Given an array arr[0.....n-1] containing n positive integers, find the length of the longest bitonic subsequence.
A subsequence of arr[] is called Bitonic if it is first increasing, then decreasing.
Analysis:
This problem is a variation of the standard Longest Increasing Subsequence(LIS) problem. In the standard LIS
problem, we use dynamic programming and create a 1D array lis[i], lis[i] is the length of the longest increasing subsequence
that ends with arr[i].
In this problem, we construct two arrays lis[i] and ids[i] using dynamic programming.
lis[i] stores the length of the longest increasing subsequence ending with arr[i];
lds[i] stores the length of the longest decreasing subsequence starting from arr[i];
Finally, we need to return the max value of lis[i] + lds[i] - 1, where i is from 0 to n - 1.
1 public class Solution {
2 public int longestBitonicSubsequence(int[] arr){
3 if(arr == null || arr.length == 0){
4 return 0;
5 }
6 int[] lis = new int[arr.length];
7 int[] lds = new int[arr.length];
8 for(int i = 0; i < arr.length; i++){
9 lis[i] = 1;
10 lds[i] = 1;
11 }
12 for(int i = 0; i < arr.length; i++){
13 for(int j = 0; j < i; j++){
14 if(arr[i] > arr[j] && lis[i] < lis[j] + 1){
15 lis[i] = lis[j] + 1;
16 }
17 }
18 }
19 for(int i = arr.length - 1; i >= 0; i--){
20 for(int j = arr.length - 1; j > i; j--){
21 if(arr[i] > arr[j] && lds[i] < lds[j] + 1){
22 lds[i] = lds[j] + 1;
23 }
24 }
25 }
26 int max = 0;
27 for(int i = 0; i < arr.length; i++){
28 if(lis[i] + lds[i] - 1 > max){
29 max = lis[i] + lds[i] - 1;
30 }
31 }
32 return max;
33 }
34 }
Related Problems
Longest Increasing Subsequence