从最大三角形周长看动态规划

Posted 2021-04-18 TypeOVOcode

题目描述：给定一个数组，从中找出三个数，使其能够构成三角形并且三角形的周长最大。

public class triangle { private int getpos(int arr[],int low,int high){ int pivotkey=arr[low]; while(low<high){ while(low<high&&arr[high]>=pivotkey){ --high; } arr[low]=arr[high]; while(low<high&&arr[low]<=pivotkey){ ++low; } arr[high]=arr[low]; } arr[low]=pivotkey; return low; } public void quicksort(int arr[],int low,int high){ if(low<high){ int pivot=getpos(arr,low,high); quicksort(arr,low,pivot-1); quicksort(arr,pivot+1,high); } } public int getangle(int arr[]){ int ans=0; int len=arr.length; quicksort(arr,0,len-1); for(int i=len-3;i>=0;i--){ if(arr[i]+arr[i+1]>arr[i+2]){ ans=(arr[i]+arr[i+1]+arr[i+2]); break; } } return ans; }
 public static void main(String[] args) { triangle tri=new triangle(); int[] arr={1,89,77,3,4,5,12,10,9}; int ans=tri.getangle(arr); for(int i=0;i<arr.length;i++){ System.out.print(arr[i]+" "); } System.out.println(ans); }}
//"C:\Program Files (x86)\Java\jdk1.8.0_121\bin\java.exe" "-javaagent:D:\Inteljj\IntelliJ IDEA 2018.1.6\lib\idea_rt.jar=39694:D:\Inteljj\IntelliJ IDEA 2018.1.6\bin" -Dfile.encoding=UTF-8 -classpath "C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\charsets.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\deploy.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\ext\access-bridge-32.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\ext\cldrdata.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\ext\dnsns.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\ext\jaccess.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\ext\jfxrt.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\ext\localedata.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\ext\nashorn.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\ext\sunec.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\ext\sunjce_provider.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\ext\sunmscapi.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\ext\sunpkcs11.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\ext\zipfs.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\javaws.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\jce.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\jfr.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\jfxswt.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\jsse.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\management-agent.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\plugin.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\resources.jar;C:\Program Files (x86)\Java\jdk1.8.0_121\jre\lib\rt.jar;D:\triangle\out\production\triangle" triangle//1 3 4 5 9 10 12 77 89 31
//Process finished with exit code 0

按照题目要求，解法一：最先想到的无非是暴力求解，设立三个变量i,j,k,依次对比，时间复杂度O(n^3);

解法二：先排序，然后从后往前遍历，若arr[n-3]+arr[n-2]>arr[n-1]不满足条件，则arr[n-4]+arr[n-3]>arr[n-1]一定不满足。故此，按照从后往前的顺序，若arr[n-3]+arr[n-2]>arr[n-1]一旦满足，即为最大周长的三角形（动态规划）。时间复杂度O(nlogn+n)=o(nlogn)。