UVA437 - The Tower of Babylon

有向无环图最长路径算法
每个立方体都可以分别以三个边为高，这样一个立方体确定高后，就有三个状态，存储在cube中。
在用Graph邻接数组存储每个状态之间的关系，这样就形成了有向无环图。在用dp[i] = max(dp[i], solve(j) + cube[i].h)(i -> j),求出每个d[i],取最大值输出.

#include <cstdio>#include <iostream>#include <algorithm>#include <cstring>#include <map>#include <vector>using namespace std;struct Cube{    Cube(){}    Cube(int a, int b, int c)    {        x = a;        y = b;        h = c;    }    int x, y;    int h;}cube[100];int Graph[100][100];int dp[100], n;bool judge(Cube &a, Cube &b){    if(a.x < a.y)        swap(a.x, a.y);    if(b.x < b.y)        swap(b.x, b.y);    if(a.x > b.x && a.y > b.y)        return true;    return false;}int solve(int m){    if(dp[m])return dp[m];    dp[m] = cube[m].h;    for(int i = 1; i <= 3 * n; i++)    {        if(Graph[m][i])            dp[m] = max(dp[m], solve(i) + cube[m].h);    }    return dp[m];}int main(){  //  freopen("in.txt", "r", stdin);    int cas =0;    while(cin >> n && n)    {        memset(Graph, 0, sizeof(Graph));        memset(dp, 0, sizeof(dp));        for(int i = 1; i <= n; i++)        {            int x, y, z;            cin >> x >> y >> z;            cube[3*i] = Cube(x, y, z);            cube[3*i-1] = Cube(x, z, y);            cube[3*i-2] = Cube(y, z, x);        }        for(int i = 1; i <= 3 * n; i++)            for(int j = i+1; j <= 3 * n; j++)        {            if(judge(cube[i], cube[j]))               Graph[i][j] = 1;            else if(judge(cube[j], cube[i]))                Graph[j][i] = 1;        }        int maxs = 0;        for(int i = 1; i <= 3 * n; i++)        {            dp[i] = solve(i);            maxs = max(maxs, dp[i]);        }        printf("Case %d: maximum height = %d\n", ++cas, maxs);    }    return 0;}