[kuangbin带你飞]专题一 简单搜索


Links:https://vjudge.net/contest/146840#overview


A - 棋盘问题

比较简单的搜索题

#include
#include
#include
#include
using namespace std;
int n, k, ans;
char map[10][10];
bool line[10];
void dfs(int lie, int num){

    if (num == k){
        ans++;
        return;
    }
    if (lie == n){
        return;
    }
    dfs(lie + 1, num);
    for (int i = 0; iif (map[lie][i] == '#'&&line[i] == false){
            line[i] = 1;
            dfs(lie + 1, num + 1);
            line[i] = 0;
        }
    }
}

int main(){
    while (~scanf("%d%d", &n, &k), n != -1){
        ans = 0;
        memset(line, 0, sizeof(line));
        for (int i = 0; icin >> map[i];
        }
            dfs(0, 0);

        printf("%d\n", ans);
    }
    return 0;
}

B - Dungeon Master

二维广搜变成三维广搜,没什么其他不同

#include
#include
#include
#include
#include
using namespace std;
int l, r, c,ans;
int map[32][32][32];
bool v[32][32][32];
int dl[6] = { 0, 0, 0, 0, 1, -1 };
int dx[6] = { -1, 0, 0, 1, 0, 0 };
int dy[6] = { 0, -1, 1, 0, 0, 0 };
struct point{
    int l;
    int x;
    int y;
    int s;
}beg;
queue que;
int bfs(){
    int ans = -1;
    while (!que.empty()){
        point cnt = que.front();
        que.pop();
        if (map[cnt.l][cnt.x][cnt.y]=='E'){ ans = cnt.s; break; }
        for (int i = 0; i < 6; i++){
            point np={ cnt.l + dl[i], cnt.x + dx[i], cnt.y + dy[i], cnt.s + 1 };
            if (np.l >= 0 && np.l=0 && np.x=0 && np.y < c){
                if (map[np.l][np.x][np.y] != '#'&&v[np.l][np.x][np.y]==0){
                    que.push(np);
                    v[np.l][np.x][np.y] = 1;
                }
            }
        }
    }
    while (!que.empty()){
        que.pop();
    }
    return ans;
}

int main(){
    while (scanf("%d%d%d", &l, &r, &c)){
        memset(v, 0, sizeof(v));
        getchar();
        if (l == 0){ return 0; }
        for (int i = 0; i < l; i++){
            for (int j = 0; j < r; j++){
                for (int k = 0; k < c; k++){
                    map[i][j][k]=getchar();
                    if (map[i][j][k] == 'S'){
                        beg.l = i, beg.x = j, beg.y = k,beg.s=0;
                        v[i][j][k] = 1;
                    }
                }
                getchar();
            }
            getchar();
        }
        que.push(beg);
        int ans = bfs();
        if (ans == -1){
            printf("Trapped!\n");
        }
        else{
            printf("Escaped in %d minute(s).\n",ans);
        }
    }
    return 0;
}

C - Catch That Cow

数轴上的bfs(),给定几个移动,求最少步骤达到要求的位置。

#include
#include
#include
#include
#include
using namespace std;
int fx, fy;
int v[300005];
struct point{
    int x;
    int s;
}beg;
queue que;
int bfs(){
    int ans = -1;
    while (!que.empty()){
        point cnt = que.front();
        que.pop();
        if (cnt.x == fy){
            return cnt.s;
        }
        if (cnt.x + 1 <= 100000&&v[cnt.x + 1] == 0){
            que.push({ cnt.x + 1, cnt.s + 1 });
            v[cnt.x + 1] = 1;
        }
        if (cnt.x - 1 >= 0 && v[cnt.x - 1] == 0){
            que.push({ cnt.x - 1, cnt.s + 1 });
            v[cnt.x - 1] = 1;
        }
        if (cnt.x != 0 &&cnt.x*2<=300000&& v[cnt.x * 2] == 0){
            que.push({ cnt.x * 2, cnt.s + 1 });
            v[cnt.x * 2] = 1;
        }
    }
    return ans;
}


int main(){
    scanf("%d%d", &fx, &fy);
    beg.x = fx, beg.s = 0;
    que.push(beg);
    int astep=bfs();
    printf("%d", astep);
    return 0;
}

