LeetCode 2834: Find the Minimum Possible Sum of a Beautiful Array Solution
Master LeetCode problem 2834 (Find the Minimum Possible Sum of a Beautiful Array), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.
Problem Explanation
Explanation
To find the minimum possible sum of a beautiful array, we need to construct an array that meets the given conditions. The key observation is that if we have a beautiful array, we can create another beautiful array by doubling all the elements and adding an arbitrary constant to each element. This property allows us to build beautiful arrays recursively.
The algorithm involves dividing the problem into subproblems and building the beautiful array iteratively. We start with a base case where n=1, and the beautiful array is simply [1]. For each subsequent iteration, we double the elements from the previous beautiful array and add an offset to ensure the pairwise distinct positive integers condition is met.
By following this approach, we can construct a beautiful array that satisfies the given conditions. The final step is to calculate the sum of the elements in the beautiful array modulo 10^9 + 7, which gives us the minimum possible sum.
- Time complexity: O(n)
- Space complexity: O(n)
Solution Code
class Solution {
public int minSumOfBeautifulArray(int n, int target) {
int MOD = 1000000007;
int[] result = {1};
while (result.length < n) {
int[] next = new int[result.length * 2 + 1];
for (int i = 0; i < result.length; i++) {
next[i * 2] = result[i] * 2;
next[i * 2 + 1] = result[i] * 2 - 1;
}
result = next;
}
long sum = 0;
for (int num : result) {
if (num != target - num) {
sum += num;
}
}
return (int) (sum % MOD);
}
}Try It Yourself
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