LeetCode 1095. Find in Mountain Array

Description

https://leetcode.com/problems/find-in-mountain-array/

(This problem is an interactive problem.)

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

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

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

You cannot 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:

  • 3 <= mountain_arr.length() <= 104
  • 0 <= target <= 109
  • 0 <= mountain_arr.get(index) <= 109

Explanation

Find the peak of the mountain first. If the target is the peak of the mountain, return the peak index. If the target is greater than the peak, return -1. Otherwise, use binary search on the uphill of the mountain first, if the target is still not found, search on the downhill of the mountain.

Python Solution

# """
# This is MountainArray's API interface.
# You should not implement it, or speculate about its implementation
# """
#class MountainArray:
#    def get(self, index: int) -> int:
#    def length(self) -> int:

class Solution:
    def findInMountainArray(self, target: int, mountain_arr: 'MountainArray') -> int:        
        peak_index = self.find_peak(mountain_arr)
        
        if target > mountain_arr.get(peak_index):
            return -1
        
        if target == mountain_arr.get(peak_index):
            return peak_index
                
        
        left = self.find_target_from_uphill(mountain_arr, target, 0, peak_index)
        
        if left != -1:
            return left
        
        right = self.find_target_from_downhill(mountain_arr, target, peak_index + 1, mountain_arr.length() - 1)
        
        if right != -1:
            return right
        
        return -1
        
    def find_peak(self, mountain_arr):        
        start = 0
        end = mountain_arr.length() - 1
                        
        while start + 1 < end:       
            mid = start + (end - start) // 2
            if mountain_arr.get(mid) > mountain_arr.get(mid - 1) and mountain_arr.get(mid) > mountain_arr.get(mid + 1):
                return mid
            elif mountain_arr.get(mid) < mountain_arr.get(mid - 1):
                end  = mid                
            elif mountain_arr.get(mid) < mountain_arr.get(mid + 1):
                start = mid
        
        if mountain_arr.get(start) > mountain_arr.get(end):
            return start
        
        return end        

        
    def find_target_from_uphill(self, mountain_arr, target, start, end):                        
        while start + 1 < end:
            mid = start + (end - start) // 2
            
            if mountain_arr.get(mid) == target:
                end = mid              
            elif mountain_arr.get(mid) > target:
                end = mid     
            elif mountain_arr.get(mid) < target:
                start = mid
        
        if mountain_arr.get(start) == target:
            return start
        
        if mountain_arr.get(end) == target:
            return end
        
        return -1
    
    def find_target_from_downhill(self, mountain_arr, target, start, end):                        
        while start + 1 < end:
            mid = start + (end - start) // 2
            
            if mountain_arr.get(mid) == target:
                end = mid              
            elif mountain_arr.get(mid) > target:
                start = mid     
            elif mountain_arr.get(mid) < target:
                end = mid
        
        if mountain_arr.get(start) == target:
            return start
        
        if mountain_arr.get(end) == target:
            return end
        
        return -1    
  • Time Complexity: O(log(N)).
  • Space Complexity: O(1).

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