HDU-2255-奔小康赚大钱(KM算法)

Posted 2021-02-12 angel-demon

KM算法的模板题，记录一下

• KM算法

  Accepted

  2255

  468MS

  1756K

  1600 B

  G++

  #include "bits/stdc++.h"
  using namespace std;
  const int INF = 0x3f3f3f3f;
  const int MAXN = 305;
  int mp[MAXN][MAXN];
  int match[MAXN], slack[MAXN];
  int ex_x[MAXN], ex_y[MAXN];
  bool vis_x[MAXN], vis_y[MAXN];
  int n;
  bool dfs(int x) {
      vis_x[x] = true;
      for (int y = 1; y <= n; y++) {
          if (vis_y[y]) {
              continue;
          }
          int gap = ex_x[x] + ex_y[y] - mp[x][y];
          if (gap == 0) {
              vis_y[y] = true;
              if (match[y] == -1 || dfs(match[y])) {
                  match[y] = x;
                  return true;
              } 
          } else {
              slack[y] = min(slack[y], gap);
          }
      }
      return false;
  }
  int KM() {
      memset(match, -1, sizeof(match));
      memset(ex_y, 0 , sizeof(ex_y));
      memset(ex_x, ~INF, sizeof(ex_x));
      for (int i = 1; i <= n; i++) {
          for (int j = 1; j <= n; j++) {
              ex_x[i] = max(ex_x[i], mp[i][j]);
          }
      }
      for (int i = 1; i <= n; i++) {
          memset(slack, INF, sizeof(slack));
          while (true) {
              memset(vis_x, false, sizeof(vis_x));
              memset(vis_y, false, sizeof(vis_y));
              if (dfs(i)) {
                  break;
              }
              int d = INF;
              for (int j = 1; j <= n; j++) {
                  if (!vis_y[j]) {
                      d = min(d, slack[j]);
                  }
              }
              for (int j = 1; j <= n; j++) {
                  if (vis_x[j]) {
                      ex_x[j] -= d;
                  }
                  if (vis_y[j]) {
                      ex_y[j] += d;
                  } else {
                      slack[j] -= d;
                  }
              }
          }
      }
      int res = 0;
      for (int i = 1; i <= n; i++) {
          res += mp[match[i]][i];
      }
      return res;
  }
  int main() {
      while (~scanf("%d", &n)) {
          for (int i = 1; i <= n; i++) {
              for (int j = 1; j <= n; j++) {
                  scanf("%d", &mp[i][j]);
              }
          }
          printf("%d
  ", KM());
      }
      return 0;
  }