第三行:空白(必须注意,否则PE)
算法:
1.Dfs搜索
2.多重背包 -> 0-1背包+二进制拆分
3.类筛法求素数
/* dfs:无回溯WA,无剪枝TLE */ #include<iostream> using namespace std; int values[7]; bool flag; int halfValue; bool visited[120001]; // visited[i]=true:数值i已经计算过,即marbles可以分为i和sum-i,该数组用于剪枝 void init() { for (int i=0; i<=120001; i++) { visited[i] = false; } } void output() { cout << values[1] << " " << values[2] << " " << values[3] << " " << values[4] << " " << values[5] << " " << values[6] << " " << endl; } void Dfs(int currVal) { if (currVal == halfValue) { flag = true; return; } for (int i=6; i>=1; i--) { if (values[i] > 0 && !flag) { if (currVal + i > halfValue) { continue; } else { values[i]--; if (!visited[currVal + i]) // 如果 数值currVal + i已经计算过,不要重复计算,如此可以减少大量计算,否则会TLE { Dfs(currVal + i); visited[currVal + i] = true; } values[i]++; // 此处需要回溯,否则0 0 3 0 3 1难过也! } } } } int main() { int cases = 1; while (cin >> values[1] >> values[2] >> values[3] >> values[4] >> values[5] >> values[6]) { int sum = values[1]*1 + values[2]*2 + values[3]*3 + values[4]*4 + values[5]*5 + values[6]*6; if (sum == 0) { break; } cout << "Collection #" << cases++ <<':' << endl; if (sum % 2 != 0) { cout << "Can't be divided." << endl << endl; //注意有空行 continue; } flag = false; halfValue = sum / 2; init(); Dfs(0); flag? cout<<"Can be divided."<<endl<<endl : cout<<"Can't be divided."<<endl<<endl; } return 0; }
/* 多重背包 -> 二进制拆分 + 0-1背包 */ #include <iostream> #include <string.h> using namespace std; const int MAX=120000; int cnt; // the total number of the marbles after binary split int marbles[MAX]; // marble[i]=j: the value of the ith marble is j int bag[MAX]; // bag[i]=j: when the capacity of the bag is i,the max value of the marbles can be put into the bag is j int values[7]; // binary split (please refer to《二进制拆分》) void binSplit(int val, int num) { int bin_num; int bin_sum = 0; for (int i=0; ; i++) { bin_num = 1<<i; if (bin_sum+bin_num > num) { break; } marbles[cnt++] = bin_num * val; bin_sum += bin_num ; } int t = val*num - bin_sum*val; if (t > 0) { marbles[cnt++] = t; } } // 0-1 bag bool dp(int c) { // For each marble which after binary split for (int i=0; i<cnt; i++) { // For each capacity of j,enumerate every marble i,judge whether it should be put into the bag or not // If put marble i into bag,then bag[j] = bag[j-marbles[i]]+marbles[i] // Surely,in order to ensure marble i can be put into the bag which it's capacity is j,j should greater than marbles[i] // If do not put marble i into bag,then bag[j] is just bag[j] // By comparing the size of bag[j] and bag[j-marbles[i]]+marbles[i],we get the answer...... for (int j=c; j>=marbles[i]; j--) { if (bag[j-marbles[i]]+marbles[i] > bag[j]) { bag[j] = bag[j-marbles[i]]+marbles[i]; } } } return bag[c] == c; } int main() { int cases = 1; int halfValue; while (cin >> values[1] >> values[2] >> values[3] >> values[4] >> values[5] >> values[6]) { int sum = values[1]*1 + values[2]*2 + values[3]*3 + values[4]*4 + values[5]*5 + values[6]*6; if (sum == 0) { break; } cout << "Collection #" << cases++ <<':' << endl; if (sum % 2 != 0) { cout << "Can't be divided." << endl << endl; // Output a blank line after each test case continue; } memset(bag,0,sizeof(bag)); memset(marbles,0,sizeof(int)); cnt = 0; for (int i=1; i<=6; i++) { if (values[i] > 0) { binSplit(i,values[i]); } } halfValue = sum / 2; dp(halfValue)? cout<<"Can be divided."<<endl<<endl:cout<<"Can't be divided."<<endl<<endl; } return 0; }
/* 类似筛法求素数:设总数为sum,flag[i]=true表示可以分为i和sum-i。显然,flag[0]=true。 如果flag[i]=true,而且存在重量为j(1<=j<=6)的marble,那么flag[i+j]=true。 而题目要求的是flag[sum/2]。 */ #include <iostream> #include <string.h> using namespace std; const int MAX=120000; bool flag[MAX]; // flag[i]=ture:marbles可以分为i和sum-i bool tmp_flag[MAX]; int values[7]; // values[i]=j:重量为i的marble有j个 int main() { int cases = 1; int halfValue; while (cin >> values[1] >> values[2] >> values[3] >> values[4] >> values[5] >> values[6]) { int sum = values[1]*1 + values[2]*2 + values[3]*3 + values[4]*4 + values[5]*5 + values[6]*6; if (sum == 0) { break; } cout << "Collection #" << cases++ <<':' << endl; // 如果sum为奇数,肯定不可分 if (sum % 2 != 0) { cout << "Can't be divided." << endl << endl; //注意有空行 continue; } memset(flag,false,sizeof(flag)); memset(tmp_flag,false,sizeof(tmp_flag)); flag[0] = true; // for each type of marble halfValue = sum / 2; for (int i=1; i<=6; i++) { if (flag[halfValue]) { break; } if (values[i] > 0) { // for each value for (int j=0; j<=halfValue; j++) { if (tmp_flag[halfValue]) { break; } if (flag[j]) { for (int k=1; k<=values[i]; k++) { if (tmp_flag[halfValue]) { break; } if (j+i*k > halfValue) { break; } tmp_flag[j+i*k] = true; } } } for (int j=0; j<=halfValue; j++) { flag[j] = flag[j] || tmp_flag[j]; } } } // output if (flag[halfValue]) { cout<<"Can be divided."<<endl<<endl; } else { cout<<"Can't be divided."<<endl<<endl; } } return 0; }