找关系在数组中

You given an array:
3, 2, 1, 6, 5, 4, 9, 8, 7
you have to find a 3 tuple which has property a < b < c, also a is before b, b is before c in array.
Answer can have multiple tuples, you have to find any one.
In this array, answer will be 3, 6, 9

answer：

O(n) time algorithm: Use the same classic algorithm for Longest Increasing Subsequence, breaking when you find a subsequence of length 3.

-Using Patience Sort --- O(n) OR
-Using Dynamic Programming --- O(n*n)

make a binary search tree from a given array
try to get right side of node which full fill this condition

package com.zhuyu_deng.test;public class Test{static int a[] = new int[] { 3, 2, 1, 6, 5, 4, 9, 8, 7 };static int c[] = new int[a.length];public static void main(String args[]){int b[] = new int[a.length];for (int i = 0; i < b.length; ++i)b[i] = 1;for (int i = 1; i < a.length; ++i){int maxLen = 1;for (int j = 0; j < i; ++j){if (a[j] < a[i] && b[j] + 1 > maxLen){maxLen = b[j] + 1;b[i] = maxLen;c[i] = j;}if (maxLen >= 3)break;}if (maxLen >= 3){print(i);System.out.println();break;}}}private static void print(int x){if (x != 0){print(c[x]);System.out.print(a[x] + " ");} else{System.out.print(a[x] + " ");}}}

package com.zhuyu_deng.test;import java.util.ArrayList;import java.util.List;public class Test{static int[] array = new int[] { 3, 2, 1, 6, 5, 4, 9, 8, 7 };static String finalString = "";public static void main(String[] args){List<String> touples = new ArrayList<String>();for (int i = 0; i < array.length; i++){getAllTouples(touples, i, 0);}System.out.println(touples);}public static List<String> getAllTouples(List<String> touples, int index, Integer pos){int pivotElement = array[index];for (int i = index + 1; i < array.length; i++){if (pivotElement < array[i] && pos < i){finalString = finalString + pivotElement;if (finalString.length() == 2){finalString = finalString + array[i];touples.add(finalString);finalString = finalString.substring(0, finalString.length() - 2);pos = i;i = index;} else{getAllTouples(touples, i, pos);finalString = finalString.substring(0, finalString.length() - 1);}}}return touples;}}