• Skip to primary navigation
  • Skip to content
  • Skip to primary sidebar
  • Skip to secondary sidebar

GoHired

Interview Questions asked in Google, Microsoft, Amazon

Join WeekEnd Online Batch from 4-April-2020 on How to Crack Coding Interview in Just 10 Weeks : Fees just 20,000 INR

  • Home
  • Best Java Books
  • Algorithm
  • Internship
  • Certificates
  • About Us
  • Contact Us
  • Privacy Policy
  • Array
  • Stack
  • Queue
  • LinkedList
  • DP
  • Strings
  • Tree
  • Mathametical
  • Puzzles
  • Graph

Longest Increasing Subsequence

December 22, 2014 by Dhaval Dave

The longest Increasing Subsequence (LIS) problem is to find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order.For example, length of LIS for { 3,2,6,4,5,1 } is 2 and LIS is {2,4,5}.

Method 1) Brute Force Approch

for (i=N; i>0 ; –i){
   Find a SubSequence of length i
   if any increasing subsequence
       Break;
}

But finding all subsequence of length i will give Time Complexity in Exponential.
as all subsequences will be N! / i! * (N-i)!

Lets think directly in DP way…

Method 2) Dynamic Programming way.

Take Example D := { 3, 2 , 6 , 4 , 5 , 1 }    We are defining vector L of vector <Numbers> such that
L[i] = A vector, Longest Increasing sequence of D that ends with D[i].

L[0] = 3.
L[1] = 2 ( because 3 > 2, and we need to find increasing sub sequence )
L[2] = 2,6
L[3] = 2,4
L[4] = 2,4,5
L[5] = 1

say L[2] = 2,6 is ‘2’ + ‘6’  where 2 is so far found max LIS, and ‘6’ is current element

So formula
L[i] is  maximum of all L[j] where j<i and D[j]<D[i] + ‘D[i]’

L[i] = MAX(L[j], where j<i, D[j]<D[i]) + D[i]

So now We have working code to print all Increasing SubSequence
Edit it your way to find larget increasing subsequence

Code :

#include <iostream>
using namespace std;
#include <iostream>
#include <vector>


void prt(vector<int>& arr, string msg = “”) {
cout << msg << ” “;
for  (auto i: arr) {
cout << i << ” “;
}
cout << endl;
}


void calc_LIS(vector<int>& D) {
vector< vector<int> > L(D.size());  // The longest increasing subsequence ends with D[i]

   L[0].push_back(D[0]);

for (int i=1; i<D.size(); i++) {
for(int j=0; j<i; j++) {
if ( (D[j] < D[i]) && ( L[i].size() < L[j].size() ) ) {
L[i] = L[j];  
}         
}
      L[i].push_back(D[i]);
}

for (auto x: L) {
prt(x);
}

}

int main() {
int a[] = {3, 2, 6, 4, 5, 1};
vector<int> arr(a, a + sizeof(a)/sizeof(a[0]));



//prt(arr, “Data In:”);
calc_LIS(arr);

return 0;
}

Working Code at : http://ideone.com/lOrktE

Similar Articles

Filed Under: Amazon Interview Question, Flipkart Interview Questions, Hacker Earth Questions, Interview Questions, Microsoft Interview Questions, problem Tagged With: Array, Dynamic Programming

Reader Interactions

Primary Sidebar

Join WeekEnd Online/Offline Batch from 4-April-2020 on How to Crack Coding Interview in Just 10 Weeks : Fees just 20,000 INR

Join WeekEnd Online/Offline Batch from 4-April-2020

WhatsApp us

Secondary Sidebar

Custom Search

  • How I cracked AMAZON
  • LeetCode
  • Adobe
  • Amazon
  • Facebook
  • Microsoft
  • Hacker Earth
  • CSE Interview

Top Rated Questions

N teams are participating. each team plays twice with all other teams. Some of them will go to the semi final. Find Minimum and Maximum number of matches that a team has to win to qualify for finals ?

Find if two rectangles overlap

Leetcode: Merge Intervals

Regular Expression Matching

ADOBE Aptitude C Language Test

Length of the longest substring without repeating characters

Check if an array has duplicate numbers in O(n) time and O(1) space

BlueStone E-commerce Interview Experience

Convert number to words java

C Program for TAIL command of UNIX

In Given LinkedList Divide LL in N Sub parts and delete first K nodes of each part

building with N steps, we can take 1,2,3 steps calculate number of ways to reach at top of building

Maximum of all subarrays of size k

Printing each word reverse in string

Add Sub Multiply very large number stored as string

Find position of the only set bit

Generate largest number arranging a no. of given non negative integer numbers

Find Pythagorean Triplets in an array in O(N)

Python Array String

DFS (Depth First Search)

Find min element in Sorted Rotated Array (Without Duplicates)

Search element in a matrix with all rows and columns in sorted order

25 horses 5 tracks Find 3 fastest puzzle

N Petrol bunks or City arranged in circle. You have Fuel and distance between petrol bunks. Is it possible to find starting point so that we can travel all Petrol Bunks

Password Predictor

Edit Distance ( Dynamic Programming )

Find Percentage of Words matching in Two Strings

Adobe Interview Questions 8 month Exp

SAP Hiring Off-Campus General Aptitude

Level order traversal in Spiral form

Copyright © 2025 · Genesis Framework · WordPress · Log in