钢条切割

来源：互联网发布：进程调度算法实验报告编辑：程序博客网时间：2024/06/11 03:48
#include <iostream>#include <vector>#include <algorithm>#include <iterator>using namespace std;int cutRod(int *p, int n){if (n == 0)return 0;int q = -1;for(int i = 1; i <= n; i++)q = max(q, p[i]+cutRod(p, n-i));   return q;}//自顶向下辅助函数 int memoizedCutRodAux(int *p, int n, int *r){if (r[n] >= 0)return r[n];int q = -1;if (n == 0)q = 0;else{for (int i = 1; i <= n; i++)q = max(q, p[i]+memoizedCutRodAux(p, n-i, r));}r[n] = q;return q;}//带备忘录的自顶向下，用r[i]记录已经求出的最优解，避免重复调用 int memoizedCutRod(int *p, int n){int r[11] = {};for (int i = 0; i <= n; i++)r[i] = -1;int q = memoizedCutRodAux(p, n, r);return q;    }//自底向下 int bottomUpCutRod(int *p, int n){int r[11] = {0};int q; for (int j = 1; j <= n; j++){q = -1;for (int i = 1; i <= j; i++)q = max(q, p[i]+r[j-i]);r[j] = q;}return r[n];           }//下面使用的是vector...都生疏了...T_T//r[]: 记录最优解//s[]：记录最优解的第一段的钢条的切割长度pair<vector<int>, vector<int> > extendedBottomUpCutRod(vector<int> p, int n){vector<int> r, s(p.size());int q = -1;r.push_back(0);for (int j = 1; j <= n; j++){q = -1;int i;for (i = 1; i <= j; i++){             if (q < p[i] + r[j-i]) { q = p[i] + r[j-i]; s[j] = i; }}r.push_back(q);}return make_pair(r, s);}void printCutRodSolution(vector<int> p, int n){pair<vector<int>, vector<int> > vvp =extendedBottomUpCutRod(p, n);cout << vvp.first.at(n) << endl;vector<int> s = vvp.second;while (n > 0){cout << s[n] << endl;n -= s[n];}}int main(){//使price[0]为0，在程序里不使用， //只是为了使截断的左右两端与数组下标保持一致，方便代码  int price[] = {0, 1, 5, 8, 9, 10, 17, 17, 20, 24, 30};int n;cout << "请输入n (ctrl+z结束):";while (cin >> n){cout << "n=" << n << endl;cout << "普通递归法：\n" << cutRod(price, n) << endl;cout << "带备忘录的自顶向下法：\n" << memoizedCutRod(price, n) << endl; cout << "自底向下法：\n" << bottomUpCutRod(price, n) << endl;vector<int> p(price, price+sizeof(price)/sizeof(price[0]));cout << "扩展的自底向下法：" << endl;printCutRodSolution(p, n);cout << endl << "请输入n (ctrl+z结束): ";}system("pause");return 0;}
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