README_EN.md

08.03. Magic Index

中文文档

Description

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. 1 <= nums.length <= 1000000

Solutions

Python3

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)

Java

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);
    }
}

JavaScript

/**
 * @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);
}

C++

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);
    }
};

Go

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)
}

TypeScript

function findMagicIndex(nums: number[]): number {
    const n = nums.length;
    const find = (l: number, r: number): number => {
        if (l > r || nums[r] < 0) {
            return -1;
        }
        const mid = l + Math.floor((r - l) / 2);
        if (nums[mid] >= l) {
            const res = find(l, mid - 1);
            if (res !== -1) {
                return res;
            }
        }
        if (nums[mid] === mid) {
            return mid;
        }
        return find(mid + 1, r);
    };
    return find(0, n - 1);
}

function findMagicIndex(nums: number[]): number {
    const n = nums.length;
    let i = 0;
    while (i < n) {
        if (nums[i] === i) {
            return i;
        }
        i = Math.max(nums[i], i + 1);
    }
    return -1;
}

Rust

impl Solution {
    fn find(nums: &Vec<i32>, l: usize, r: usize) -> i32 {
        if l >= r || nums[r - 1] < 0 {
            return -1;
        }
        let mid = l + (r - l) / 2;
        if nums[mid] >= l as i32 {
            let res = Self::find(nums, l, mid);
            if res != -1 {
                return res;
            }
        }
        if nums[mid] == mid as i32 {
            return mid as i32;
        }
        Self::find(nums, mid + 1, r)
    }

    pub fn find_magic_index(nums: Vec<i32>) -> i32 {
        Self::find(&nums, 0, nums.len())
    }
}

impl Solution {
    pub fn find_magic_index(nums: Vec<i32>) -> i32 {
        let n = nums.len();
        let mut i = 0 as i32;
        while (i as usize) < n {
            let num = nums[i as usize];
            if num == i {
                return i;
            }
            i = num.max(i + 1);
        }
        -1
    }
}

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