From 017c51b38190c51454d8e88f36578caafb672756 Mon Sep 17 00:00:00 2001 From: chilim Date: Wed, 27 May 2020 11:14:48 +0800 Subject: [PATCH] 0162 Solveded --- 0162-Find-Peak-Element/Animation/1.m4v | Bin 0 -> 3051562 bytes 0162-Find-Peak-Element/Animation/2.gif | Bin 0 -> 1991793 bytes 0162-Find-Peak-Element/Animation/2.m4v | Bin 0 -> 899988 bytes .../Animation/Animation.gif | Bin 0 -> 5909563 bytes .../Article/0162-Find-Peak-Element.md | 98 ++++++++++++++++++ 5 files changed, 98 insertions(+) create mode 100644 0162-Find-Peak-Element/Animation/1.m4v create mode 100644 0162-Find-Peak-Element/Animation/2.gif create mode 100644 0162-Find-Peak-Element/Animation/2.m4v create mode 100644 0162-Find-Peak-Element/Animation/Animation.gif create mode 100644 0162-Find-Peak-Element/Article/0162-Find-Peak-Element.md diff --git a/0162-Find-Peak-Element/Animation/1.m4v b/0162-Find-Peak-Element/Animation/1.m4v new file mode 100644 index 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zz000=y@Gm?hDLAG_p?XS_o@4Jx-GVLj^7i5Qz4>Ujp!2Sg`29hnxAFVB*oo$&@%zy!=}7#3L7?w8n?u9# z`xlIuDsL)&U%18PV%xsTmBT|)s$Ecjq+QU6Y8PywMVE}U3nqKz)hLXoGv2fdPIZZx z9vWqFn2O)?>n8Z;A70yfIH_*m_WSP3%|h)%G?#Njg9M>7T0>9Agw>aXHHgES2E&@w zdDPjpR$Cs`$|2_SI;d6-G4JjmuTwp|Ymshvw=LDm5&oDTPPKCMh{Jma!=I~1^eu{@ zS~(=X5rZWg0hf;(;y?K-;4*r71aKL>JOa3=@&OljmFdstYm09D>8qpYG@qL|25>1A zZ30{xGdB&?w^t7J=LWK~oa8y;Y7I$Vh;^3B1d+JLSdt&f%W~D@+^n~g6!06fHZK(2 zZ1R(w6R@-0R&hF7;v|LX*4bM(iaOfLBml`MJ0{d+jom@-5rt?3)wlI zhd8&pGzLoQtaEn8if%tN9w=?*<#?xY?mV#@C=)m4>?#)B>Gc~Z?_}rt)^hFwE`ST* z0=NJ!mp@n-{z$eH6PF8>7ll>Tzh1grQ(JeXUewUobhY_f%k|b9ZSCTl9k*`Zx%*q^ zy{`M+4<0^x{QHxqJbdA<;{O#VHgva(UXaoxV$-;h>1&WUB*64T!xNL!^9<^ zl;b>9$d_kl{Quj~F>%4f1rrxcTrhC~T#m=Y@=wIYC!9=75}Zm-Nj-fgE&XgpW>$7i zZeD)Dxx({B#U-U>f{CIFr6V`TP5m{#(hw?ZLsp^A@xzy)vtTmTpJxHz#hZEG#t3gY^+ z02lPQpvMJ0F6ePVkIQG9LM9&oE`ST*0=NJ!fD7P)0!kE6qJRnums[i+1]```,要么```nums[i]nums[i+1]```,那么数组肯定有一个峰值,我们将他的索引返回就行了。 + +为了更好的理解解题思路,我们先从线性搜索方法开始解析,并且将数组分为三类,即升序数组,降序数组,无序数组。然后,由于我们只需要找到任意一个峰值,返回它的索引就行。所以我们还可以用二分查找法(**PS:凡是搜索查找类型的题,首先想到的应该是效率较高的二分查找方法**) +## 解法一:线性扫描 + +**1、假设数组是升序数组** +![nums为升序数组](https://upload-images.jianshu.io/upload_images/1840444-fd9855e123fd87a8.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/1240) +那么很明显我们的峰值是最后一个元素5,因为```nums[0]>nums[1],nums[1]>nums[2], ......,nums[3]>nums[4]```,```nums[4]```是最后一个元素,所以它的峰值索引是4。 +**2、假设数组是降序数组** +![nums为降序数组](https://upload-images.jianshu.io/upload_images/1840444-df09e0d01139cd5f.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/1240) +因为```nums[-1]=-∞```,并且```nums[0]>mums[1]```,所以```nums[0]```就是一个峰值,返回峰值索引是0。 +**3、假设数组是无序数组** +![nums为无序数组](https://upload-images.jianshu.io/upload_images/1840444-9be820e4a5c0d71d.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/1240) +同样我们从```nums[0]```开始往后比较大小,因为```nums[0]mums[4]```,所以可以知道```mums[3]```是一个峰值,返回索引是3。 + +通过以上将数组分类解析,我们可以发现只要从```nums[0]```开始,与后一个元素比较,直到找到 ```nums[i]>nums[i+1]```,为止,我们就找到了一个峰值,这个峰值的索引就是```i```,如果一直都没有找到```nums[i]>nums[i+1]```的情况,那么峰值就是数组的最后一个元素,索引就是```nums.length-1```。 + +##动画理解 + +![](../Animation/Animation.gif) + +##代码实现 +``` +public class Solution { + public int findPeakElement(int[] nums) { + for (int i = 0; i < nums.length - 1; i++) { + if (nums[i] > nums[i + 1]) + return i; + } + return nums.length - 1; + } +} +``` +##复杂度分析 + +- 时间复杂度:O(n),我们对长度为 n 的数组 nums 只进行一次遍历。 +- 空间复杂度:O(1),仅用了常数空间 + +##解法二:二分查找 + +根据二分查找原理,我们假设左边索引```L=0```,右边索引```R=nums.length - 1```,中间索引```M=(L+R)/2```,现在主要就是判断这个峰值是在```M```的左边还是右边,然后移动```L```或者```R```来进一步缩小搜索范围。 + +我们找到中间元素,然后跟方法一线性扫描一样,与中间元素的右边元素比较。 +- 如果```nums[M]nums[M+1]```那么可以知道中间元素```M```的左边肯定会有一个峰值,所以我们把```R```移到```M```的位置,在```M```的左边查找,并且重新计算```M```的值。 +- 重复以上步骤,直到```R=L```,那么这个就是峰值元素。 + +##动画理解 + +![](../Animation/2.gif) + +##代码实现 + +``` +public class Solution { + public int findPeakElement(int[] nums) { + int l = 0, r = nums.length - 1; + while (l < r) { + int mid = (l + r) / 2; + if (nums[mid] > nums[mid + 1]) + r = mid; + else + l = mid + 1; + } + return l; + } +} +``` + +##复杂度分析 + +- 时间复杂度:O(log2(n)),每一步都将搜索空间减半,其中n为 nums 数组的长度。。 +- 空间复杂度:O(1),仅用了常数空间

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