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Maximum elements which can be crossed using given units of a and b in C++
Given a binary array arr[] and two variables a and b with some initial values. To cross an element in the array arr[] there are two ways −
If arr[i] == 1, then 1 unit can be used from a, with no change in b. If 1 unit is used from b, then a increases by 1 unit. (Note that the value of a cannot be incremented above its original value.)
If arr[i] == 0, then 1 unit can be used from a or b.
Let’s now understand what we have to do using an example −
Input
arr[] = {0, 0, 0, 1, 1}, a = 2, b = 2Output
5
Explanation
To cross 1st element, use 1 unit from a (a = 1, b = 2).
To cross 2nd element, use 1 unit from a (a = 0, b = 2).
To cross 3rd element, use 1 unit from b (a = 0, b = 1).
To cross 4th element, use 1 unit from b which increases a by 1 unit (a = 1, b = 0).
To cross 5th element, use 1 unit from a (a = 0, b = 0).
Therefore, we crossed all elements and output becomes 5.
Input
arr[] = {1, 1, 1, 0, 1}, a = 1, b = 2Output
4
Approach used in the below program as follows
In function MaxElements() initialize variables Oa = 0 and max = 0, both of type int to store the original value of a and the final answer respectively.
Loop from i = 0 till i<size to check for every element in the array.
First Check if both a and b are equal to zero, then break out of the loop.
Else check if (a == 0) and if so, then check if the current element = 1 and subtract 1 from b to cross that element and put a = min(Oa, a + 1) so that a does not exceed its original value.
Else simply subtract 1 from b without affecting a.
Else check if (b == 0) and if so, then simply subtract 1 from a.
Else check if (arr[i] == 1 && a < Oa) and if so, then check if the current element = 1 and subtract 1 from b to cross that element and put a = min(Oa, a + 1).
Else simply subtract 1 from a and increment max.
Outside the loop, return max.
Example
#include <bits/stdc++.h>
using namespace std;
int MaxElements(int arr[], int a, int b, int size){
// Oa will have original value of a
int Oa = a;
int max = 0;
// Iterate in the binary array
for (int i = 0; i < size; i++){
// Break loop if a and b, both are = 0
if (a == 0 && b == 0)
break;
// If a is not present, use b
else if (a == 0){
//increase a by 1 if arr[i] == 1
if (arr[i] == 1){
b -= 1;
//Checking if original value is not exceeded
a = min(Oa, a + 1);
}
else
b -= 1;
}
// If b is not present, use a
else if (b == 0)
a--;
// if arr[i] == 1,use b
else if (arr[i] == 1 && a < Oa){
b -= 1;
a = min(Oa, a + 1);
}
else
a--;
max++;
}
return max;
}
//main function
int main(){
int arr[] = { 1, 1, 1, 0, 1 };
int size = sizeof(arr) / sizeof(arr[0]);
int a = 1;
int b = 2;
cout << MaxElements(arr, a, b, size);
return 0;
}Output
4
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