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A magic index in an array A[0...n-1]
is defined to be an index such that A[i] = i
. Given a sorted array of distinct integers, write a method to find a magic index, if one exists, in array A. If not, return -1. If there are more than one magic index, return the smallest one.
Example1:
Input: nums = [0, 2, 3, 4, 5] Output: 0
Example2:
Input: nums = [1, 1, 1] Output: 1
Note:
1 <= nums.length <= 1000000
class Solution:
def findMagicIndex(self, nums: List[int]) -> int:
def find(nums, left, right):
if left > right:
return -1
mid = (left + right) >> 1
left_index = find(nums, left, mid - 1)
if left_index != -1:
return left_index
if nums[mid] == mid:
return mid
return find(nums, mid + 1, right)
return find(nums, 0, len(nums) - 1)
class Solution {
public int findMagicIndex(int[] nums) {
int left = 0, right = nums.length - 1;
return find(nums, left, right);
}
private int find(int[] nums, int left, int right) {
if (left > right) {
return -1;
}
int mid = (left + right) >> 1;
int leftIndex = find(nums, left, mid - 1);
if (leftIndex != -1) {
return leftIndex;
}
if (nums[mid] == mid) {
return mid;
}
return find(nums, mid + 1, right);
}
}
/**
* @param {number[]} nums
* @return {number}
*/
var findMagicIndex = function (nums) {
return helper(nums, 0, nums.length - 1);
};
function helper(nums, left, right) {
if (left > right) return -1;
let mid = Math.floor((left + right) / 2);
let leftIndex = helper(nums, left, mid - 1);
if (leftIndex != -1) return leftIndex;
if (nums[mid] == mid) return mid;
return helper(nums, mid + 1, right);
}
class Solution {
public:
int findMagicIndex(vector<int>& nums) {
return find(nums, 0, nums.size() - 1);
}
int find(vector<int>& nums, int left, int right) {
if (left > right) {
return -1;
}
int mid = left + right >> 1;
int leftIndex = find(nums, left, mid - 1);
if (leftIndex != -1) {
return leftIndex;
}
if (nums[mid] == mid) {
return mid;
}
return find(nums, mid + 1, right);
}
};
func findMagicIndex(nums []int) int {
return find(nums, 0, len(nums)-1)
}
func find(nums []int, left, right int) int {
if left > right {
return -1
}
mid := (left + right) >> 1
leftIndex := find(nums, left, mid-1)
if leftIndex != -1 {
return leftIndex
}
if nums[mid] == mid {
return mid
}
return find(nums, mid+1, right)
}
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