Hiho coder: #1200 : Increase Charisma Points
Posted 计算机科学家的世界
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<span style="font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 17.7778px; line-height: 25.3968px; background-color: rgb(255, 255, 255);">时间限制:</span><span style="font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 17.7778px; line-height: 25.3968px; box-sizing: border-box; margin-left: 10px; background-color: rgb(255, 255, 255);">10000ms</span>
单点时限:
1000ms
内存限制:
256MB
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3 10 0 2 3 4 0 2 3 4 0
样例输出
4
算法分析:
显然,可以修改floyd算法,定义一个如下的状态方程
dp(i,j,k)表示图中从i到j走k步的最小代价,则有如下的状态转移方程
dp(i,j,k)=mindp(i,l,k-1)+dp(l,j,k-1) for l = 0,1,2,...n-1
至于原问题的解,我们可以使用二分查找,即给定一个步数s,我们判断在s步内是否存在两个点i,j,使得从i走s步到j,并使用的代价不大于M。
代码:
#include <iostream> #include <string.h> #include <vector> #include <stdlib.h> using namespace std; unsigned int NXUpperPow2(unsigned int v) --v; v |= v >> 1; v |= v >> 2; v |= v >> 4; v |= v >> 8; v |= v >> 16; return ++v; unsigned int NXLowerPow2(unsigned int x) unsigned int v = NXUpperPow2(x); return v == x ? v : v >> 1; unsigned int NXPow2(unsigned int x) int bc = 0; while(x) ++bc; x >>= 1; return bc; class Matrix public: friend inline Matrix operator * (const Matrix &lhs, const Matrix &rhs); friend inline Matrix QuickPow(const int n); public: explicit Matrix(int iScale); Matrix(); public: vector<unsigned int>& operator[] (const int idx) return m_Elem[idx]; const vector<unsigned int> & operator[] (const int idx) const return m_Elem[idx]; void SetScale(int iScale); public: vector<vector<unsigned int > > m_Elem; int m_iScale; ; Matrix pm[32]; class Solution public: bool ReadData(); int GetResult(); private: bool Check(const Matrix &m); public: int N; int M; Matrix cost; ; inline Matrix operator * (const Matrix &lhs, const Matrix &rhs) int iScale = lhs.m_iScale; int mv; Matrix result(iScale); for(int r = 0; r < iScale; ++r) for(int c = 0; c < iScale; ++c) result[r][c] = -1; for(int k = 0; k < iScale; ++k) if(lhs[r][k] == -1 || rhs[k][c] == -1) continue; mv = lhs[r][k] + rhs[k][c]; if(mv < result[r][c]) result[r][c] = mv; return result; inline Matrix QuickPow(const int n) if(n == 1) return pm[0]; int p2 = NXLowerPow2(n); int l2 = NXPow2(n); return p2 == n ? pm[l2 - 1] : pm[l2 - 1] * QuickPow(n - p2); Matrix::Matrix(int iScale) SetScale(iScale); Matrix::Matrix() void Matrix::SetScale(int iScale) m_iScale = iScale; m_Elem.resize(iScale); for(int i = 0; i < iScale; ++i) m_Elem[i].resize(iScale); bool Solution::ReadData() if(! (cin >> N)) return false; cin >> M; cost.SetScale(N); for(int r = 0; r < N; ++r) for(int c = 0; c < N; ++c) cin >> cost[r][c]; cost[r][r] = -1; pm[0] = cost; int l = NXPow2(M); for(int i = 1; i < l; ++i) pm[i] = pm[i- 1] * pm[i - 1]; return true; bool Solution::Check(const Matrix &m) for(int r = 0; r < N; ++r) for(int c = 0; c < N; ++c) if(m[r][c] <= M) return true; return false; int Solution::GetResult() if(!Check(cost)) return 0; int l = 1, r = M; int m; while(l < r) m = (l + r) >> 1; if(Check(QuickPow(m))) l = m + 1; else r = m - 1; while(!Check(QuickPow(l))) --l; return l; int main() Solution so; while(so.ReadData()) cout << so.GetResult() << endl;
描述
Little Ho is playing a role-playing game. There are N cities in the game which are numbered from 1 to N. Every time Little Ho moves to another city his charisma (a kind of character attribute) will increase by 1 point no matter whether the city is visited before. For example if Little Ho’s moving path is 1->2->3->2->3->1 his charisma will increase by 5.
Little Ho wants to maximize his charisma. However moving between cities costs action points. More precisely moving from city i to city j costs him Aij action points. Little Ho wants to know how many points of charisma he can get by using no more than M action points? He may start at any city.
输入
Line 1: N and M, the number of cities and the initial action points.
Line 2~N+1: An N x N matrix A. Aij is the action point cost as described above.
For 30% of the data: 2≤N≤5,1≤M≤50,0≤Aij≤10
For 60% of the data: 2≤N≤50,1≤M≤2000,0≤Aij≤10
For 100% of the data: 2≤N≤100,1≤M≤1,000,000,000,0≤Aij≤20
输出
The maximum points of charisma Little Ho can get.
样例提示
The optimal path is 1->2->3->1->2.
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