162 Find Peak Element

1. Question

A peak element is an element that is greater than its neighbors.
Given an input array wherenum[i] ≠ num[i+1], find a peak element and return its index.
The array may contain multiple peaks, in that case return the index to any one of the peaks is fine.
You may imagine thatnum[-1] = num[n] = -∞.
For example, in array[1, 2, 3, 1], 3 is a peak element and your function should return the index number 2.

2. Implementation

(1) Binary Search
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class Solution {
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public int findPeakElement(int[] nums) {
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if (nums.length <= 1) {
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return 0;
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}
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int start = 0, end = nums.length - 1, mid = 0;
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while (start + 1 < end) {
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mid = start + (end - start) / 2;
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if (nums[mid - 1] < nums[mid] && nums[mid] > nums[mid + 1]) {
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return mid;
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}
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else if (nums[mid - 1] < nums[mid] && nums[mid] < nums[mid + 1]) {
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start = mid + 1;
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}
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else {
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end = mid - 1;
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}
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}
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return nums[start] > nums[end] ? start : end;
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}
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}
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3. Time & Space Complexity

Binary Search: 时间复杂度O(logn), 空间复杂度O(1)