CF1023B Pair of Toys

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  • 题目来源 CodeForces 1023B
  • 评测方式 RemoteJudge
  • 标签
  • 难度 普及/提高-
  • 时空限制 1000ms / 256MB

题解

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    题意翻译

    给定n个玩具要你选出两个玩具求出k的价值。
    第i个玩具的价值为i。
    样例1:从8个玩具里选出两个使价值为5.
    有以下方案:(1 4)(2 3)。
    若是没有选择方案,输出0 补充:玩具A与玩具B 和 玩具B和玩具A 是同一种选择

    题目描述

    Tanechka is shopping in the toy shop. There are exactly $ n $ toys in the shop for sale, the cost of the $ i $ -th toy is $ i $ burles. She wants to choose two toys in such a way that their total cost is $ k $ burles. How many ways to do that does she have?

    Each toy appears in the shop exactly once. Pairs $ (a, b) $ and $ (b, a) $ are considered equal. Pairs $ (a, b) $ , where $ a=b $ , are not allowed.

    输入输出格式

    输入格式:

    The first line of the input contains two integers $ n $ , $ k $ ( $ 1 \le n, k \le 10^{14} $ ) — the number of toys and the expected total cost of the pair of toys.

    输出格式:

    Print the number of ways to choose the pair of toys satisfying the condition above. Print 0, if Tanechka can choose no pair of toys in such a way that their total cost is $ k $ burles.

    输入输出样例

    输入样例#1: 复制
    8 5
    
    输出样例#1: 复制
    2
    
    输入样例#2: 复制
    8 15
    
    输出样例#2: 复制
    1
    
    输入样例#3: 复制
    7 20
    
    输出样例#3: 复制
    0
    
    输入样例#4: 复制
    1000000000000 1000000000001
    
    输出样例#4: 复制
    500000000000
    

    说明

    In the first example Tanechka can choose the pair of toys ( $ 1, 4 $ ) or the pair of toys ( $ 2, 3 $ ).

    In the second example Tanechka can choose only the pair of toys ( $ 7, 8 $ ).

    In the third example choosing any pair of toys will lead to the total cost less than $ 20 $ . So the answer is 0.

    In the fourth example she can choose the following pairs: $ (1, 1000000000000) $ , $ (2, 999999999999) $ , $ (3, 999999999998) $ , ..., $ (500000000000, 500000000001) $ . The number of such pairs is exactly $ 500000000000 $ .

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