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1064. Fixed Point

Description

Given an array of distinct integers arr, where arr is sorted in ascending order, return the smallest index i that satisfies arr[i] == i. If there is no such index, return -1.

 

Example 1:

Input: arr = [-10,-5,0,3,7]
Output: 3
Explanation: For the given array, arr[0] = -10, arr[1] = -5, arr[2] = 0, arr[3] = 3, thus the output is 3.

Example 2:

Input: arr = [0,2,5,8,17]
Output: 0
Explanation: arr[0] = 0, thus the output is 0.

Example 3:

Input: arr = [-10,-5,3,4,7,9]
Output: -1
Explanation: There is no such i that arr[i] == i, thus the output is -1.

 

Constraints:

  • 1 <= arr.length < 104
  • -109 <= arr[i] <= 109

 

Follow up: The O(n) solution is very straightforward. Can we do better?

Solutions

Binary search.

  • class Solution {
        public int fixedPoint(int[] arr) {
            int left = 0, right = arr.length - 1;
            while (left < right) {
                int mid = (left + right) >> 1;
                if (arr[mid] >= mid) {
                    right = mid;
                } else {
                    left = mid + 1;
                }
            }
            return arr[left] == left ? left : -1;
        }
    }
    
  • class Solution {
    public:
        int fixedPoint(vector<int>& arr) {
            int left = 0, right = arr.size() - 1;
            while (left < right) {
                int mid = left + right >> 1;
                if (arr[mid] >= mid) {
                    right = mid;
                } else {
                    left = mid + 1;
                }
            }
            return arr[left] == left ? left : -1;
        }
    };
    
  • class Solution:
        def fixedPoint(self, arr: List[int]) -> int:
            left, right = 0, len(arr) - 1
            while left < right:
                mid = (left + right) >> 1
                if arr[mid] >= mid:
                    right = mid
                else:
                    left = mid + 1
            return left if arr[left] == left else -1
    
    
  • func fixedPoint(arr []int) int {
    	left, right := 0, len(arr)-1
    	for left < right {
    		mid := (left + right) >> 1
    		if arr[mid] >= mid {
    			right = mid
    		} else {
    			left = mid + 1
    		}
    	}
    	if arr[left] == left {
    		return left
    	}
    	return -1
    }
    
  • function fixedPoint(arr: number[]): number {
        let left = 0;
        let right = arr.length - 1;
        while (left < right) {
            const mid = (left + right) >> 1;
            if (arr[mid] >= mid) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return arr[left] === left ? left : -1;
    }
    
    

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