D - Fliptile

经典的翻牌子,枚举搜索。

E - Find The Multiple

着给定数字的倍数中全为0.1的,一开始看位数最多为200认为dfs会超时,然后就用了广搜,结果爆内存,最后打了表过的,其实答案用longlong就能存的下,深搜就能解决。

mle的广搜代码

#include
#include
#include
#include
#include
#include
using namespace std;
int n;
struct kk{
    bool ans[105];
    int n;
    int mod;
};

queue que;

kk bfs(){
    kk ans;
    while (~que.empty()){
        kk cnt = que.front();
        que.pop();
        int cnt_mod = cnt.mod;
        int cnt_n = cnt.n;
        if (cnt_n > 101){ continue; }
        cnt.ans[cnt_n] = 1;
        int newmod = (cnt_mod * 10 + 1) % n;
        if (newmod == 0){ ans = cnt; break; }
        cnt.mod = newmod, cnt.n += 1; que.push(cnt);
        cnt.n--;
        cnt.ans[cnt_n] = 0;
        newmod = (cnt_mod*10) % n;
        if (newmod == 0){ ans = cnt; break; }
        cnt.mod = newmod,cnt.n+=1; que.push(cnt);
    }
    while (!que.empty()){ que.pop(); }
    return ans;
}

int main(){
    while (~scanf("%d", &n), n != 0){
        if (n == 1){ printf("1\n"); }
        else if (n == 0){ printf("0\n"); }
        else{
            kk beg, ans;
            beg.ans[0] = 1;
            beg.mod = 1, beg.n = 1;
            que.push(beg);
            ans = bfs();
            int k = ans.n;
            for (int i = 0; i <= k; i++){
                printf("%d", ans.ans[i]);
            }
            printf("\n");
        }
    }
    return 0;
}

F - Prime Path

很经典的搜索题了。

#include
#include
#include
#include
#include
#include
#include
#include
using namespace std;
int n,beg,en;
bool isprim[10000];
bool v[10000];
void is_prim(){
    for (int i = 1000; i <= 9999; i++){
        bool r = true;
        for (int j = 2; j < sqrt((double)i) + 1; j++){
            if (i%j == 0){ r = false; break; }
        }
        if (r == true){ isprim[i] = true; }
    }
}

struct N{
    int step;
    int num[4];
};
queue que;

int getnum(int *n){
    return n[0] * 1000 + n[1] * 100 + n[2] * 10 + n[3];
}

int bfs(){
    int ans = 0;
    while (!que.empty()){
        N cnt = que.front();
        que.pop();
        int cntnum = getnum(cnt.num);
        //int cntnum = cnt.num[0] * 1000 + cnt.num[1] * 100 + cnt.num[2] * 10 + cnt.num[3];
        v[cntnum] = true;
        if (cntnum == en){ ans = cnt.step; break; }
        cnt.step++;
        for (int k = 0; k < 4; k++){
            int cc = cnt.num[k];
            for (int i = 0; i < 10; i++){
                cnt.num[k] = i;
                int newnum = getnum(cnt.num);
                if (v[newnum] == 0 && isprim[newnum]){
                    que.push(cnt);
                }
            }
            cnt.num[k] = cc;
        }
    }
    while (!que.empty()){ que.pop(); }
    return ans;
}

int main(){
    is_prim();
    int t;
    scanf("%d", &t);
    while (t--){
        memset(v, 0, sizeof(v));
        scanf("%d%d", &beg, &en);
        N b;
        for (int i = 3; i >=0; i--){
            b.num[i] = beg % 10;
            beg /= 10;
        }
        b.step = 0;
        que.push(b);
        int ans = bfs();
        printf("%d\n", ans);
    }
    return 0;
}

