1992: 【基础】螺旋矩阵
内存限制:128 MB
时间限制:1.000 S
评测方式:文本比较
命题人:
提交:3
解决:2
题目描述
一个 n 行 n 列的螺旋矩阵可由如下方法生成:
从矩阵的左上角(第 1 行第 1 列)出发,初始时向右移动;如果前方是未曾经过的格子,则继续前进,否则右转;重复上述操作直至经过矩阵中所有格子。根据经过顺序,在格子中依次填入 1, 2, 3, ... , n2,便构成了一个螺旋矩阵。
下图是一个 n = 4 时的螺旋矩阵。
![](http://oj.czos.cn:443/admin/../data:image/png;base64,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)
![](https://oj.czos.cn/uploads/20211116/576e11a73c4a94dc7d6b724c8523f371.png)
现给出矩阵大小 n 以及 i 和 j,请你求出该矩阵中第 i 行第 j 列的数是多少。
从矩阵的左上角(第 1 行第 1 列)出发,初始时向右移动;如果前方是未曾经过的格子,则继续前进,否则右转;重复上述操作直至经过矩阵中所有格子。根据经过顺序,在格子中依次填入 1, 2, 3, ... , n2,便构成了一个螺旋矩阵。
下图是一个 n = 4 时的螺旋矩阵。
![](https://oj.czos.cn/uploads/20211116/576e11a73c4a94dc7d6b724c8523f371.png)
现给出矩阵大小 n 以及 i 和 j,请你求出该矩阵中第 i 行第 j 列的数是多少。
输入
输入共一行,包含三个整数 n, i, j,每两个整数之间用一个空格隔开,分别表示矩阵大小、 待求的数所在的行号和列号。
输出
输出共一行,包含一个整数,表示相应矩阵中第 i 行第 j 列的数。
样例输入 复制
4 2 3
样例输出 复制
14
提示
【数据说明】
对于 50%的数据, 1 ≤ n ≤ 100;
对于 100%的数据, 1 ≤ n ≤ 30,000, 1 ≤ i ≤ n, 1 ≤ j ≤ n。
【来源】noip2014普及组第3题。
对于 50%的数据, 1 ≤ n ≤ 100;
对于 100%的数据, 1 ≤ n ≤ 30,000, 1 ≤ i ≤ n, 1 ≤ j ≤ n。
【来源】noip2014普及组第3题。