USACO算法系列四十六——milk4

   题目：http://www.nocow.cn/index.php/Translate:USACO/milk4

   一个整数使用给定的整数集合当中最小的整数集合进行划分，要求使用的集合最少，其次使用的整数最小。

   第一个方法，我想使用0-1背包进行解决，但是发现做出来可以满足，最小的整数集，但是无法保证集合最小。代码如下：

#include <iostream>#include <fstream>#include <algorithm>#define QSIZE 20001#define PSIZE 100using namespace std;int q;int p;int bucket[PSIZE] = {0};bool quart[QSIZE];bool isuse[PSIZE];int path[QSIZE] = {0};//文件流ifstream fin("milk4.in");ofstream fout("milk4.out");int dpquart(int index){int c = bucket[index];for (int i=c; i <= q; i ++){if (quart[i-c]){quart[i] = true;}//end if}if (quart[q]){return index;}else if (index < p){return dpquart(index+1);}return -1;}bool recordpath(int qnumber, int step, int s, int n){if (qnumber == 0){return true;}else{for (int i=s; i <=n; i ++){int c = bucket[i];if (quart[qnumber-c]){path[step] = i;if (recordpath( qnumber-c, step+1, i, n)){return true;}}//end if}//end for}//end else}int main(){//输入数据fin >> q >> p;for (int i=0; i < p; i ++){fin >> bucket[i];}//初始化数据quart[0] = true;sort(bucket, bucket+p);memset(path, -1, sizeof(int) * QSIZE);int n = dpquart(0);path[0] = n;recordpath(q-bucket[n], 1, 0, n);int pl = 0;while (path[pl] != -1){isuse[path[pl]] = true;pl ++;}//输出结果for (int i=0; i < p; i ++){if (isuse[i]){fout << bucket[i] << " ";}}fout << endl;return 0;}

   第二个方法，使用的DFS深度搜索，加上剪枝的方法。

#include <iostream>#include <fstream>#include <algorithm>#include <string.h>#define QSIZE 20001#define PSIZE 101 using namespace std;int q, p;int bucket[PSIZE];int path[QSIZE];bool isuse[PSIZE];int rtype= 0X07777777;//文件流ifstream fin("milk4.in");ofstream fout("milk4.out");void dpmilk(int num, int index, int step,int type){//剪枝if (type > rtype){return;}if(num == 0){if (type < rtype){memset(isuse, false, sizeof(bool) * PSIZE);rtype = type;for (int i=1; i< step; i ++){isuse[path[i]] = true;}//end for}//类型少，直接覆盖else{bool temp[PSIZE];memset(temp, false, sizeof(bool) * PSIZE);for (int i=1; i< step; i ++){temp[path[i]] = true;}//end forbool flag = false;for (int i=1; i <= p; i ++){if (temp[i]&&!isuse[i]){flag = true;break;}else if (!temp[i] && isuse[i]){flag = false;break;}}if (flag){for (int i=1; i <= p; i ++){isuse[i] = temp[i];}//end for}//end if flag}//类型相同，判断最小编号的罐return;}//end num == 0for (int i=index; i <= p; i ++){if (bucket[i] <= num){path[step] = i;if (path[step-1] != i){dpmilk(num-bucket[i], i, step+1, type+1);}elsedpmilk(num-bucket[i], i, step+1, type);}//end ifelsebreak;}}int main(){//输入数据fin >> q >> p;bucket[0] = 0;for(int i=1; i <= p; i ++){fin >> bucket[i];}sort(bucket, bucket+p+1);if(path[1] == 1){rtype = 1;isuse[1] = true;}else{path[0] = 0;dpmilk(q, 1, 1, 0);}fout << rtype;for (int i=1; i <=p; i ++){if (isuse[i]){fout << " " << bucket[i];}}fout <<endl;return 0;}

    运行超时了，有点悲剧：

Executing... Test 1: TEST OK [0.000 secs, 3088 KB] Test 2: TEST OK [0.011 secs, 3088 KB] Test 3: TEST OK [0.000 secs, 3088 KB] Test 4: TEST OK [0.000 secs, 3088 KB] Test 5: TEST OK [0.000 secs, 3088 KB] Test 6: TEST OK [0.011 secs, 3088 KB] Test 7: TEST OK [0.054 secs, 3088 KB] > Run 8: Execution error: Your program (`milk4') used more than the allotted runtime of 1 seconds (it ended or was stopped at 1.296 seconds) when presented with test case 8. It used 3088 KB of memory.

   再想想如何优化吧！