【CF1031D】Minimum path

题面

https://www.luogu.org/problem/CF1031D

题解

#include<iostream>
#include<cstdio>
#include<cstdlib>
using namespace std;
const int dx[]={0,1},dy[]={1,0};

char map[2050][2050],mx,mn;
bool vis[2050][2050];
int n,k,f[2050][2050],maxstep,nowl,x0,y0,nx,ny;
struct node{
  int pre,x,y,l;
} que[8500500];

string nows;

void solve (int p) {
  string ans="";
  while (p!=-1) {
    ans.push_back(map[que[p].x][que[p].y]);
    p=que[p].pre;
  }
  int l=ans.size(),i;
  for (i=l-1;i>=0;i--) cout<<ans[i];
  exit(0);
}

int main(){
  int i,j,ii,head,tail;
  ios::sync_with_stdio(false);

  cin>>n>>k;
  for (i=1;i<=n;i++)
    for (j=1;j<=n;j++) cin>>map[i][j];

  if (n==1 && k==0) {
    cout<<map[1][1]<<endl;
    return 0;
  }
  f[1][1]=(map[1][1]=='a');
  for (i=2;i<=n;i++) f[1][i]=f[1][i-1]+(map[1][i]=='a');
  for (i=2;i<=n;i++) f[i][1]=f[i-1][1]+(map[i][1]=='a');

  maxstep=0;
  for (i=2;i<=n;i++)
    for (j=2;j<=n;j++) f[i][j]=max(f[i-1][j],f[i][j-1])+(map[i][j]=='a');
  maxstep=0;
  for (i=1;i<=n;i++)
    for (j=1;j<=n;j++) if (f[i][j]+k>=i+j-1) maxstep=max(maxstep,i+j-1);
  //cout<<maxstep<<endl;
  for (i=1;i<=maxstep;i++) cout<<'a';
  if (maxstep==2*n-1) return 0;
  head=1; tail=0;
  mn=(char)((int)'z'+1);
  for (i=1;i<=n;i++)
    for (j=1;j<=n;j++) if (f[i][j]+k==maxstep && i+j-1==maxstep) {
      for (ii=0;ii<=1;ii++) {
        nx=i+dx[ii]; ny=j+dy[ii];
        if (nx<=n && ny<=n && map[nx][ny]<=mn && (!vis[nx][ny])) {
          vis[nx][ny]=true;
          mn=map[nx][ny];
          que[++tail]=(node){-1,nx,ny,1};
          if (ny==n && nx==n) solve(tail);
        }
      }
  }
  if (maxstep==0) {tail++; que[1]=(node){-1,1,1,1};}
  while (head<=tail) {
    x0=que[head].x; y0=que[head].y;
    if (que[head].l==que[head-1].l+1) {mx=mn; mn=(char)((int)'z'+1);}
    if (map[x0][y0]>mx) {head++; continue;}
    for (ii=0;ii<=1;ii++) {
      nx=x0+dx[ii]; ny=y0+dy[ii];
      if (nx<=n && ny<=n && map[nx][ny]<=mn && (!vis[nx][ny])) {
        vis[nx][ny]=true;
        mn=map[nx][ny];
        que[++tail]=(node){head,nx,ny,que[head].l+1};
        if (ny==n && nx==n) solve(tail);
      }
    }
    head++;
  }
}