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点集配对问题
点集配对问题 空间里n个点,使它们配成n/2对点,使得每个点恰好在一个点对中。
要求所有点队中,两点距离之和尽量下 n <= 20
d(s) = min(d{S - {i} - {j}+ |Pi Pj| | j属于S, j > i, i = min{S}}
//#pragma comment(linker, "/STACK:102400000,102400000") //HEAD #include <cstdio> #include <cstring> #include <vector> #include <iostream> #include <algorithm> #include <queue> #include <string> #include <set> #include <stack> #include <map> #include <cmath> #include <cstdlib> using namespace std; //LOOP #define FE(i, a, b) for(int i = (a); i <= (b); ++i) #define FED(i, b, a) for(int i = (b); i>= (a); --i) #define REP(i, N) for(int i = 0; i < (N); ++i) #define CLR(A,value) memset(A,value,sizeof(A)) //STL #define PB push_back //INPUT #define RI(n) scanf("%d", &n) #define RII(n, m) scanf("%d%d", &n, &m) #define RIII(n, m, k) scanf("%d%d%d", &n, &m, &k) #define RS(s) scanf("%s", s) typedef long long LL; const int INF = 0x3f3f3f3f; const int MAXN = 1010; #define FF(i, a, b) for(int i = (a); i < (b); ++i) #define FD(i, b, a) for(int i = (b) - 1; i >= (a); --i) #define CPY(a, b) memcpy(a, b, sizeof(a)) #define FC(it, c) for(__typeof((c).begin()) it = (c).begin(); it != (c).end(); it++) #define EQ(a, b) (fabs((a) - (b)) <= 1e-10) #define ALL(c) (c).begin(), (c).end() #define SZ(V) (int)V.size() #define RIV(n, m, k, p) scanf("%d%d%d%d", &n, &m, &k, &p) #define RV(n, m, k, p, q) scanf("%d%d%d%d%d", &n, &m, &k, &p, &q) #define WI(n) printf("%d\n", n) #define WS(s) printf("%s\n", s) #define sqr(x) (x) * (x) typedef vector <int> VI; typedef unsigned long long ULL; const double eps = 1e-10; const LL MOD = 1e9 + 7; int inx[25], iny[25], inz[25]; double dp[1 << 20]; int n; double dis(int x, int y) { return sqrt(sqr(inx[x] - inx[y]) + sqr(iny[x] - iny[y]) + sqr(inz[x] - inz[y])); } double dfs(int x) { if (dp[x] < INF) return dp[x]; int i, u = -1, v = -1; for (i = 0; i < n; i++) if ((x & (1 << i)) == 0) { u = i; break;} for (int j = i + 1; j < n; j++) { if ((x & (1 << j)) == 0) dp[x] = min(dfs(x | (1 << j) | (1 << u)) + dis(u, j), dp[x]); } return dp[x]; } int main() { while (~RI(n)) { int x, y, z; REP(i, n) RIII(inx[i], iny[i], inz[i]); REP(i, 1 << n) dp[i] = INF; dp[(1 << n) - 1] = 0; dfs(0); printf("%.10lf\n", dp[0]); } return 0; }
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