uva 10808 - Rational Resistors(基尔霍夫定律+高斯消元)
来源:互联网 发布:c语言的index函数用法 编辑:程序博客网 时间:2024/06/02 05:32
题目链接:uva 10808 - Rational Resistors
题目大意:给出一个博阿含n个节点,m条导线的电阻网络,求节点a和b之间的等效电阻。
解题思路:基尔霍夫定律,任何一点的电流向量为0。就是说有多少电流流入该节点,就有多少电流流出。
对于每次询问的两点间等效电阻,先判断说两点是否联通,不连通的话绝逼是1/0(无穷大)。联通的话,将同一个联通分量上的节点都扣出来,假设电势作为变元,然后根据基尔霍夫定律列出方程,因为对于每个节点的电流向量为0,所以每个节点都有一个方程,所有与该节点直接连接的都会有电流流入,并且最后总和为0,(除了a,b两点,一个为1,一个为-1)。用高斯消元处理,但是这样列出的方程组不能准确求出节点的电势,只能求出各个节点之间电势的关系。所以我们将a点的电势置为0,那么用求出的b点电势减去0就是两点间的电压,又因为电流设为1,所以等效电阻就是电压除以电流。
#include <cstdio>#include <cstring>#include <algorithm>using namespace std;typedef long long type;struct Fraction { type member; // 分子; type denominator; // 分母; Fraction (type member = 0, type denominator = 1); void operator = (type x) { this->set(x, 1); } Fraction operator * (const Fraction& u); Fraction operator / (const Fraction& u); Fraction operator + (const Fraction& u); Fraction operator - (const Fraction& u); Fraction operator *= (const Fraction& u) { return *this = *this * u; } Fraction operator /= (const Fraction& u) { return *this = *this / u; } Fraction operator += (const Fraction& u) { return *this = *this + u; } Fraction operator -= (const Fraction& u) { return *this = *this - u; } void set(type member, type denominator);};inline type gcd (type a, type b) { return b == 0 ? (a > 0 ? a : -a) : gcd(b, a % b);}inline type lcm (type a, type b) { return a / gcd(a, b) * b;}/*Code*//////////////////////////////////////////////////////const int maxn = 105;typedef long long ll;typedef Fraction Mat[maxn][maxn];int N, M, f[maxn];Mat G, A;bool cmp (Fraction& a, Fraction& b) { return a.member * b.denominator < b.member * a.denominator;}inline int getfar (int x) { return x == f[x] ? x : f[x] = getfar(f[x]);}inline void link (int u, int v) { int p = getfar(u); int q = getfar(v); f[p] = q;}void init () { scanf("%d%d", &N, &M); for (int i = 0; i < N; i++) { f[i] = i; for (int j = 0; j < N; j++) G[i][j] = 0; } int u, v; ll R; for (int i = 0; i < M; i++) { scanf("%d%d%lld", &u, &v, &R); if (u == v) continue; link(u, v); G[u][v] += Fraction(1, R); G[v][u] += Fraction(1, R); }}Fraction gauss_elimin (int u, int v, int n) { /* printf("\n"); for (int i = 0; i < n; i++) { for (int j = 0; j <= n; j++) printf("%lld/%lld ", A[i][j].member, A[i][j].denominator); printf("\n"); } */ for (int i = 0; i < n; i++) { int r; for (int j = i; j < n; j++) if (A[j][i].member) { r = j; break; } if (r != i) { for (int j = 0; j <= n; j++) swap(A[i][j], A[r][j]); } if (A[i][i].member == 0) continue; for (int j = i + 1; j < n; j++) { Fraction t = A[j][i] / A[i][i]; for (int k = 0; k <= n; k++) A[j][k] -= A[i][k] * t; } } for (int i = n-1; i >= 0; i--) { for (int j = i+1; j < n; j++) { if (A[j][j].member) A[i][n] -= A[i][j] * A[j][n] / A[j][j]; } } /* Fraction U = A[u][n] / A[u][u]; printf("%lld/%lld!\n", A[u][n].member, A[u][n].denominator); printf("%lld/%lld!