A stack is the natural fit. Process each asteroid from left to right. If it's moving right (positive), push it onto the stack since it can't collide with anything yet.
If it's moving left (negative), you check the stack's top. If the top is also negative or the stack is empty, no collision occurs. Just push. If the top is positive, a collision happens. Compare sizes: if the top is smaller, pop it and keep checking (the left-moving asteroid might destroy multiple right-moving ones). If they're equal, pop the top and discard the current asteroid. If the top is larger, the current asteroid is destroyed.
After processing all asteroids, the stack holds the survivors.