ZISUOJ 数据结构--队列及其应用

说明：

        基本都是bfs的常见模板题型，思路都很直接，不过后面有两道题很搞心态，它们给的坐标x、y是反的，导致刚开始一直错。题目还是要看仔细，不能先入为主。

题目列表：

问题 A: 围圈报数(完善程序) 

参考题解：

#include
#include
using namespace std;
int n,m,k=1,tmp;
queue<int> arr;
int main()
{
    cin>>n>>m;
    for(int i=1;i<=n;i++)
        arr.push(i);
        // _____(1)____//依次进入队列
        while(arr.size())
        // while(_____(2)_____)//判断队列里是否还有人
        {
            tmp=arr.front();
            if(k%m==0)
                cout<" ";
            else
                arr.push(tmp);
                // ______(3)______//如果不是第m个人，则重新入队
            // _____(4)_____//从队列里删除
            arr.pop();
            k++;
        }
    return 0;
}

问题 B: 围圈报数

参考题解：

#include 
#include 
using std::cin;
using std::cout;
int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    int n,m,count = 0;cin >> n >> m;
    std::queue<int> q;
    for(int i = 1;i<=n;i++) q.push(i);
    while(q.size()){
        auto t = q.front();
        count++;
        if(count%m==0) {
            cout << t << ' ';
        }else {
            q.push(t);
        }
        q.pop();
    }
    cout << std::endl;
    return 0;
}

问题 C: 报数相同次数circle

参考题解：

#include 
#include 
using std::cin;
using std::cout;
int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    int n;cin >> n;
    int a,b;cin >> a >> b;
    std::queue<int> q1,q2;
    for(int i = 1;i<=a;i++) q1.push(i);
    for(int i = 1;i<=b;i++) q2.push(i);
    int count = 0;
    for(int i = 1;i<=n;i++) {
        auto t1 = q1.front(),t2 = q2.front();
        if(t1==t2) count++;
        q1.push(t1),q2.push(t2);
        q1.pop(),q2.pop();
    }
    cout << count << std::endl;
    return 0;
}

问题 D: 最小倍数

参考题解：

#include 
#include 
using std::cin;
using std::cout;
using ll = long long;
ll n,x;
void bfs() {
    std::queue q;
    q.push(1);
    while(q.size()) {
        x = q.front();q.pop();
        if(x%n==0&&x>=n) {
            cout << x << '\n';
            return;
        }
        q.push(x*10);
        q.push(x*10+1);
    }
    cout << x << '\n';
}
int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    while(cin >> n,n) {
        bfs();
    }
    return 0;
}

问题 E: 迷宫的最短路径

参考题解：

#include 
#include 
#include 
using std::cin;
using std::cout;
int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    constexpr int N = 1e2+5;
    int sx = 1,sy = 1,ex = 1,ey = 1;
    struct node {
        int x,y,s;
    }t,t1;
    char g[N][N];
    bool vis[N][N];
    memset(vis,false,sizeof vis);
    int dx[] = {0,0,-1,1};
    int dy[] = {-1,1,0,0};
    std::queue q;
    int n,m;cin >> n >> m;
    for(int i = 1;i<=n;i++) {
        for(int j = 1;j<=m;j++) {
            cin >> g[i][j];
            if(g[i][j]=='S') {
                sx=i,sy=j;
            }else if(g[i][j]=='G') {
                ex=i,ey=j;
            }
        }
    }
    auto bfs = [&]()->void{
        t.x = sx,t.y = sy,t.s = 0;
        q.push(t);
        vis[sx][sy] = true;
        while(!q.empty()) {
            t = q.front();q.pop();
            if(t.x==ex&&t.y==ey) {
                cout << "The min steps are:" << t.s << "!\n";
                return;
            }
            for(int i = 0;i<4;i++) {
                int u = t.x+dx[i],v = t.y+dy[i];
                if(u<1||u>n||v<1||v>m||vis[u][v]||g[u][v]=='#') continue;
                vis[u][v] = true;
                t1.x = u,t1.y = v,t1.s = t.s+1;
                q.push(t1);
            }
        }
        cout << "sorry!\n";
    };
    bfs();
    return 0;
}

