有界数组中指定下标处的最大值

/*
题目思路：
1. 使用Java Stream实现二分查找和计算。
2. 通过stream将数字范围映射为可行的nums[index]值，然后使用条件过滤。
3. 使用max查找最大值。
*/

import java.util.stream.IntStream;

public class Solution {
    public int maxValue(int n, int index, int maxSum) {
        return IntStream.rangeClosed(1, maxSum)
                .filter(mid -> canConstruct(n, index, maxSum, mid))
                .max()
                .orElse(1);
    }

    private boolean canConstruct(int n, int index, int maxSum, int target) {
        long sum = target;
        sum += sumLeft(index, target);
        sum += sumRight(n - index - 1, target);
        return sum <= maxSum;
    }

    private long sumLeft(int count, int peak) {
        if (peak > count) {
            long fullSum = (long) (peak - 1) * peak / 2;
            long excess = (long) (peak - count - 1) * (peak - count) / 2;
            return fullSum - excess;
        } else {
            long fullSum = (long) peak * (peak - 1) / 2;
            return fullSum + count - peak + 1;
        }
    }

    private long sumRight(int count, int peak) {
        return sumLeft(count, peak);
    }
}