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3745. Maximize Expression of Three Elements

Description

You are given an integer array nums.

Choose three elements a, b, and c from nums at distinct indices such that the value of the expression a + b - c is maximized.

Return an integer denoting the maximum possible value of this expression.

 

Example 1:

Input: nums = [1,4,2,5]

Output: 8

Explanation:

We can choose a = 4, b = 5, and c = 1. The expression value is 4 + 5 - 1 = 8, which is the maximum possible.

Example 2:

Input: nums = [-2,0,5,-2,4]

Output: 11

Explanation:

We can choose a = 5, b = 4, and c = -2. The expression value is 5 + 4 - (-2) = 11, which is the maximum possible.

 

Constraints:

  • 3 <= nums.length <= 100
  • -100 <= nums[i] <= 100

Solutions

Solution 1: Find Maximum, Second Maximum, and Minimum Values

According to the problem description, we need to choose three elements \(a\), \(b\), and \(c\) at distinct indices such that the value of the expression \(a + b - c\) is maximized.

We only need to traverse the array to find the largest two elements \(a\) and \(b\) and the smallest element \(c\). Then we can calculate the value of the expression.

The time complexity is \(O(n)\), where \(n\) is the length of the array. The space complexity is \(O(1)\).

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class Solution:
    def maximizeExpressionOfThree(self, nums: List[int]) -> int:
        a = b = -inf
        c = inf
        for x in nums:
            if x < c:
                c = x
            if x >= a:
                a, b = x, a
            elif x > b:
                b = x
        return a + b - c

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class Solution {
    public int maximizeExpressionOfThree(int[] nums) {
        final int inf = 1 << 30;
        int a = -inf, b = -inf, c = inf;
        for (int x : nums) {
            if (x < c) {
                c = x;
            }
            if (x >= a) {
                b = a;
                a = x;
            } else if (x > b) {
                b = x;
            }
        }
        return a + b - c;
    }
}

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class Solution {
public:
    int maximizeExpressionOfThree(vector<int>& nums) {
        const int inf = 1 << 30;
        int a = -inf, b = -inf, c = inf;
        for (int x : nums) {
            if (x < c) {
                c = x;
            }
            if (x >= a) {
                b = a;
                a = x;
            } else if (x > b) {
                b = x;
            }
        }
        return a + b - c;
    }
};

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func maximizeExpressionOfThree(nums []int) int {
    const inf = 1 << 30
    a, b, c := -inf, -inf, inf
    for _, x := range nums {
        if x < c {
            c = x
        }
        if x >= a {
            b = a
            a = x
        } else if x > b {
            b = x
        }
    }
    return a + b - c
}

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function maximizeExpressionOfThree(nums: number[]): number {
    const inf = 1 << 30;
    let [a, b, c] = [-inf, -inf, inf];

    for (const x of nums) {
        if (x < c) {
            c = x;
        }
        if (x >= a) {
            b = a;
            a = x;
        } else if (x > b) {
            b = x;
        }
    }
    return a + b - c;
}

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