Square?

Key idea

A square is brutally picky: all four sides must have the same length.

We are given exactly four sticks, and we cannot break or bend them. That means each stick has to be used as one full side of the square. So there is no clever construction, no hidden geometry trick, no “maybe if we rotate it” nonsense. If one stick has a different length, one side of the square would be different, and the square is dead.

So the condition is simply:

$a=b=c=d$

If that is true, we can place the four sticks as the four sides of a square. If not, we cannot.

Why pairs are not enough

A common wrong thought is: “If opposite sides match, that should work.” Nope. That gives you a rectangle, not necessarily a square.

For example:

$1,2,1,2$

These can form a rectangle with side lengths $1$ and $2$, but a square needs all sides equal. Rectangles are square cosplay, not squares.

Algorithm

For each test case:

1. Read $a,b,c,d$.
2. Check whether all four are equal.
3. Print YES if they are, otherwise print NO.

Correctness proof

We prove the algorithm prints YES exactly when a square can be formed.

If the algorithm prints YES, then $a=b=c=d$. Since all four sticks have equal length, we can use them as the four equal sides of a square. Therefore, forming a square is possible.

If a square can be formed, then its four sides must all have equal length by definition. Since the four given sticks are exactly the four sides and cannot be changed, their lengths must satisfy $a=b=c=d$. Therefore, the algorithm prints YES.

Thus, the algorithm is correct.

Complexity

Each test case uses only a constant number of comparisons.

Time complexity: $O(1)$ per test case, or $O(t)$ total.

Memory complexity: $O(1)$.

Tiny problem, tiny solution. The geometry got folded into one equality check.