G - Shuffle’m Up

模拟洗牌的搜索题

#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
using namespace std;
string target;
int len;
set<string> s;
struct N{
    string str;
    int step;
};

queue que;

string getstr(string a,string b){
    string cnt = "";
    for (int i = 0; i < len; i++){
        cnt.push_back(a[i]);
        cnt.push_back(b[i]);
    }
    return cnt;
}


int bfs(){
    int ans = -1;
    while (!que.empty()){
        N cnt = que.front();
        que.pop();
        string cntstr = cnt.str;
        s.insert(cntstr);
        if (cntstr == target){ ans = cnt.step; break; }
        string a = cntstr.substr(0, len);
        string b = cntstr.substr(len, 2 * len);
        //string newa = getstr(a, b);
        //if (!s.count(newa)){
        //  s.insert(newa);
        //  que.push({ newa, cnt.step + 1 });
        //}
        string newb = getstr(b, a);
        if (!s.count(newb)){
            s.insert(newb);
            que.push({ newb, cnt.step + 1 });
        }
    }
    while (!que.empty()){ que.pop(); }
    return ans;
}

int main(){
    int t;
    string a, b;
    scanf("%d", &t);
    for(int k=1;k<=t;k++){
        s.clear();
        scanf("%d", &len);
        cin >> a >> b >> target;
        N start = { a + b, 0 };
        que.push(start);
        int ans = bfs();
        printf("%d %d\n", k, ans);
    }
    return 0;
}

H - Pots

两个水杯倒水,给定几个操作,要求最少步骤使一个杯子里的水等于c,并且输出步骤,这点比较烦,所以我在bfs队列的结构体里加了一个string存步骤,就很方便了。纯属对代码,注意无法完成要输出impossible。

#include
#include
#include
#include
#include
using namespace std;
int a, b, c;
bool v[105][105];
struct wa{
    int l, r;
    int step;
    string str;
};
queue que;
wa bfs(){
    wa ans = {0,0,-1,""};
    while (!que.empty()){
        wa cnt = que.front();
        que.pop();
        int step = cnt.step;
        if (cnt.l == c || cnt.r == c){ return cnt; }
        if (cnt.l > 0){//a倒水
            wa newp = { 0, cnt.r, step + 1, cnt.str };
            newp.str.insert(newp.str.length(), "DROP(1)\n");
            if (v[newp.l][newp.r] == 0){
                v[newp.l][newp.r] = 1;
                que.push(newp);
            }
        }
        if (cnt.l.r, step + 1, cnt.str };
            nnewp.str.insert(nnewp.str.length(), "FILL(1)\n");
            if (v[nnewp.l][nnewp.r] == 0){
                v[nnewp.l][nnewp.r] = 1;
                que.push(nnewp);
            }
        }
        if (cnt.r.l - b + cnt.r, b, step + 1, cnt.str };
            if (cnt.l.r){
                nnewp.l = 0, nnewp.r = cnt.r + cnt.l;
            }
            nnewp.str.insert(nnewp.str.length(), "POUR(1,2)\n");
            if (v[nnewp.l][nnewp.r] == 0){
                v[nnewp.l][nnewp.r] = 1;
                que.push(nnewp);
            }
        }
        if (cnt.r >0){//b倒水
            wa newp = { cnt.l, 0, step + 1, cnt.str };
            newp.str.insert(newp.str.length(), "DROP(2)\n");
            if (v[newp.l][newp.r] == 0){
                v[newp.l][newp.r] = 1;
                que.push(newp);
            }
        }
        if (cnt.r.l,b, step + 1, cnt.str };
            nnewp.str.insert(nnewp.str.length(), "FILL(2)\n");
            if (v[nnewp.l][nnewp.r] == 0){
                v[nnewp.l][nnewp.r] = 1;
                que.push(nnewp);
            }
        }
        if (cnt.l.r-a+cnt.l, step + 1, cnt.str };
            if (cnt.r.l){
                nnewp.r = 0, nnewp.l = cnt.r + cnt.l;
            }
            nnewp.str.insert(nnewp.str.length(), "POUR(2,1)\n");
            if (v[nnewp.l][nnewp.r] == 0){
                v[nnewp.l][nnewp.r] = 1;
                que.push(nnewp);
            }
        }
    }
    return ans;
}

