because you choose for each row all available columns that can match with it and vice versa ..

because the result of multiplying matrix A by matrix B differ from multiplying matrix B by matrix A

some thing like this

1

4

2 3

2 3

3 2

3 2

all available pairs of indices i and j exist are 8

(1 , 3)

(1 , 4)

(2 , 3)

(2 , 4)

(3 , 1)

(3 , 2)

(4 , 1)

(4 , 2)

let's suppose your lines of boxes starts with box with index a and finishes with box with index b, if you play first you can pick either box a or b, leaving the other player with boxes (a+1..b) or (a..b-1) and we know he will do the optimal move and leave us with either (a+2..b) or (a+1..b-1) (if we picked box "a" in the previous turn) and (a+1..b-1) or (a..b-2) (if we picked "b" in the previous turn). since this is a zero-sum game, we can think of his move as he's trying to minimize our score. so our next move will be in the position that gives us the minimum score. now let's go back to the beginning of the game before picking either a or b, we pick the box that gives us a maximum minimum in our next possible moves, and we do it recursively for all positions of boxes we can achieve. more formally,

if (a>b)
 return 0;
return  max(t[a] + min(solve(a+2,b),solve(a+1,b-1)) , t[b]+min(solve(a,b-2),solve(a+1,b-1)) );

my solution

If the amount of money you have is TotalMoney, and the price per orange is OrangePrice then the number of oranges you can buy is (assuming that TotalMoney is divisible by OrangePrice):

We can use this equation to find TotalMoney, which is equal to:

TotalMoney = Oranges × OrangePrice

Let's take the first test case as an example to explain the solution. If the price of the orange was increased by 25%, then the new price is equal to:

NewOrangePrice = OrangePrice × 1.25

The number of oranges that can be bought after the price increase is equal to:

From the problem statement, we know that the amount of money didn't change, which mean:

NewTotalMoney ≡ TotalMoney

So, we can write the equation as follows:

Also, we know the following from the explanation above:

TotalMoney ≡ Oranges × OrangePrice

NewOrangePrice ≡ OrangePrice × 1.25

So, we can write the equation as follows:

Which can be written as follows:

In general, to calculate the answer you can use the following equation:

.

To avoid floating-point issues with compilers, you can multiply the equation by 100 to get the following equation:

.

We can find the current number of other figures can be reached, the establishment of a map, the shortest road

BFS

and Remember that you can't do the following transitions:

1 <-> 6 (ie: if top is 1, you can go to 3,4,5,2 but not 6, same for 6 can go the same set but not 1)

3 <-> 4

5 <-> 2