title: How can we assure that a Bitonic sequence will be formed from one longest increasing subsequence and one longest decreasing subsequence?
body: <p>For example we have an <code>array[]={1,3,2,7,4,6,8,9}</code>.</p>
  
  <p>longest increasing subsequence of this <code>array[]={1,3,4,6,8,9}</code> and its length=6.</p>
  
  <p>longest decreasing subsequence of this <code>array[]={3,2}</code> and its length=2.</p>
  
  <p>Then is Bitonic subsequence of this <code>array[]={1,3,4,6,8,9}</code>? if Yes then its length=6.But length of Bitonic subsequence =length of lis + length of lds -1,
  here they are not equal.</p>
  
  <p>if no how can you prove that length of bitonic subsequence=length of lis+length of lds-1</p>
  
  <p>Correct me if I am wrong.
  Thank you.</p>