int main(){
    cin >> a >> b >> c;
    wa beg = { 0, 0, 0, "" };
    v[0][0] = 1;
    que.push(beg);
    wa ans=bfs();
    if (ans.step == -1){
        cout << "impossible\n";
    }
    else{
        cout << ans.step << endl;
        cout << ans.str;
    }
    return 0;
}

I - Fire Game

可以在两个地方点火,问所有草地被烧着的最短时间,数据较小,枚举点就行,两个点相同时只往队列里加一个点。
oj炸了,不知道代码对不对

#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
using namespace std;
int N, M;
int total,cntnum;
char map[105][105];
bool v[105][105];
int dx[4] = { -1, 0, 0, 1 };
int dy[4] = { 0, -1, 1, 0 };

struct sit{
    int x,y;
    int step;
};
queue que;


int bfs(){
    int ans = 0x3f3f;
    while (!que.empty()){
        sit cnt = que.front();
        que.pop();
        cntnum++;
        if (cntnum == total){ ans = cnt.step; break; }
        for (int i = 0; i < 4; i++){
            sit newp = { cnt.x + dx[i], cnt.y + dy[i], cnt.step + 1 };
            if (newp.x >= 0 && newp.x < N&&newp.y >= 0 && newp.y < M&&v[newp.x][newp.y] == 0&&map[newp.x][newp.y]=='#'){
                v[newp.x][newp.y] = 1;
                que.push(newp);
            }
        }
    }
    while (!que.empty()){ que.pop(); }
    return ans;
}

int main(){
    int t;
    scanf("%d", &t);
    for (int k = 1; k <= t; k++){
        scanf("%d%d",&N, &M);
        for (int i = 0; i < N; i++){
            scanf("%s", map[i]);
        }
        total =cntnum= 0;
        for (int i = 0; i < N; i++){
            for (int j = 0; j < M; j++){
                if (map[i][j] == '#'){ total++; }
            }
        }
        int ans = 0x3f3f;
        for (int i = 0; i < N; i++){
            for (int j = 0; j < M; j++){
                for (int k = 0; k < N; k++){
                    for (int l = 0; l < M; l++){
                        if (map[i][j] == '#'&&map[k][l] == '#'){
                            cntnum = 0;
                            memset(v, 0, sizeof(v));
                            sit beg = { i, j, 0 };
                            v[i][j] = 1;
                            que.push(beg);
                            if (i != k||j != l){
                                sit beg1 = {k, l, 0};
                                que.push(beg1);
                                v[k][l] = 1;
                            }
                            ans = min(ans, bfs());
                        }
                    }
                }
            }
        }
        printf("Case %d: ", k);
        if (ans == 0x3f3f){ printf("-1\n"); }
        else{ printf("%d\n",ans); }
    }
    return 0;
}

J - Fire!