\n", A[u][u].member, A[u][u].denominator); printf("%lld/%lld\n", U.member, U.denominator); Fraction V = A[v][n] / A[v][v]; printf("%lld/%lld\n", V.member, V.denominator); */ return A[u][n] / A[u][u] - A[v][n] / A[v][v];}Fraction solve (int u, int v) { int n = 0, hash[maxn]; int hu, hv; for (int i = 0; i < N; i++) { if (i == u) hu = u; if (i == v) hv = v; if (getfar(i) == getfar(u)) hash[n++] = i; } n++; for (int i = 0; i <= n; i++) { for (int j = 0; j <= n; j++) A[i][j] = 0; } for (int i = 0; i < n - 1; i++) { for (int j = 0; j < n - 1; j++) { if (i == j) continue; int p = hash[i]; int q = hash[j]; A[i][i] += G[p][q]; A[i][j] -= G[p][q]; } } A[hu][n] = 1; A[hv][n] = -1; A[n-1][0] = 1; return gauss_elimin (hu, hv, n);}int main () { int cas; scanf("%d", &cas); for (int kcas = 1; kcas <= cas; kcas++) { init(); int Q, u, v; scanf("%d", &Q); printf("Case #%d:\n", kcas); for (int i = 0; i < Q; i++) { scanf("%d%d", &u, &v); printf("Resistance between %d and %d is ", u, v); if (getfar(u) == getfar(v)) { Fraction ans = solve(u, v); printf("%lld/%lld\n", ans.member, ans.denominator); } else printf("1/0\n"); } printf("\n"); } return 0;}/////////////////////////////////////////////////////Fraction::Fraction (type member, type denominator) { this->set(member, denominator);}Fraction Fraction::operator * (const Fraction& u) { type tmp_p = gcd(member, u.denominator); type tmp_q = gcd(u.member, denominator); return Fraction( (member / tmp_p) * (u.member / tmp_q), (denominator / tmp_q) * (u.denominator / tmp_p) );}Fraction Fraction::operator / (const Fraction& u) { type tmp_p = gcd(member, u.member); type tmp_q = gcd(denominator, u.denominator); return Fraction( (member / tmp_p) * (u.denominator / tmp_q), (denominator / tmp_q) * (u.member / tmp_p));}Fraction Fraction::operator + (const Fraction& u) { type tmp_l = lcm (denominator, u.denominator); return Fraction(tmp_l / denominator * member + tmp_l / u.denominator * u.member, tmp_l);}Fraction Fraction::operator - (const Fraction& u) { type tmp_l = lcm (denominator, u.denominator); return Fraction(tmp_l / denominator * member - tmp_l / u.denominator * u.member, tmp_l);}void Fraction::set (type member, type denominator) { if (denominator == 0) { denominator = 1; member = 0; } if (denominator < 0) { denominator = -denominator; member = -member; } type tmp_d = gcd(member, denominator); this->member = member / tmp_d; this->denominator = denominator / tmp_d;}
1 0
- uva 10808 - Rational Resistors(基尔霍夫定律+高斯消元)
- UVA 10808 - Rational Resistors(高斯消元+并查集+分数+基尔霍夫定律)
- UVA 10808 - Rational Resistors 高斯消元
- uva 10808 - Rational Resistors
- UVA 4566 - Resistors
- 基尔霍夫定律
- uva 11657 - Rational Billiard(数学)
- 《电路基础》基尔霍夫定律
- Introduction to Resistors
- UVa 332 - Rational Numbers from Repeating Fractions
- Uva 7363 -- A rational Sequence(简单)
- UVA, 332 Rational Numbers from Repeating Fractions
- RATIONAL
- Rational
- 递归搜索 ( 水题 )——A Rational Sequence ( UVA 7363 )
- Hdu 3429 Resistors (分数模板 递归读入)
- Pull-up and Pull-down Resistors
- 精密电阻排行榜 List of Precision Resistors
- 用例图的泛化、扩展和包含
- 用Comparator对List<Map>进行排序
- Android杂谈--ListView之BaseAdapter的使用
- NOJ1110奇数排序——超时,看写法,需要较灵活的思维!
- hdu-oj 1200 To and Fro
- uva 10808 - Rational Resistors(基尔霍夫定律+高斯消元)
- hibernate proxool 配置
- 数据存储之SharedPreferences
- poj1459 Power Network
- Queue1 -using two stacks impliment
- IOS百度地图开发
- TCP为什么要三次握手,不是两次四次?
- POJ 3233 矩阵链乘
- mvc 4 windows server 2008 64 位 部署 显示目录