问题 F: 象棋中的马之进阶

参考题解：

#include 
#include 
#include 
using std::cin;
using std::cout;
int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    constexpr int N = 15;
    struct node {
        int x,y,s;
    }t,t1;
    int dx[] = {-1,1,2,2,1,-1,-2,-2};
    int dy[] = {2,2,1,-1,-2,-2,-1,1};
    int sx,sy,ex,ey;
    bool vis[N][N];
    memset(vis,false,sizeof vis);
    cin >> sy >> sx >> ey >> ex;
    std::queue q;
    auto bfs = [&]() ->void {
        t.x = sx,t.y = sy,t.s = 0;
        vis[sx][sy] = true;
        q.push(t);
        while(!q.empty()) {
            t = q.front();q.pop();
            if(t.x==ex&&t.y==ey) {
                cout << t.s << std::endl;
                return;
            }
            for(int i = 0;i<8;i++) {
                int u = t.x+dx[i],v = t.y+dy[i];
                if(u<1||u>10||v<1||v>9||vis[u][v]) continue;
                vis[u][v] = true;
                t1.x = u,t1.y = v,t1.s = t.s+1;
                q.push(t1);
            }
        }
        cout << 0 << std::endl;
    };
    bfs();
    return 0;
}

 

问题 G: 迷宫探险

参考题解：

#include 
#include 
#include 
#include 
using std::cin;
using std::cout;
int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    constexpr int N = 1e2+5;
    struct node {
        int x,y,s;
        bool operator > (const node &W) const {
            return s > W.s;
        }
    }t,t1;
    char g[N][N];
    bool vis[N][N];
    int dx[] = {0,0,-1,1};
    int dy[] = {-1,1,0,0};
    int n,sx = 1,sy = 1,ex = 1,ey = 1;
    std::priority_queue,std::greater> pq;
    auto bfs = [&]() ->void {
        while(!pq.empty()) pq.pop();
        memset(vis,false,sizeof vis);
        t.x = sx,t.y = sy,t.s = 0;
        vis[sx][sy] = true;
        pq.push(t);
        while(!pq.empty()) {
            t = pq.top();pq.pop();
            if(t.x==ex&&t.y==ey) {
                cout << t.s << '\n';
                return;
            }
            for(int i = 0;i<4;i++) {
                int u = t.x+dx[i],v = t.y+dy[i];
                if(u<1||u>n||v<1||v>n||vis[u][v]||g[u][v]=='#') continue;
                vis[u][v] = true;
                int ds = 1;
                if(g[u][v]!='.') ds += int(g[u][v]^48);
                t1.x = u,t1.y = v,t1.s = t.s+ds;
                pq.push(t1);
            }
        }
        cout << -1 << '\n';
    };
    while(cin >> n) {
        ex = n,ey = n;
        for(int i = 1;i<=n;i++) {
            for(int j = 1;j<=n;j++) {
                cin >> g[i][j];
            }
        }
        bfs();
    }
    return 0;
}

问题 H: 迷宫

 

参考题解：

#include 
#include 
#include 
#include 
using std::cin;
using std::cout;
int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    constexpr int N = 1e2+5;
    struct node {
        int x,y,s;
    }t,t1;
    char g[N][N];
    bool vis[N][N];
    int dx[] = {0,0,-1,1};
    int dy[] = {-1,1,0,0};
    int sx,sy,ex,ey,k,n,m;
    std::queue q;
    auto bfs = [&]()->void {
        memset(vis,false,sizeof vis);
        while(!q.empty()) q.pop();
        t.x = sx,t.y = sy,t.s = -1;
        vis[sx][sy] = true;
        q.push(t);
        while(!q.empty()) {
            t = q.front();q.pop();
            if(t.x==ex&&t.y==ey&&t.s<=k) {
                cout << "yes\n";
                return;
            }
            for(int i = 0;i<4;i++) {
                t1.x = t.x+dx[i],t1.y = t.y+dy[i];
                int &u = t1.x,&v = t1.y;
                while(u>=1&&u<=n&&v>=1&&v<=m&&g[u][v]=='.') {
                    if(!vis[u][v]) {
                        t1.s=t.s+1;
                        vis[u][v] = true;
                        q.push(t1);
                    }
                    u+=dx[i],v+=dy[i];
                }
            }
        }
        cout << "no\n";
    };
    int T = 1;cin >> T;
    while(T--) {
        cin >> n >> m;
        for(int i = 1;i<=n;i++) {
            for(int j = 1;j<=m;j++) {
                cin >> g[i][j];
            }
        }
        cin >> k >> sy >> sx >> ey >> ex;
        bfs();
    }
    return 0;
}