SRM335 D1M ExpensiveTravel

TopCoder Statistics - Problem Statement

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$(startRow, startCol)$から$(endRow, endCol)$に移動したい.各マスは$k(1 \leq k \leq 9)$の種類があって,コストは$\frac{1}{k}$である.一回の移動はマスのコストの和が$1$以下でなければならない.何回の移動で$(endRow, endCol)$にたどり着けるか.


コスト和が$1$以下の$(x1, y1) \to (x2, y2)$を辺の重み$1$としてグラフを構成して,dijkstra.

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#include <bits/stdc++.h>

#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define REP(i,k,n) for(int i=k;i<(int)(n);i++)
#define each(it,v) for(__typeof((v).begin()) it=(v).begin();it!=(v).end();it++)
#define INF 1<<30
#define mp make_pair
#define EPS 1e-4

#define fi first
#define se second

using namespace std;
typedef long long ll;
typedef pair<int, int> P;
typedef pair<double, int> D;

int h, w;
int dx[4] = {1,0,-1,0};
int dy[4] = {0,1,0,-1};

bool can(int y, int x) {
  if(0 <= y && y < h && 0 <= x && x < w) return true;
  return false;
}

struct edge {
  int from,to;
  int cost;

  edge(int t,int c) : to(t),cost(c) {}
  edge(int f,int t,int c) : from(f),to(t),cost(c) {}

  bool operator<(const edge &e) const {
      return cost < e.cost;
  }
};

int d[100005];
vector<edge> G[10005];

void dijkstra(int s, int n) {
  priority_queue<P, vector<P>, greater<P> > que;
  rep(i, n) {
      d[i] = INF;
  }

  d[s] = 0;
  que.push(P(0,s));

  while(que.size()) {
      P p = que.top();
      que.pop();

      int v = p.second;
      if(d[v] < p.first) continue;

      rep(i, G[v].size()) {
          edge e = G[v][i];
          if(d[e.to] > d[v] + e.cost) {
              d[e.to] = d[v] + e.cost;
              que.push(P(d[e.to],e.to));
          }
      }
  }
}

class ExpensiveTravel {
  public:
  int minTime(vector <string> m, int startRow, int startCol, int endRow, int endCol) {
      h = m.size(), w = m[0].size();
      int n = h * w;

      double v[55][55];
      memset(v, 0, sizeof(v));
      rep(i, h) {
          rep(j, w) {
              int t = (m[i][j] - '0');
              v[i][j] = t;
          }
      }

      double cost[2505];

      rep(i, n) {
          G[i].clear();
      }

      rep(i, h) {
          rep(j, w) {
              rep(k, n) cost[k] = INF;
              cost[i*w+j] = 0;
              priority_queue<D, vector<D>, greater<D> > que;
              que.push(mp(1.0 / v[i][j], i * w + j));

              while(que.size()) {
                  D di = que.top(); que.pop();
                  int y = di.second / w;
                  int x = di.second % w;

                  rep(k, 4) {
                      int ny = y + dy[k];
                      int nx = x + dx[k];

                      if(can(ny, nx) && cost[ny*w+nx] > di.first + 1.0 / v[ny][nx]) {
                          cost[ny*w+nx] = di.first + 1.0 / v[ny][nx];
                          if(cost[ny*w+nx] < 1.0 + EPS) {
                              que.push(mp(cost[ny*w+nx], ny * w + nx));
                              G[i*w+j].push_back(edge(ny*w+nx, 1));
                          }
                      }
                  }
              }

          }
      }

      startRow--;
      startCol--;
      dijkstra(startRow * w + startCol, n);

      endRow--;
      endCol--;
      if(d[endRow * w + endCol] == INF) {
          return -1;
      }

      return d[endRow * w + endCol];
  }
};
Feb 5th, 2017