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Maximum elements which can be crossed using given units of a and b

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  • Last Updated : 14 Jun, 2022
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Given a binary array of N elements and two initial values a and b. We can cross the i-th element if: 
 

  1. If a[i] == 0, then we can use 1 unit from either of b or a to cross the i-th element.
  2. If a[i] == 1, then if we use 1 unit from b, a increases by 1 unit. In case 1 unit is used from a, then there is no increase in either of a or b.

The task is to find the maximum number of elements that can be crossed using a and b units. 
Note: When we increase a by 1 at any step, it cannot exceed the original value of a. 
Examples: 
 

Input: arr[] = {0, 1, 0, 1, 0}, a = 1, b = 2; 
Output:
Use 1 unit from a to cross 1st element. (a = 0 and b = 2) 
Use 1 unit from b to cross 2nd element. (a = 1 and b = 1) 
Use 1 unit from a to cross 3rd element. (a = 0 and b = 1) 
Use 1 unit from b to cross 4th element. (a = 1 and b = 0) 
Use 1 unit from a to cross 5th element. (a = 0 and b = 0) 
Input: a[] = {1, 0, 0, 1, 0, 1}, a = 1, b = 2 
Use 1 unit from b to cross first element. (a = 1 and b = 1) 
Use 1 unit from b to cross second element. (a = 1 and b = 0) 
Use 1 unit from a to cross third element. (a = 0 and b = 0) 
Output:

 

Approach: Iterate in the array element and perform the following steps: 
 

  • Break if we do not have either of b or a to pass the element.
  • Else, use b if there is no a left, and increase a by 1 if arr[i] == 1.
  • Else, use a if there is no b left.
  • Else, use b if arr[i]==1 and increase a by 1 till the maximum of the original a.
  • Else, simply use 1 unit from a.

Below is the implementation of the above approach: 
 

C++




// C++ program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the number
// of elements crossed
int findElementsCrossed(int arr[], int a, int b, int n)
{
    // Keep a copy of a
    int aa = a;
    int ans = 0;
 
    // Iterate in the binary array
    for (int i = 0; i < n; i++) {
 
        // If no a and b left to use
        if (a == 0 && b == 0)
            break;
 
        // If there is no a
        else if (a == 0) {
 
            // use b and increase a by 1
            // if arr[i] is 1
            if (arr[i] == 1) {
                b -= 1;
                a = min(aa, a + 1);
            }
 
            // simply use b
            else
                b -= 1;
        }
 
        // Use a if theres no b
        else if (b == 0)
            a--;
 
        // Increase a and use b if arr[i] == 1
        else if (arr[i] == 1 && a < aa) {
            b -= 1;
            a = min(aa, a + 1);
        }
 
        // Use a
        else
            a--;
        ans++;
    }
 
    return ans;
}
 
// Driver code
int main()
{
    int arr[] = { 1, 0, 0, 1, 0, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int a = 1;
    int b = 2;
    cout << findElementsCrossed(arr, a, b, n);
 
    return 0;
}

Java




// Java program to implement
// the above approach
import java.util.*;
 
class GFG
{
 
// Function to find the number
// of elements crossed
static int findElementsCrossed(int arr[],
                        int a, int b, int n)
{
    // Keep a copy of a
    int aa = a;
    int ans = 0;
 
    // Iterate in the binary array
    for (int i = 0; i < n; i++)
    {
 
        // If no a and b left to use
        if (a == 0 && b == 0)
            break;
 
        // If there is no a
        else if (a == 0)
        {
 
            // use b and increase a by 1
            // if arr[i] is 1
            if (arr[i] == 1)
            {
                b -= 1;
                a = Math.min(aa, a + 1);
            }
 
            // simply use b
            else
                b -= 1;
        }
 
        // Use a if theres no b
        else if (b == 0)
            a--;
 
        // Increase a and use b if arr[i] == 1
        else if (arr[i] == 1 && a < aa)
        {
            b -= 1;
            a = Math.min(aa, a + 1);
        }
 
        // Use a
        else
            a--;
        ans++;
    }
 
    return ans;
}
 
// Driver code
public static void main(String args[])
{
    int arr[] = { 1, 0, 0, 1, 0, 1 };
    int n = arr.length;
    int a = 1;
    int b = 2;
    System.out.println(findElementsCrossed(arr, a, b, n));
 
}
}
 
// This code is contributed by
// Surendra_Gangwar

Python3




# Python3 program to implement
# the above approach
 
# Function to find the number
# of elements crossed
def findElementsCrossed(arr, a, b, n):
 
    # Keep a copy of a
    aa = a
    ans = 0
 
    # Iterate in the binary array
    for i in range(n):
 
        # If no a and b left to use
        if (a == 0 and b == 0):
            break
 
        # If there is no a
        elif (a == 0):
 
            # use b and increase a by 1
            # if arr[i] is 1
            if (arr[i] == 1):
                b -= 1
                a = min(aa, a + 1)
             
