503. Next Greater Element II

 

Given a circular array (the next element of the last element is the first element of the array), print the Next Greater Number for every element. The Next Greater Number of a number x is the first greater number to its traversing-order next in the array, which means you could search circularly to find its next greater number. If it doesn’t exist, output -1 for this number.

Example 1:

Input: [1,2,1]
Output: [2,-1,2]
Explanation: The first 1's next greater number is 2;   
The number 2 can't find next greater number;   
The second 1's next greater number needs to search circularly, which is also 2.

 

Note: The length of given array won’t exceed 10000.

 

这道题是之前那道 Next Greater Element I 的拓展,不同的是,此时数组是一个循环数组,就是说某一个元素的下一个较大值可以在其前面,那么对于循环数组的遍历,为了使下标不超过数组的长度,我们需要对n取余,下面先来看暴力破解的方法,遍历每一个数字,然后对于每一个遍历到的数字,遍历所有其他数字,注意不是遍历到数组末尾,而是通过循环数组遍历其前一个数字,遇到较大值则存入结果 res 中,并 break,再进行下一个数字的遍历,参见代码如下: 

 

解法一:

class Solution {
public:
    vector<int> nextGreaterElements(vector<int>& nums) {
        int n = nums.size();
        vector<int> res(n, -1);
        for (int i = 0; i < n; ++i) {
            for (int j = i + 1; j < i + n; ++j) {
                if (nums[j % n] > nums[i]) {
                    res[i] = nums[j % n];
                    break;
                }
            }
        }
        return res;
    }
};

 

我们可以使用栈来进行优化上面的算法,遍历两倍的数组,然后还是坐标i对n取余,取出数字,如果此时栈不为空,且栈顶元素小于当前数字,说明当前数字就是栈顶元素的右边第一个较大数,那么建立二者的映射,并且去除当前栈顶元素,最后如果i小于n,则把i压入栈。因为 res 的长度必须是n,超过n的部分我们只是为了给之前栈中的数字找较大值,所以不能压入栈,参见代码如下:

 

解法二:

class Solution {
public:
    vector<int> nextGreaterElements(vector<int>& nums) {
        int n = nums.size();
        vector<int> res(n, -1);
        stack<int> st;
        for (int i = 0; i < 2 * n; ++i) {
            int num = nums[i % n];
            while (!st.empty() && nums[st.top()] < num) {
                res[st.top()] = num; st.pop();
            }
            if (i < n) st.push(i);
        }
        return res;
    }
};

 

Github 同步地址:

https://github.com/grandyang/leetcode/issues/503

 

类似题目:

Next Greater Element I 

Next Greater Element III

 

参考资料:

https://leetcode.com/problems/next-greater-element-ii/

https://leetcode.com/problems/next-greater-element-ii/discuss/98270/JavaC%2B%2BPython-Loop-Twice

https://leetcode.com/problems/next-greater-element-ii/discuss/98273/Java-10-lines-and-C%2B%2B-12-lines-linear-time-complexity-O(n)-with-explanation

 

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