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面试题 08.03. 魔术索引

English Version

题目描述

魔术索引。 在数组A[0...n-1]中，有所谓的魔术索引，满足条件A[i] = i。给定一个有序整数数组，编写一种方法找出魔术索引，若有的话，在数组A中找出一个魔术索引，如果没有，则返回-1。若有多个魔术索引，返回索引值最小的一个。

示例1:

 输入：nums = [0, 2, 3, 4, 5]
 输出：0
 说明: 0下标的元素为0

示例2:

 输入：nums = [1, 1, 1]
 输出：1

提示:

1. nums长度在[1, 1000000]之间

解法

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)
}

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