USACO 1.2.2 Transformations（模拟）

分析

       这是我第一次在ACM的题目中用OO的思想写的程序，看到标程，竟不谋而合，结构是类似的。对正方形这个类分析，将会使问题变得简单，我觉得OO的分析和设计挺关键的，其实我一开始也没设计好，原先准备把7个bool函数当成类的成员方法，其实这个设计是不好的，有点过了。其实应该是把旋转90度和轴对称这两个方法作为类的成员方法，这样main中调用就方便自如了。

       最后，我觉得搞ACM，不仅是把题目A掉，同时也应注意程序的结构设计，因为”程序是给人看的“。

2013/3/31

       关于顺时针旋转90度，怎么由原来的坐标得到转换后的坐标，可以用计算机图像学里二维变换的知识，将连续推广到离散的，如下图所示。

       为了与二维数组对应，我将坐标系顺时针旋转了90度，这样就与二维数组的下标情况对应了，假设n为4。

关于变换矩阵，先把参考点移到原点，再顺时针旋转90度，最后移回原来参考点。复合变换矩阵：

MATLAB程序如下：

clc;clear all;syms x y n;P = [x y 1];xF = (n - 1) / 2.0;   % center = (xF yF)yF = xF;% theta = -pi / 2.0;Tt1 = [    1 0 0;    0 1 0;    -xF -yF 1    ];% 精度有损失% Tr = [%     cos(theta) sin(theta) 0;%     -sin(theta) cos(theta) 0;%     0 0 1%     ];Tr = [    0 -1 0;    1 0 0;    0 0 1    ];Tt2 = [    1 0 0;    0 1 0;    xF yF 1    ];Pt = P * Tt1 * Tr * Tt2;display(P);display(Pt);

变换结果

P = [ x, y, 1]  Pt = [ y, n - x - 1, 1]

源程序

// #define ONLINE_JUDGE#define MY_DEBUG#define _CRT_SECURE_NO_WARNINGS#include <iostream>#include <vector>#include <string>#include <algorithm>#include <cstdio>#include <cassert>using namespace std;class Square {private:typedef vector<char> vChar;typedef vector<vChar> vvChar;vvChar data;unsigned n;public:// 用边长来构造Square (unsigned _n) : n(_n) {}Square rotateClockwise90() {Square tmp(n);for (unsigned int i = 0; i < tmp.n; ++i) {Square::vChar vcTmp;for (unsigned int j = 0; j < tmp.n; ++j){vcTmp.push_back(this->data[n - 1 - j][i]);}tmp.data.push_back(vcTmp);}return tmp;}Square rotateClockwise180() {return this->rotateClockwise90().rotateClockwise90();}Square rotateClockwise270() {return this->rotateClockwise180().rotateClockwise90();}Square reflecteHorizontal() {Square tmp(n);for (unsigned int i = 0; i < tmp.n; ++i) {Square::vChar vcTmp;for (unsigned int j = 0; j < tmp.n; ++j){vcTmp.push_back(this->data[i][n - j - 1]);}tmp.data.push_back(vcTmp);}return tmp;}bool operator==(const Square &other) const {if (this->n != other.n) {return false;}for (unsigned i = 0; i < n; ++i) {for (unsigned j = 0; j < n; ++j) {if (this->data[i][j] != other.data[i][j]) {return false;}}}return true;}friend istream & operator>>(istream& is, Square &s) {for (unsigned int i = 0; i < s.n; ++i) {Square::vChar vcTmp;for (unsigned int j = 0; j < s.n; ++j){char cTmp;cin >> cTmp;vcTmp.push_back(cTmp);}s.data.push_back(vcTmp);}return is;}friend ostream & operator<<(ostream& os, const Square &s) {for (unsigned int i = 0; i < s.n; ++i) {if (i >= 1) {cout << endl;}for (unsigned int j = 0; j < s.n; ++j){if (j >= 1) {cout << " ";}cout << s.data[i][j];}}return os;}};int main(){#ifndef ONLINE_JUDGEfreopen("transform.in", "r", stdin);freopen("transform.out", "w", stdout);#endifunsigned sideLen;cin >> sideLen;Square sa(sideLen);Square sb(sideLen);cin >> sa >> sb;#ifndef MY_DEBUGcout << "sa=\n" << sa << "\n" << endl;cout << "sb=\n" << sb << "\n" << endl;assert(sa.rotateClockwise270() == sa.rotateClockwise90().rotateClockwise90().rotateClockwise90());#endifif (sa.rotateClockwise90() == sb) {cout << "1" << endl;return 0;}if (sa.rotateClockwise180() == sb) {cout << "2" << endl;return 0;}if (sa.rotateClockwise270() == sb) {cout << "3" << endl;return 0;}if (sa.reflecteHorizontal() == sb) {cout << "4" << endl;return 0;}Square saRe(sa.reflecteHorizontal());if (saRe.rotateClockwise90() == sb|| saRe.rotateClockwise180() == sb|| saRe.rotateClockwise270() == sb) {cout << "5" << endl;return 0;}if (sa == sb) {cout << "6" << endl;return 0;}cout << "7" << endl;return 0;}

