UVa 10161 Ant on a Chessboard
2014-07-01 08:33
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一道数学水题,找找规律。
首先要判断给的数在第几层,比如说在第n层。然后判断(n * n - n + 1)(其坐标也就是(n,n)) 之间的关系。
还要注意n的奇偶。
At the first second, Alice was standing at (1,1). Firstly she went up for a grid, then a grid to the right, a grid downward. After that, she went a grid to the right, then two grids upward, and then two grids to the left…in a word, the path was like a snake.
For example, her first 25 seconds went like this:
( the numbers in the grids stands for the time when she went into the grids)
5
4
3
2
1
1 2 3 4 5
At the 8th second , she was at (2,3), and at 20th second, she was at (5,4).
Your task is to decide where she was at a given time.
(you can assume that M is large enough)
20
25
0
5 4
1 5
AC代码:
代码君
首先要判断给的数在第几层,比如说在第n层。然后判断(n * n - n + 1)(其坐标也就是(n,n)) 之间的关系。
还要注意n的奇偶。
Problem A.Ant on a Chessboard |
Background
One day, an ant called Alice came to an M*M chessboard. She wanted to go around all the grids. So she began to walk along the chessboard according to this way: (you can assume that her speed is one grid per second)At the first second, Alice was standing at (1,1). Firstly she went up for a grid, then a grid to the right, a grid downward. After that, she went a grid to the right, then two grids upward, and then two grids to the left…in a word, the path was like a snake.
For example, her first 25 seconds went like this:
( the numbers in the grids stands for the time when she went into the grids)
25 | 24 | 23 | 22 | 21 |
10 | 11 | 12 | 13 | 20 |
9 | 8 | 7 | 14 | 19 |
2 | 3 | 6 | 15 | 18 |
1 | 4 | 5 | 16 | 17 |
4
3
2
1
1 2 3 4 5
At the 8th second , she was at (2,3), and at 20th second, she was at (5,4).
Your task is to decide where she was at a given time.
(you can assume that M is large enough)
Input
Input file will contain several lines, and each line contains a number N(1<=N<=2*10^9), which stands for the time. The file will be ended with a line that contains a number 0.Output
For each input situation you should print a line with two numbers (x, y), the column and the row number, there must be only a space between them.Sample Input
820
25
0
Sample Output
2 35 4
1 5
AC代码:
//#define LOCAL #include <iostream> #include <cstdio> #include <cstring> #include <cmath> using namespace std; int main(void) { #ifdef LOCAL freopen("10161in.txt", "r", stdin); #endif int N; while(scanf("%d", &N) == 1 && N) { int n = (int)ceil(sqrt(N)); int x, y; if(n & 1 == 1) { if(N < n * n - n + 1) { x = n; y = N - (n - 1) * (n - 1); } else { y = n; x = n * n - N + 1; } } else { if(N < n * n - n + 1) { y = n; x = N - (n - 1) * (n - 1); } else { x = n; y = n * n - N + 1; } } cout << x << " " << y << endl; } return 0; }
代码君
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