            # simply use b
            else:
                b -= 1
         
        # Use a if theres no b
        elif (b == 0):
            a -= 1
 
        # Increase a and use b if arr[i] == 1
        elif (arr[i] == 1 and a < aa):
            b -= 1
            a = min(aa, a + 1)
         
        # Use a
        else:
            a -= 1
        ans += 1
     
    return ans
 
# Driver code
arr = [1, 0, 0, 1, 0, 1]
n = len(arr)
a = 1
b = 2
print(findElementsCrossed(arr, a, b, n))
 
# This code is contributed by mohit kumar

C#




// C# implementation of the above approach
using System;
 
class GFG
{
 
// Function to find the number
// of elements crossed
static int findElementsCrossed(int []arr,
                        int a, int b, int n)
{
    // Keep a copy of a
    int aa = a;
    int ans = 0;
 
    // Iterate in the binary array
    for (int i = 0; i < n; i++)
    {
 
        // If no a and b left to use
        if (a == 0 && b == 0)
            break;
 
        // If there is no a
        else if (a == 0)
        {
 
            // use b and increase a by 1
            // if arr[i] is 1
            if (arr[i] == 1)
            {
                b -= 1;
                a = Math.Min(aa, a + 1);
            }
 
            // simply use b
            else
                b -= 1;
        }
 
        // Use a if theres no b
        else if (b == 0)
            a--;
 
        // Increase a and use b if arr[i] == 1
        else if (arr[i] == 1 && a < aa)
        {
            b -= 1;
            a = Math.Min(aa, a + 1);
        }
 
        // Use a
        else
            a--;
        ans++;
    }
 
    return ans;
}
 
// Driver code
public static void Main(String []args)
{
    int []arr = { 1, 0, 0, 1, 0, 1 };
    int n = arr.Length;
    int a = 1;
    int b = 2;
    Console.WriteLine(findElementsCrossed(arr, a, b, n));
 
}
}
 
// This code contributed by Rajput-Ji

PHP




<?php
// PHP program to implement
// the above approach
 
// Function to find the number
// of elements crossed
function findElementsCrossed($arr, $a, $b, $n)
{
    // Keep a copy of a
    $aa = $a;
    $ans = 0;
 
    // Iterate in the binary array
    for ($i = 0; $i < $n; $i++)
    {
 
        // If no a and b left to use
        if ($a == 0 && $b == 0)
            break;
 
        // If there is no a
        else if ($a == 0)
        {
 
            // use b and increase a by 1
            // if arr[i] is 1
            if ($arr[$i] == 1)
            {
                $b -= 1;
                $a = min($aa, $a + 1);
            }
 
            // simply use b
            else
                $b -= 1;
        }
 
        // Use a if theres no b
        else if ($b == 0)
            $a--;
 
        // Increase a and use b if arr[i] == 1
        else if ($arr[$i] == 1 && $a < $aa)
        {
            $b -= 1;
            $a = min($aa, $a + 1);
        }
 
        // Use a
        else
            $a--;
        $ans++;
    }
 
    return $ans;
}
 
// Driver code
$arr = array(1, 0, 0, 1, 0, 1);
$n = sizeof($arr);
$a = 1;
$b = 2;
echo findElementsCrossed($arr, $a, $b, $n);
 
// This code is contributed by Akanksha Rai
?>

Javascript




<script>
// javascript program to implement
// the above approach
 
    // Function to find the number
    // of elements crossed
    function findElementsCrossed(arr , a , b , n) {
        // Keep a copy of a
        var aa = a;
        var ans = 0;
 
        // Iterate in the binary array
        for (i = 0; i < n; i++) {
 
            // If no a and b left to use
            if (a == 0 && b == 0)
                break;
 
            // If there is no a
            else if (a == 0) {
 
                // use b and increase a by 1
                // if arr[i] is 1
                if (arr[i] == 1) {
                    b -= 1;
                    a = Math.min(aa, a + 1);
                }
 
                // simply use b
                else
                    b -= 1;
            }
 
            // Use a if theres no b
            else if (b == 0)
                a--;
 
            // Increase a and use b if arr[i] == 1
            else if (arr[i] == 1 && a < aa) {
                b -= 1;
                a = Math.min(aa, a + 1);
            }
 
            // Use a
            else
                a--;
            ans++;
        }
 
        return ans;
    }
 
    // Driver code
     
        var arr = [ 1, 0, 0, 1, 0, 1 ];
        var n = arr.length;
        var a = 1;
        var b = 2;
        document.write(findElementsCrossed(arr, a, b, n));
 
 
// This code contributed by umadevi9616
</script>

Output: 

3

 

Time Complexity: O(n), to iterate over the array where n is the size of the array
Auxiliary Space: O(1)


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