附：

标程

注：它的旋转函数中坐标变换错了。

#include <stdio.h>#include <stdlib.h>#include <string.h>#include <assert.h>#define MAXN 10typedef struct Board Board;struct Board {    int n;    char b[MAXN][MAXN];};/* rotate 90 degree clockwise: [r, c] -> [c, n+1 - r] */Boardrotate(Board b){    Board nb;    int r, c;    nb = b;    for(r=0; r<b.n; r++)    for(c=0; c<b.n; c++)        nb.b[c][b.n+1 - r] = b.b[r][c];    return nb;}/* reflect board horizontally: [r, c] -> [r, n-1 -c] */Boardreflect(Board b){    Board nb;    int r, c;    nb = b;    for(r=0; r<b.n; r++)    for(c=0; c<b.n; c++)        nb.b[r][b.n-1 - c] = b.b[r][c];    return nb;}/* return non-zero if and only if boards are equal */inteqboard(Board b, Board bb){    int r, c;    if(b.n != bb.n)        return 0;    for(r=0; r<b.n; r++)    for(c=0; c<b.n; c++)        if(b.b[r][c] != bb.b[r][c])            return 0;    return 1;}Boardrdboard(FILE *fin, int n){    Board b;    int r, c;    b.n = n;    for(r=0; r<n; r++) {        for(c=0; c<n; c++)            b.b[r][c] = getc(fin);        assert(getc(fin) == '\n');    }    return b;}voidmain(void){    FILE *fin, *fout;    Board b, nb;    int n, change;    fin = fopen("transform.in", "r");    fout = fopen("transform.out", "w");    assert(fin != NULL && fout != NULL);    fscanf(fin, "%d\n", &n);    b = rdboard(fin, n);    nb = rdboard(fin, n);    if(eqboard(nb, rotate(b)))        change = 1;    else if(eqboard(nb, rotate(rotate(b))))        change = 2;    else if(eqboard(nb, rotate(rotate(rotate(b)))))        change = 3;    else if(eqboard(nb, reflect(b)))        change = 4;    else if(eqboard(nb, rotate(reflect(b)))         || eqboard(nb, rotate(rotate(reflect(b))))         || eqboard(nb, rotate(rotate(rotate(reflect(b))))))        change = 5;    else if(eqboard(nb, b))        change = 6;    else        change = 7;    fprintf(fout, "%d\n", change);    exit(0);}

题目

Transformations

A square pattern of size N x N (1 <= N <= 10) black and white square tiles is transformed into another square pattern. Write a program that will recognize the minimum transformation that has been applied to the original pattern given the following list of possible transformations:

• #1: 90 Degree Rotation: The pattern was rotated clockwise 90 degrees.
• #2: 180 Degree Rotation: The pattern was rotated clockwise 180 degrees.
• #3: 270 Degree Rotation: The pattern was rotated clockwise 270 degrees.
• #4: Reflection: The pattern was reflected horizontally (turned into a mirror image of itself by reflecting around a vertical line in the middle of the image).
• #5: Combination: The pattern was reflected horizontally and then subjected to one of the rotations (#1-#3).
• #6: No Change: The original pattern was not changed.
• #7: Invalid Transformation: The new pattern was not obtained by any of the above methods.

In the case that more than one transform could have been used, choose the one with the minimum number above.

PROGRAM NAME: transform

INPUT FORMAT

Line 1:A single integer, NLine 2..N+1:N lines of N characters (each either `@' or `-'); this is the square before transformationLine N+2..2*N+1:N lines of N characters (each either `@' or `-'); this is the square after transformation

SAMPLE INPUT (file transform.in)

3@-@---@@-@-@@----@

OUTPUT FORMAT

A single line containing the the number from 1 through 7 (described above) that categorizes the transformation required to change from the `before' representation to the `after' representation.

SAMPLE OUTPUT (file transform.out)

1