LeetCode 845. 数组中的最长山脉

思路

方法一：暴力法

对每一个数，都向两边一一扩散，寻找山脉。

class Solution {
public:
    int longestMountain(vector<int>& arr) {
        int n = arr.size();
        
        int maxMountainLen = 0;
        int left, right;
        for(int i = 1; i <= n-2; ++i) {
            left = i - 1;
            right = i + 1;
            if(arr[left] >= arr[i] || arr[right] >= arr[i]) {
                continue;
            }

            int tmpLeftValue = arr[left];
            int tmpRightValue = arr[right];
            left--;
            right++;
            while(left >= 0 && arr[left] < tmpLeftValue) {
                tmpLeftValue = arr[left];
                --left;
            }

            while(right < n && arr[right] < tmpRightValue) {
                tmpRightValue = arr[right];
                ++right;
            }
            
            if(right-left-1 > maxMountainLen) {
                maxMountainLen = right-left-1;
            }
        }

        return maxMountainLen;
    }
};

复杂度分析

时间复杂度：O(n²)，比如这种数据：1,2,3,4,5,6,9,7

空间复杂度：O(n)

方法二：动态规划 - 枚举山顶

class Solution {
private:
    vector<int> left, right;
public:
    int longestMountain(vector<int>& arr) {
        int n = arr.size();

        left = vector<int>(n, 0);
        right = vector<int>(n, 0);

        for(int i = 1; i < n; ++i) {
            if(arr[i] > arr[i-1]) {
                left[i] = left[i-1] + 1;
            } else {
                left[i] = 0;
            }
        }

        for(int i = n-2; i >= 0; --i) {
            if(arr[i] > arr[i+1]) {
                right[i] = right[i+1] + 1;
            } else {
                right[i] = 0;
            }
        }

        int maxMountainLen = 0;
        // int lIndex, rIndex;    //答案的左右边界 
        for(int i = 0; i < n; ++i) {
            if(left[i] > 0 && right[i] > 0 && left[i]+right[i]+1 > maxMountainLen) {
                maxMountainLen = left[i] + right[i] + 1;
                // lIndex = i - left[i];
                // rIndex = i + right[i];
            }
        }
        
        //输出"山脉"，即答案序列 
        // for(int i = lIndex; i <= rIndex; ++i) {
        //     cout << arr[i] << ' ';
        // }

        return maxMountainLen;
    }
};

方法三：双指针 - 枚举山脚

class Solution {
public:
    int longestMountain(vector<int>& arr) {
        int n = arr.size();
        int ans = 0;
        int left = 0;
        // int lIndex, rIndex; //答案的左右边界 
        while (left + 2 < n) {
            int right = left + 1;
            if (arr[left] < arr[left + 1]) {
                while (right + 1 < n && arr[right] < arr[right + 1]) {
                    ++right;
                }
                if (right + 1 < n && arr[right] > arr[right + 1]) {
                    while (right + 1 < n && arr[right] > arr[right + 1]) {
                        ++right;
                    }
                    if(right-left+1 > ans) {
                        ans = right-left+1;
                        // lIndex = left;
                        // rIndex = right;
                    } 
                }
                else {
                    ++right;
                }
            }
            left = right;
        }
        
        //输出"山脉"，即答案序列
        // for(int i = lIndex; i <= rIndex; ++i) {
        //     cout << arr[i] << ' ';
        // }
        
        return ans;
    }
};

参考文章

原文：LeetCode官方题解 - 数组中的最长山脉