leetcode 1095. Find in Mountain Array

(This problem is an interactive problem.)

You may recall that an array A is a mountain array if and only if:

• A.length >= 3
• There exists some i with 0 < i < A.length - 1 such that:
  • A[0] < A[1] < ... A[i-1] < A[i]
  • A[i] > A[i+1] > ... > A[A.length - 1]

Given a mountain array mountainArr, return the minimum index such that mountainArr.get(index) == target.  If such an index doesn't exist, return -1.

You can't access the mountain array directly.  You may only access the array using a MountainArray interface:

• MountainArray.get(k) returns the element of the array at index k (0-indexed).
• MountainArray.length() returns the length of the array.

Submissions making more than 100 calls to MountainArray.get will be judged Wrong Answer.  Also, any solutions that attempt to circumvent the judge will result in disqualification.

 

Example 1:

Input: array = [1,2,3,4,5,3,1], target = 3
Output: 2
Explanation: 3 exists in the array, at index=2 and index=5. Return the minimum index, which is 2.

Example 2:

Input: array = [0,1,2,4,2,1], target = 3
Output: -1
Explanation: 3 does not exist in the array, so we return -1.

 

Constraints:

1. 3 <= mountain_arr.length() <= 10000
2. 0 <= target <= 10^9
3. 0 <= mountain_arr.get(index) <= 10^9

解題思路：

二分搜索只能用在有序的數組中，但是山脈數組並不符合這樣的條件，但是其是分爲兩段有序的，[0,peak)升序，[peak + 1  ,len)降序 ；這兩段區間就可以使用二分搜索。所以要先找到peak，peak的特徵是mountainArr[peak] > mountainArr[peak-1] && mountainArr[peak] > mountain[peak + 1]；

如果mountainArr[index-1] < mountainArr[index] && mountainArr[index] < mountain[index + 1] ,說明peak在index的右邊，

如果mountainArr[index-1] > mountainArr[index] && mountainArr[index] > mountain[index + 1]，說明peak在index的左邊；

如果mountainArr[index-1] < mountainArr[index] && mountainArr[index] > mountain[index + 1],說明index就是peak；

 

/**
 * // This is the MountainArray's API interface.
 * // You should not implement it, or speculate about its implementation
 * class MountainArray {
 *   public:
 *     int get(int index);
 *     int length();
 * };
 */
class Solution {
public:
    int findInMountainArray(int target, MountainArray &mountainArr) 
    {
        int len = mountainArr.length() ;
        int peak = getMaxEle(mountainArr) ;
        
        if(peak == -1)
        {
            return inorder(0 , len , mountainArr , target) ;
        }
        else
        {
            if(mountainArr.get(peak) == target) return peak ;
            cout<<"the peak is"<<mountainArr.get(peak)<<endl;
            
            int index = inorder(0 , peak , mountainArr , target) ;
            if(index == -1)
                return deorder(peak + 1 , len , mountainArr , target) ;
            else
                return index ;
        }
    }
    
    int getMaxEle(MountainArray &mountainArr )
    {
        int left = 0 , len = mountainArr.length() , right = len ;
        
        while(left < right)
        {
            int mid = left + (right - left) / 2 ;
            cout<<"mid:"<<mid<<endl ;
            
            if(mid >= 1 && mid < len - 1)
            {
                int num_left = mountainArr.get(mid - 1) , num_mid = mountainArr.get(mid) , num_right = mountainArr.get(mid + 1) ;
                
                if(num_left < num_mid && num_right < num_mid) return mid ;
                else if(num_left < num_mid && num_mid < num_right) left = mid + 1 ;
                else right = mid ;
            }
            else
            {
                if(mid == len - 1) right = len - 1 ;
                else if(mid == 0) left = 1 ;
            }
        }
        
        return -1 ;
    }
    
    int inorder(int posl , int posr , MountainArray& mountainArr , int target)
    {
        while(posl < posr)
        {
            int mid = posl + (posr - posl) / 2 ;
            
            int num_mid = mountainArr.get(mid) ;
            
            if(num_mid < target)
                posl = mid + 1 ;
            else if(num_mid > target)
                posr = mid ;
            else
                return mid ;
        }
        
        return -1 ;
    }
    
    int deorder(int posl , int posr , MountainArray& mountainArr , int target)
    {
        while(posl < posr)
        {
            int mid = posl + (posr - posl) / 2 ;
            
            int num_mid = mountainArr.get(mid) ;
            
            if(num_mid > target)
                posl = mid + 1 ;
            else if(num_mid < target)
                posr = mid ;
            else
                return mid ;
        }
        
        return -1 ;
    }
};