Leetcode 374. Guess Number Higher or Lower

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原文链接：http://www.cnblogs.com/Deribs4/p/5691859.html

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#数据结构与算法

本文详细解析了猜数字游戏的二分查找算法实现，通过两个不同的模板展示了如何在指定范围内高效地找出目标数字。适用于初学者理解二分查找的基本原理及其应用场景。

374. Guess Number Higher or Lower

Total Accepted: 7396
Total Submissions: 23391
Difficulty: Easy

We are playing the Guess Game. The game is as follows:

I pick a number from 1 to n. You have to guess which number I picked.

Every time you guess wrong, I'll tell you whether the number is higher or lower.

You call a pre-defined API guess(int num) which returns 3 possible results (-1, 1, or 0):

-1 : My number is lower
 1 : My number is higher
 0 : Congrats! You got it!

Example:

n = 10, I pick 6.

Return 6.

思路：二分查找。这里的二分查找模板可以推广。下面有2个模板，注意各自的应用场景。

代码：

这个是在左闭右闭区间[low,high]中查找元素值>=查找值的第1个元素的位置，这里也考虑high位置和查找值的大小。

 1 // Forward declaration of guess API.
 2 // @param num, your guess
 3 // @return -1 if my number is lower, 1 if my number is higher, otherwise return 0
 4 int guess(int num);
 5 
 6 class Solution {
 7 public:
 8     int guessNumber(int n) {
 9         int low=1,high=n,mid;
10         while(low<=high){
11             mid=low+(high-low)/2;
12             if(guess(mid)==1){
13                 low=mid+1;
14             }
15             else{
16                 high=mid-1;
17             }
18         }
19         return low;
20     }
21 };

这个是在左闭右开区间[low,high)中查找元素值>=查找值的第1个元素的位置，这里不考虑high位置和查找值的大小。相当于STL的函数lower_bound()。

本题有些特殊，就算high所在位置不被比较，如果排查了high之前所有位置和查找值的大小，最后low和high都停留在同1个位置，这时high虽然不被比较，但肯定就是high位置元素==查找值。例如在[1,2,3]中查找3。

 1 // Forward declaration of guess API.
 2 // @param num, your guess
 3 // @return -1 if my number is lower, 1 if my number is higher, otherwise return 0
 4 int guess(int num);
 5 
 6 class Solution {
 7 public:
 8     int guessNumber(int n) {
 9         int low=1,high=n,mid;
10         while(low<high){
11             mid=low+(high-low)/2;
12             if(guess(mid)==1){
13                 low=mid+1;
14             }
15             else{
16                 high=mid;
17             }
18         }
19         return low;
20     }
21 };