pku 3301 Texas Trip 三分法解题报告

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3301 Texas Trip 解题报告

首次领教了三分法，对于二分、三分解决一些数学问题有了更加深刻的领悟。

题意：求最小面积的正方形，覆盖平面上给定的N个点。

算法：三分逐步细分。标准正放正方形的比较好做只要找出minx,miny,maxx,maxy即可但是最小正方形不一定是标准正放,每个点对角度坐标表换的值，( x = node[j].x * cos(angle) - node[j].y * sin(angle);y = node[j].y * cos(angle) + node[j].x * sin(angle);)然后求标准正放的最小正方形即可。

AC代码：

#include <math.h>

#include <stdio.h>

#define MAX 1000000000

#define MIN -1000000000

#define pi (asin(1.)*2)

struct Texas

{

int x, y;

};

int main()

{

freopen("1.txt", "r", stdin);

int i, j, test, n;

scanf("%d", &test);

while (test--)

{

Texas node[31];

scanf("%d", &n);

for (i = 0; i < n; i++)

{

scanf("%ld%ld", &node[i].x, &node[i].y);

}

int times = 40;

double cumulative = pi / 6, angle = 0, minboundary = MAX, from = 0, boundary;

double downx, downy, upx, upy, x, y;

while (times--)

{

for (i = 0; i < 4; i++) //角度初始为0,那么4次相加后,将超过90

{

downx = downy = MAX; upx = upy = MIN;

for (j = 0; j < n; j++)

{

x = node[j].x * cos(angle) - node[j].y * sin(angle);

y = node[j].y * cos(angle) + node[j].x * sin(angle);

if (x < downx) downx = x;

if (x > upx) upx = x;

if (y < downy) downy = y;

if (y > upy) upy = y;

}

boundary = (upx - downx) > (upy - downy) ? (upx - downx) : (upy - downy);

if (boundary < minboundary)

{

minboundary = boundary;

from = angle;

}

angle += cumulative;

}

//逐步细分

if (angle)

{

angle = from - cumulative;

}

//三分思想的应用

if (angle == 0 || angle == 3)

{

cumulative /= 3;

}

else

{

cumulative = cumulative * 2 / 3;

}

printf("%.2lf/n", minboundary * minboundary);

}

return 0;

}

pku 3301 Texas Trip 三分法 解题报告