UVA 618 - Doing Windows（數論）

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題目連結：618 - Doing Windows題意：給定一個大小不能變的螢幕，和四個大小可以變的視窗，變化要保持長寬比，問這四個視窗能不能調整後全部放下正好填滿螢幕，不能重疊思路：情況一共就幾種：4個疊一起，3個疊一起+一個，2個和2個，一個和兩個疊一起在一個，把這幾種情況全判斷了就可以了，判斷過程利用gcd，lcm可以求邊長。代碼：

#include <stdio.h>#include <string.h>long long gcd(long long a, long long b) {    if (b == 0) return a;    return gcd(b, a % b);}long long lcm(long long a, long long b) {    return a / gcd(a, b) * b;}struct Win {    long long x, y;    bool scanf_() {scanf("%lld%lld", &x, &y);if (x == 0 || y == 0)     return false;long long t = gcd(x, y); x /= t; y /= t;return true;    }    void swap() {long long t = x; x = y; y = t;    }} win, w[4];bool check1(Win a, Win b, Win c, Win d) {    long long sum = 0;    if (win.y % a.y) return false;    sum += win.y / a.y * a.x;    if (win.y % b.y) return false;    sum += win.y / b.y * b.x;    if (win.y % c.y) return false;    sum += win.y / c.y * c.x;    if (win.y % d.y) return false;    sum += win.y / d.y * d.x;    if (sum != win.x) return false;    return true;}bool check(Win a, Win b, Win c, long long wx, long long wy) {    if (wy <= wx / a.x * a.y) return false;    long long yy = wy - wx / a.x * a.y;    long long sum = 0;    if (yy % b.y) return false;    sum += yy / b.y * b.x;    if (yy % c.y) return false;    sum += yy / c.y * c.x;    if (sum != wx) return false;    return true;}bool judge3(Win a, Win b, Win c, long long wx, long long wy) {    if (check(a, b, c, wx, wy)     || check(b, a, c, wx, wy)     || check(c, a, b, wx, wy)) return true;    return false;}bool judge2(Win a, Win b, Win c, long long wx, long long wy) {    if (judge3(a, b, c, wx, wy))return true;    a.swap();     b.swap();     c.swap();    if (judge3(a, b, c, wy, wx))return true;    return false;}bool check2(Win a, Win b, Win c, Win d) {    long long sum = 0;    if (win.x % d.x) return false;    long long wy = win.x / d.x * d.y;    if (wy >= win.y) return false;    long long yy = win.y - wy;    if (judge2(a, b, c, win.x, yy)) return true;    if (yy % a.y) return false;    sum += yy / a.y * a.x;    if (yy % b.y) return false;    sum += yy / b.y * b.x;    if (yy % c.y) return false;    sum += yy / c.y * c.x;    int flag = 0;    if (sum == win.x) flag = 1;    return flag;}bool check3(Win a, Win b, Win c, Win d) {    long long sum = 0;    long long wy = lcm(a.y, b.y);    if (wy >= win.y) return false;    sum += wy / a.y * a.x;    sum += wy / b.y * b.x;    if (win.x % sum) return false;    if (win.y <= win.x / sum * wy) return false;    long long yy = win.y - win.x / sum * wy;    sum = 0;    if (yy % c.y)       return false;    sum += yy / c.y * c.x;    if (yy % d.y) return false;    sum += yy / d.y * d.x;    if (win.x != sum) return false;    return true;}bool judge() {    if (check1(w[0], w[1], w[2], w[3])) return true;    if (check2(w[0], w[1], w[2], w[3])    || check2(w[0], w[1], w[3], w[2])    || check2(w[0], w[3], w[2], w[1])    || check2(w[3], w[1], w[2], w[0]))       return true;    if (check3(w[0], w[1], w[2], w[3])    || check3(w[0], w[2], w[1], w[3])    || check3(w[0], w[3], w[1], w[2])) return true;    return false;}bool solve() {    if (judge()) return true;    win.swap();     for (long long i = 0; i < 4; i++) w[i].swap();    if (judge()) return true;    return false;}int main() {    long long cas = 0;    while (~scanf("%lld%lld", &win.x, &win.y) && win.x || win.y) {for (long long i = 0; i < 4; i++)    w[i].scanf_();printf("Set %lld: %s\n", ++cas, solve()? "Yes":"No");    }    return 0;}