In this approach, the task is broken into three main steps:
arr[i] > arr[i+1] and arr[i] > arr[i-1].Time Complexity: O(log n) for peak finding and 2 * O(log n) for the two binary searches.
Total: O(log n).
Space Complexity: O(1) because we use a constant amount of space.
1interface MountainArray {
2 int get(int index);
3 int length();
4}
5
6public class Solution {
7 private int findPeakIndex(MountainArray mountainArr) {
8 int left = 0;
9 int right = mountainArr.length() - 1;
10 while (left < right) {
11 int mid = left + (right - left) / 2;
12 if (mountainArr.get(mid) < mountainArr.get(mid + 1)) {
13 left = mid + 1;
14 } else {
15 right = mid;
16 }
17 }
18 return left;
19 }
20
21 private int binarySearch(MountainArray mountainArr, int start, int end, int target, boolean isAscending) {
22 while (start <= end) {
23 int mid = start + (end - start) / 2;
24 int value = mountainArr.get(mid);
25 if (value == target) {
26 return mid;
27 }
28 if (isAscending) {
29 if (value < target) {
30 start = mid + 1;
31 } else {
32 end = mid - 1;
33 }
34 } else {
35 if (value > target) {
36 start = mid + 1;
37 } else {
38 end = mid - 1;
39 }
40 }
41 }
42 return -1;
43 }
44
45 public int findInMountainArray(int target, MountainArray mountainArr) {
46 int peak = findPeakIndex(mountainArr);
47 int index = binarySearch(mountainArr, 0, peak, target, true);
48 if (index != -1) {
49 return index;
50 }
51 return binarySearch(mountainArr, peak + 1, mountainArr.length() - 1, target, false);
52 }
53}The Java solution performs similarly to the C/C++ implementations. It identifies the peak using a binary search, which enables the array to be divided into two segments for additional binary searches to locate the target. Each binary search operation effectively reduces the time complexity to O(log n).
This approach involves directly accessing each element linearly until the condition is satisfied (even though this is not allowed by the problem constraints). It is less optimal and efficient compared to the above implementations, requiring traversal of the entire array.
Time Complexity: O(n) as each element could potentially be checked once.
Space Complexity: O(1) as no extra space is used except for variables.
1interface MountainArray {
2 int get(int index);
3 int length();
4}
5
6public class Solution {
7 public int findInMountainArray(int target, MountainArray mountainArr) {
8 int len = mountainArr.length();
9 for (int i = 0; i < len; i++) {
10 if (mountainArr.get(i) == target) {
11 return i;
12 }
13 }
14 return -1;
15 }
16}The Java implementation performs a linear search across the mountain array elements, comparing each element against the target. As soon as the target is found, its index is returned, otherwise, the loop runs through all elements. Despite being simple, the efficiency is reduced compared to optimized techniques due to increased function calls and potential worst-case traversal across all elements.