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Longest subsequence with no 0 after 1
  • Last Updated : 24 May, 2021

Given a binary array, find the length of the longest subsequence such that there is no 0 after a 1.

Examples:  

Input : 1 1 0 1
Output : 3
Explanation : 
If we remove 0 from the array, then no
zero comes right after one (satisfying 
the condition) and the maximum game 
left are 3 (i.e. 1 1 1)

Input : 0
Output : 1
Explanation : 
Since he wants to save maximum game in
the array. He doesn't remove any game. 

Let’s find out how many zeros will be in this sequence and then take all ones which come after the last zero. On each step take the next zero from the beginning of the sequence and count the ones after it. Update answer with the maximum value.
You can pre-calculate the number of ones on the suffix. 
E.g. 0 1 0 0 1 1 1
After calculating the suffix, the array becomes : 
0 4 0 0 3 2 1
Move from start to end and each time zero is found in the array increment numberofzeros by 1. If the array[index] is not zero then res = max(res, numberofzeros + value of the array at that index). 
And then after the loop: res = max(res, numberofzeros)  

C++




// CPP program to find longest subsequence
// such that there is no 0 after 1.
#include <bits/stdc++.h>
using namespace std;
 
int maxSubseq(int vec[], int n) {   
         
    // Store the count of number of ones
    // from right to left in the array
    int suffix = 0;
    for (int i = n - 1; i >= 0; i--)
    {
        if (vec[i] == 1)
        {
            suffix++;
            vec[i] = suffix;
        }
    }
     
    // Traverse from left to right, keep count
    // of 0s and for every 0, check number of
    // 1s after it. Update the result if needed.
    int res = 0;
    int zero = 0;   
    for (int i = 0; i < n; i++)
    {
        if (vec[i] == 0)
            zero++;
     
        // Checking the maximum size
        if (vec[i] > 0)
            res = max(res, zero + vec[i]);
    }
     
    // Checking the maximum size
    return max(res, zero);
}
 
// Driver Code
int main()
{
    int input[] = { 0, 1, 0, 0, 1, 0 };
    int n = sizeof(input) / sizeof(input[0]);   
    cout << maxSubseq(input, n);
    return 0;
}

Java




// java program to find longest subsequence
// such that there is no 0 after 1.
import java.io.*;
 
public class GFG {
 
    static int maxSubseq(int []vec, int n)
    {
             
        // Store the count of number of
        // ones from right to left in
        // the array
        int suffix = 0;
         
        for (int i = n - 1; i >= 0; i--)
        {
            if (vec[i] == 1)
            {
                suffix++;
                vec[i] = suffix;
            }
        }
         
        // Traverse from left to right, keep
        // count of 0s and for every 0, check
        // number of 1s after it. Update the
        // result if needed.
        int res = 0;
        int zero = 0;
         
        for (int i = 0; i < n; i++)
        {
            if (vec[i] == 0)
                zero++;
         
            // Checking the maximum size
            if (vec[i] > 0)
                res = Math.max(res, zero + vec[i]);
        }
         
        // Checking the maximum size
        return Math.max(res, zero);
    }
     
    // Driver Code
    static public void main (String[] args)
    {
         
        int []input = { 0, 1, 0, 0, 1, 0 };
        int n = input.length;
         
        System.out.println(maxSubseq(input, n));
    }
}
 
// This code is contributed by vt_m.

Python3




# Python 3 program to find longest subsequence
# such that there is no 0 after 1.
 
def maxSubseq(vec, n):
    # Store the count of number of ones
    # from right to left in the array
    suffix = 0
    i = n-1
    while(i >= 0):
        if (vec[i] == 1):
            suffix += 1
            vec[i] = suffix
        i -= 1
             
    # Traverse from left to right, keep count
    # of 0s and for every 0, check number of
    # 1s after it. Update the result if needed.
    res = 0
    zero = 0
    for i in range(0,n,1):
        if (vec[i] == 0):
            zero += 1
     
        # Checking the maximum size
        if (vec[i] > 0):
            res = max(res, zero + vec[i])
     
    # Checking the maximum size
    return max(res, zero)
 
# Driver code
 if __name__ == '__main__':
    input = [0, 1, 0, 0, 1, 0]
    n = len(input)
    print(maxSubseq(input, n))
 
# This code is contributed by
# Surendra_Gangwar

C#




// C# program to find longest subsequence
// such that there is no 0 after 1.
using System;
 
public class GFG {
 
    static int maxSubseq(int []vec, int n)
    {
             
        // Store the count of number of
        // ones from right to left in
        // the array
        int suffix = 0;
         
        for (int i = n - 1; i >= 0; i--)
        {
            if (vec[i] == 1)
            {
                suffix++;
                vec[i] = suffix;
            }
        }
         
        // Traverse from left to right, keep
        // count of 0s and for every 0, check
        // number of 1s after it. Update the
        // result if needed.
        int res = 0;
        int zero = 0;
         
        for (int i = 0; i < n; i++)
        {
            if (vec[i] == 0)
                zero++;
         
            // Checking the maximum size
            if (vec[i] > 0)
                res = Math.Max(res, zero + vec[i]);
        }
         
        // Checking the maximum size
        return Math.Max(res, zero);
    }
     
    // Driver Code
 
    static public void Main ()
    {
         
        int []input = { 0, 1, 0, 0, 1, 0 };
        int n = input.Length;
         
        Console.WriteLine(maxSubseq(input, n));
    }
}
 
// This code is contributed by vt_m.

PHP




<?php
// PHP program to find longest
// subsequence such that there
// is no 0 after 1.
 
function maxSubseq($vec, $n)
{
         
    // Store the count of
    // number of ones from
    // right to left in
    // the array
    $suffix = 0;
    for ($i = $n - 1;
         $i >= 0; $i--)
    {
        if ($vec[$i] == 1)
        {
            $suffix++;
            $vec[$i] = $suffix;
        }
    }
     
    // Traverse from left to
    // right, keep count of
    // 0s and for every 0,
    // check number of 1s after
    // it. Update the result if
    // needed.
    $res = 0;
    $zero = 0;
    for ($i = 0; $i < $n; $i++)
    {
        if ($vec[$i] == 0)
            $zero++;
     
        // Checking the
        // maximum size
        if ($vec[$i] > 0)
            $res = max($res, $zero +
                             $vec[$i]);
    }
     
    // Checking the
    // maximum size
    return max($res, $zero);
}
 
// Driver Code
$input = array(0, 1, 0, 0, 1, 0);
$n = count($input);
echo maxSubseq($input, $n);
 
// This code is contributed
// by anuj_67.
?>

Javascript




<script>
    // Javascript program to find longest subsequence
    // such that there is no 0 after 1.
     
    function maxSubseq(vec, n)
    {
               
        // Store the count of number of
        // ones from right to left in
        // the array
        let suffix = 0;
           
        for (let i = n - 1; i >= 0; i--)
        {
            if (vec[i] == 1)
            {
                suffix++;
                vec[i] = suffix;
            }
        }
           
        // Traverse from left to right, keep
        // count of 0s and for every 0, check
        // number of 1s after it. Update the
        // result if needed.
        let res = 0;
        let zero = 0;
           
        for (let i = 0; i < n; i++)
        {
            if (vec[i] == 0)
                zero++;
           
            // Checking the maximum size
            if (vec[i] > 0)
                res = Math.max(res, zero + vec[i]);
        }
           
        // Checking the maximum size
        return Math.max(res, zero);
    }
     
    let input = [ 0, 1, 0, 0, 1, 0 ];
    let n = input.length;
 
    document.write(maxSubseq(input, n));
         
</script>

Output:  

4

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