LintCode 1745: Monotonic Array

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本文介绍了一种用于判断数组是否为单调递增或单调递减的算法。通过一次遍历，该算法可以确定数组A是否满足单调性条件，即对于所有i<=j，A[i]<=A[j]或A[i]>=A[j]。文章提供了具体的实现代码，并附带了示例输入输出。

Monotonic Array

An array is monotonic if it is either monotone increasing or monotone decreasing.

An array A is monotone increasing if for all i <= j, A[i] <= A[j]. An array A is monotone decreasing if for all i <= j, A[i] >= A[j].

Return true if and only if the given array A is monotonic.

Example
Example 1:

Input: [1,2,2,3]
Output: true
Example 2:

Input: [1,3,2]
Output: false
Notice
1 \leq A.length \leq 500001≤A.length≤50000
-100000 \leq A[i] \leq 100000−100000≤A[i]≤100000

解法1：

class Solution {
public:
    /**
     * @param A: a array
     * @return: is it monotonous
     */
    bool isMonotonic(vector<int> &A) {
        int n = A.size();
        if (n <= 1) return true;
        bool increasing, decreasing;
        
        if (A[1] > A[0]) {
            increasing = true;
            decreasing = false;
        } else if (A[1] < A[0]) {
            increasing = false;
            decreasing = true;
        } else {
            increasing = true;
            decreasing = true;
        }
 
        for (int i = 2; i < n; ++i) {
            if (increasing && A[i] >= A[i - 1]) continue;
            if (decreasing && A[i] <= A[i - 1]) continue;
            return false;
        }
        return true;
    }
};