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  • B. Sereja and Mirroring

    B. Sereja and Mirroring
    time limit per test
    1 second
    memory limit per test
    256 megabytes
    input
    standard input
    output
    standard output

    Let's assume that we are given a matrix b of size x × y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a2x × y matrix c which has the following properties:

    • the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
    • the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).

    Sereja has an n × m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several(possibly zero) mirrorings. What minimum number of rows can such matrix contain?

    Input

    The first line contains two integers, n and m (1 ≤ n, m ≤ 100). Each of the next n lines contains m integers — the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 ≤ aij ≤ 1) — the i-th row of the matrix a.

    Output

    In the single line, print the answer to the problem — the minimum number of rows of matrix b.

    Sample test(s)
    input
    4 3
    0 0 1
    1 1 0
    1 1 0
    0 0 1
    
    output
    2
    
    input
    3 3
    0 0 0
    0 0 0
    0 0 0
    
    output
    3
    
    input
    8 1
    0
    1
    1
    0
    0
    1
    1
    0
    
    output
    2
    
    Note

    In the first test sample the answer is a 2 × 3 matrix b:

    001
    110
    

    If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:

    001
    110
    110
    001
    


    #include <stdio.h>
    #include <stdlib.h>
    #include <string.h>
    
    int num[111][111];
    
    int main ()
    {
        int n,m;
        scanf ("%d%d",&n,&m);
    
        int i,k;
    
        for (i = 0;i < n;i++)
            for (k = 0;k < m;k++)
                scanf ("%d",&num[i][k]);
    
        int ans = n;a
    
        if (n % 2)
            printf ("%d
    ",n);
        else
        {
            int tn = n;
            while (1)
            {
                int tf = 1;
                for (i = 0;i < tn / 2;i++)
                    for (k = 0;k < m;k++)
                        if (num[i][k] != num[tn - 1 - i][k])
                            tf = 0;
                if (tf)
                {
                    if (tn % 2)
                        break;
                    tn /= 2;
                }else
                {
                    //tn *= 2;
                    break;
                }
            }
            printf ("%d
    ",tn);
        }
    
        return 0;
    }
    


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  • 原文地址:https://www.cnblogs.com/zfyouxi/p/5231079.html
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