In C, the maximum amount that can be withdrawn in two steps

We have two lockers, called L1 and L2, which contain some coins. L1 has A coins and L2 has B coins. We must remove coins from the locker to maximize the amount withdrawn. Each time a coin is removed from any locker, it is replaced with the previous amount minus 1 coin. If we take A coins from L1, then it will be replaced by A-1 coins, and if we take B coins from L2, then it will be replaced by B-1 coins. The task is to maximize the amount withdrawn in two steps. This means that the coin can only be withdrawn twice.

Input - L1 - 10, L2 - 11

Output - Maximum amount that can be withdrawn in two steps - 21

Explanation - In the first step, we take 11 coins from L2, L2 will be replaced by 11-1=10 coins.

In the second step, both L1 and L2 have 10 coins, so it can be taken from either one, and we have 11 10 = 21 coins, which is the maximum.

Input - L1-5, L2-5

Output - Maximum amount that can be withdrawn in two steps - 10

Explanation - In the first step, we take 5 coins from L1, L1 will be replaced by 5-1=4 coins.

In the second step, L1 has 4 coins and L2 has 5 coins, so we take 5 coins from L2 and we have 5 5 = 10 coins, which is the maximum.

The method used by the following program is as follows

• We have two integer lockers L1 and L2, which contain some coins.

• The function maxMoney(int A, int B) takes the number of coins in the locker as input.

• In the maxMoney() function, we use the variable 'money' to store the maximum amount.

• Initially, the value of money comes from the larger of A or B. (money=A>B?A:B)

• Compare the value of money with A or B to determine which container's coin was removed.

• Now replace the container with the previous amount minus 1 coin. (A-- or B--)

• Add the value of money to the larger of A or B again. (money =A>B?A:B)

  If k is small, the sum of the smallest k elements is the smallest -

• Storage abs((sum of the entire array) in D1 - (twice the sum of the smallest k elements)). Twice because the array sum also contains these elements.

  If k is larger, the sum of the largest k elements is the largest -

• Store abs ((sum of the entire array) - (the largest k twice the sum of elements)). Twice because the array sum also contains these elements.

• Compare D1 with D2 and store the maximum value in maxD.

• Return maxD as the result.

Example

Live Demonstration

Code:
#include <stdio.h>
#include <math.h>
// Function to return the maximum coins we can get
int maxMoney(int A, int B){
   //take coins
   int money=A>B?A:B;
   //refill the lockers with 1 less no.of coins
   if(money==A)
      A--;
   else
      B--;
   //withdraw again
   money+=A>B?A:B;
   return money;
}
// Driver code
int main(){
   int L1 = 8, L2 = 9;
   printf("Maximum money that can be withdrawn in two steps: %d" , maxMoney(L1, L2));
   return 0;
}

Output

If we run the above code, it will generate the following output−

Maximum money that can be withdrawn in two steps: 17

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