[LeetCode] 153. Find Minimum in Rotated Sorted Array

Suppose an array sorted in ascending order is rotated at some pivot unknown to you beforehand.
(i.e., 0 1 2 4 5 6 7 might become 4 5 6 7 0 1 2).
Find the minimum element.
You may assume no duplicate exists in the array.

Thought process:
O(n) solution is trivial, so we aim to solve this problem using binary search. For each middle element we find, we compare it with the last element of the array. There are two cases:
  1. nums[mid] <= last element: mid is on the part that's been rotated to the right. The minimum element is to the left of mid.
  2. nums[mid] > last element: mid is on the part that's not rotated. The minimum element is to the right of mid.

Solution:
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
public class Solution {
    public int findMin(int[] nums) {
        int start = 0;
        int end = nums.length - 1;
        int last = nums[end];
        
        while (start + 1 < end) {
            int mid = start + (end - start) / 2;
            
            if (nums[mid] < last) {
                end = mid;
            } else {
                start = mid;
            }
        }
        
        if (nums[start] < nums[end]) {
            return nums[start];
        } else {
            return nums[end];
        }
    }
}

Note that start is not always going to be the minimum element. Think about the case when there're only two numbers.

 Time complexity: O(logn).
Location: Philadelphia, PA, USA

Comments

Post a Comment

Popular posts from this blog

[LeetCode] 714. Best Time to Buy and Sell Stock with Transaction Fee

Your are given an array of integers  prices , for which the  i -th element is the price of a given stock on day  i ; and a non-negative integer  fee  representing a transaction fee. You may complete as many transactions as you like, but you need to pay the transaction fee for each transaction. You may not buy more than 1 share of a stock at a time (ie. you must sell the stock share before you buy again.) Return the maximum profit you can make. Example 1: Input: prices = [1, 3, 2, 8, 4, 9], fee = 2 Output: 8 Explanation: The maximum profit can be achieved by: Buying at prices[0] = 1 Selling at prices[3] = 8 Buying at prices[4] = 4 Selling at prices[5] = 9 The total profit is ((8 - 1) - 2) + ((9 - 4) - 2) = 8. Note: 0 < prices.length <= 50000 . 0 < prices[i] < 50000 . 0 <= fee < 50000 . Thought process: Each day there are two options, buy or sell. Use two variables buy and sell to keep track of the max profit. Solutio...
Read more

[LeetCode] 269. Alien Dictionary

There is a new alien language which uses the latin alphabet. However, the order among letters are unknown to you. You receive a list of  non-empty  words from the dictionary, where  words are sorted lexicographically by the rules of this new language . Derive the order of letters in this language. Example 1: Given the following words in dictionary, [ "wrt", "wrf", "er", "ett", "rftt" ] The correct order is:  "wertf" . Example 2: Given the following words in dictionary, [ "z", "x" ] The correct order is:  "zx" . Example 3: Given the following words in dictionary, [ "z", "x", "z" ] The order is invalid, so return  "" . Note: You may assume all letters are in lowercase. You may assume that if a is a prefix of b, then a must appear before b in the given dictionary. If the order is invalid, return an empty string...
Read more

[LeetCode] 631. Design Excel Sum Formula

Your task is to design the basic function of Excel and implement the function of sum formula. Specifically, you need to implement the following functions: Excel(int H, char W):  This is the constructor. The inputs represents the height and width of the Excel form.  H  is a positive integer, range from 1 to 26. It represents the height.  W  is a character range from 'A' to 'Z'. It represents that the width is the number of characters from 'A' to  W . The Excel form content is represented by a height * width 2D integer array  C , it should be initialized to zero. You should assume that the first row of  C  starts from 1, and the first column of  C  starts from 'A'. void Set(int row, char column, int val):  Change the value at  C(row, column)  to be val. int Get(int row, char column):  Return the value at  C(row, column) . int Sum(int row, char column, List of Strings : numbers):  This function...
Read more