            if (d[x] > 0) {
                ans = Math.max(ans, d[x] + v);
            }
            d[x] = Math.max(d[x], v);
        }
        return ans;
    }
}

C++ Code
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class Solution {
public:
    int maximumSum(vector<int>& nums) {
        int d[100]{};
        int ans = -1;
        for (int v : nums) {
            int x = 0;
            for (int y = v; y; y /= 10) {
                x += y % 10;
            }
            if (d[x]) {
                ans = max(ans, d[x] + v);
            }
            d[x] = max(d[x], v);
        }
        return ans;
    }
};

Go Code
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func maximumSum(nums []int) int {
	d := [100]int{}
	ans := -1
	for _, v := range nums {
		x := 0
		for y := v; y > 0; y /= 10 {
			x += y % 10
		}
		if d[x] > 0 {
			ans = max(ans, d[x]+v)
		}
		d[x] = max(d[x], v)
	}
	return ans
}

TypeScript Code
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function maximumSum(nums: number[]): number {
    const d: number[] = Array(100).fill(0);
    let ans = -1;
    for (const v of nums) {
        let x = 0;
        for (let y = v; y; y = (y / 10) | 0) {
            x += y % 10;
        }
        if (d[x]) {
            ans = Math.max(ans, d[x] + v);
        }
        d[x] = Math.max(d[x], v);
    }
    return ans;
}

Rust Code
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impl Solution {
    pub fn maximum_sum(nums: Vec<i32>) -> i32 {
        let mut d = vec![0; 100];
        let mut ans = -1;

        for &v in nums.iter() {
            let mut x: usize = 0;
            let mut y = v;
            while y > 0 {
                x += (y % 10) as usize;
                y /= 10;
            }
            if d[x] > 0 {
                ans = ans.max(d[x] + v);
            }
            d[x] = d[x].max(v);
        }

        ans
    }
}