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2535. Difference Between Element Sum and Digit Sum of an Array

Description

You are given a positive integer array nums.

  • The element sum is the sum of all the elements in nums.
  • The digit sum is the sum of all the digits (not necessarily distinct) that appear in nums.

Return the absolute difference between the element sum and digit sum of nums.

Note that the absolute difference between two integers x and y is defined as |x - y|.

 

Example 1:

Input: nums = [1,15,6,3]
Output: 9
Explanation: 
The element sum of nums is 1 + 15 + 6 + 3 = 25.
The digit sum of nums is 1 + 1 + 5 + 6 + 3 = 16.
The absolute difference between the element sum and digit sum is |25 - 16| = 9.

Example 2:

Input: nums = [1,2,3,4]
Output: 0
Explanation:
The element sum of nums is 1 + 2 + 3 + 4 = 10.
The digit sum of nums is 1 + 2 + 3 + 4 = 10.
The absolute difference between the element sum and digit sum is |10 - 10| = 0.

 

Constraints:

  • 1 <= nums.length <= 2000
  • 1 <= nums[i] <= 2000

Solutions

Solution 1: Simulation We traverse the array \(\textit{nums}\), calculate the sum of the elements \(x\) and the sum of the digits \(y\), and finally return \(|x - y|\). Since \(x\) is always greater than or equal to \(y\), we can directly return \(x - y\).

The time complexity is \(O(n \times \log_{10} M)\), where \(n\) and \(M\) are the length of the array \(\textit{nums}\) and the maximum value of the elements in the array, respectively. The space complexity is \(O(1)\).

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class Solution:
    def differenceOfSum(self, nums: List[int]) -> int:
        x = y = 0
        for v in nums:
            x += v
            while v:
                y += v % 10
                v //= 10
        return x - y

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class Solution {
    public int differenceOfSum(int[] nums) {
        int x = 0, y = 0;
        for (int v : nums) {
            x += v;
            for (; v > 0; v /= 10) {
                y += v % 10;
            }
        }
        return x - y;
    }
}

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class Solution {
public:
    int differenceOfSum(vector<int>& nums) {
        int x = 0, y = 0;
        for (int v : nums) {
            x += v;
            for (; v; v /= 10) {
                y += v % 10;
            }
        }
        return x - y;
    }
};

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func differenceOfSum(nums []int) int {
    var x, y int
    for _, v := range nums {
        x += v
        for ; v > 0; v /= 10 {
            y += v % 10
        }
    }
    return x - y
}

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function differenceOfSum(nums: number[]): number {
    let [x, y] = [0, 0];
    for (let v of nums) {
        x += v;
        for (; v; v = Math.floor(v / 10)) {
            y += v % 10;
        }
    }
    return x - y;
}

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impl Solution {
    pub fn difference_of_sum(nums: Vec<i32>) -> i32 {
        let mut x = 0;
        let mut y = 0;

        for &v in &nums {
            x += v;
            let mut num = v;
            while num > 0 {
                y += num % 10;
                num /= 10;
            }
        }

        x - y
    }
}

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int differenceOfSum(int* nums, int numsSize) {
    int x = 0, y = 0;
    for (int i = 0; i < numsSize; i++) {
        int v = nums[i];
        x += v;
        while (v > 0) {
            y += v % 10;
            v /= 10;
        }
    }
    return x - y;
}

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