Robot Program (Codeforces 1452A)
Tags: Math, math

There is an infinite 2-dimensional grid. The robot stands in cell $$$(0, 0)$$$ and wants to reach cell $$$(x, y)$$$. Here is a list of possible commands the robot can execute:  move north from cell $$$(i, j)$$$ to $$$(i, j + 1)$$$;  move east from cell $$$(i, j)$$$ to $$$(i + 1, j)$$$;  move south from cell $$$(i, j)$$$ to $$$(i, j - 1)$$$;  move west from cell $$$(i, j)$$$ to $$$(i - 1, j)$$$;  stay in cell $$$(i, j)$$$. The robot wants to reach cell $$$(x, y)$$$ in as few commands as possible. However, he can't execute the same command two or more times in a row.What is the minimum number of commands required to reach $$$(x, y)$$$ from $$$(0, 0)$$$?

Input: The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of testcases.Each of the next $$$t$$$ lines contains two integers $$$x$$$ and $$$y$$$ ($$$0 \le x, y \le 10^4$$$) — the destination coordinates of the robot.

Output: For each testcase print a single integer — the minimum number of commands required for the robot to reach $$$(x, y)$$$ from $$$(0, 0)$$$ if no command is allowed to be executed two or more times in a row.

Note: The explanations for the example test:We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.In the first test case, the robot can use the following sequence: NENENENENE.In the second test case, the robot can use the following sequence: NENENEN.In the third test case, the robot can use the following sequence: ESENENE0ENESE.In the fourth test case, the robot doesn't need to go anywhere at all.In the fifth test case, the robot can use the following sequence: E0E.

Sample Inputs:
5
5 5
3 4
7 1
0 0
2 0

Sample Outputs:
10
7
13
0
3

Solution (Python):
for _ in range(0, int(input())):
    (x, y) = sorted(map(int, input().split()))
    print(x + y + max(0, y - x - 1))

Solution (Python):
for _ in range(0, int(input())):
    (x, y) = sorted(map(int, input().split()))
    print(x + y + max(0, y - x - 1))

Solution (Python):
test_cases = int(input())
for i in range(test_cases):
    (x, y) = map(int, input().split())
    ans = max(x, y) * 2 - 1
    if x == y:
        ans += 1
    print(ans)