有人有火,着火的地方不能走,问逃出去的最少步骤。
注意清空队列。

#include
#include
#include
#include
#include
#include
#include
#include
using namespace std;
int N, M;
char map[1005][1005];
bool fire[1005][1005];
int dx[4] = { -1, 0, 0, 1 };
int dy[4] = { 0, -1, 1, 0 };

struct sit{
    int x, y;
    int step;
    bool is_fire;
};
queue que;


int bfs(){
    int ans = -1;
    while (!que.empty()){
        sit cnt = que.front();
        que.pop();
        for (int i = 0; i < 4; i++){
            sit newp = { cnt.x + dx[i], cnt.y + dy[i], cnt.step + 1, cnt.is_fire };
            if (newp.is_fire){
                if (newp.x >= 0 && newp.x < N&&newp.y >= 0 && newp.y < M&&map[newp.x][newp.y] != '#'&&fire[newp.x][newp.y] == 0){
                    fire[newp.x][newp.y] = 1, que.push(newp);
                }
            }
            else{
                if (newp.x < 0 || newp.y < 0 || newp.x >= N || newp.y >= M){ ans = newp.step; return ans; }
                else{
                    if (fire[newp.x][newp.y] == 0 && map[newp.x][newp.y] != '#'){
                        fire[newp.x][newp.y] = 1; que.push(newp);
                    }
                }
            }
        }
    }
    return ans;
}

int main(){
    int t;
    scanf("%d", &t);
    while (t--){
        memset(fire, 0, sizeof(fire));
        scanf("%d%d", &N, &M);
        for (int i = 0; i < N; i++){
            scanf("%s", map[i]);
        }
        sit p = { 0, 0, 0, 0 }, f = { 0, 0, 0, 1 };
        for (int i = 0; i < N; i++){
            for (int j = 0; j < M; j++){
                if (map[i][j] == 'J'){ p.x = i, p.y = j; }
                else if (map[i][j] == 'F'){ f.x = i, f.y = j; fire[f.x][f.y] = 1; que.push(f); }
            }
        }
        fire[p.x][p.y] = 1;
        que.push(p);
        int ans = bfs();
        while (!que.empty()){ que.pop(); }
        if (ans == -1){ printf("IMPOSSIBLE\n"); }
        else{ printf("%d\n", ans); }
    }
    return 0;
}

M - 非常可乐

经典模拟广搜,

#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
using namespace std;
int S, N, M;
struct sit{
    int a, b, c;
    int step;
};
queue que;
bool v[101][101][101];

int bfs(){
    int ans = -1;
    while (!que.empty()){
        sit cnt = que.front();
        que.pop();
        if ((cnt.a == S / 2 && cnt.b == S / 2) || (cnt.a == S / 2 && cnt.c == S / 2) || (cnt.b == S / 2 && cnt.c == S / 2)){ ans = cnt.step; break; }
        if (cnt.a != 0){
            sit newp = { cnt.a - N + cnt.b, N, cnt.c,cnt.step+1 }; if (v[newp.a][newp.b][newp.c] == 0){ v[newp.a][newp.b][newp.c] = 1; que.push(newp); } 
            sit newp1 = { cnt.a - M + cnt.c, cnt.b, M, cnt.step + 1 };
            if (v[newp1.a][newp1.b][newp1.c] == 0){ v[newp1.a][newp1.b][newp1.c] = 1; que.push(newp1); }
        }
        if (cnt.b != 0){
            sit newp = { cnt.a + cnt.b, 0, cnt.c, cnt.step + 1 }; if (v[newp.a][newp.b][newp.c] == 0){ v[newp.a][newp.b][newp.c] = 1; que.push(newp); }
            if (M - cnt.c >= cnt.b){ sit newp1 = { cnt.a, 0, cnt.c + cnt.b, cnt.step + 1 }; if (v[newp1.a][newp1.b][newp1.c] == 0){ v[newp1.a][newp1.b][newp1.c] = 1; que.push(newp1); } }
            else{ sit newp1 = { cnt.a, cnt.b - M + cnt.c, M, cnt.step + 1 }; if (v[newp1.a][newp1.b][newp1.c] == 0){ v[newp1.a][newp1.b][newp1.c] = 1; que.push(newp1); } }
        }
        if (cnt.c != 0){
            sit newp = { cnt.a + cnt.c, cnt.b, 0, cnt.step + 1 }; if (v[newp.a][newp.b][newp.c] == 0){ v[newp.a][newp.b][newp.c] = 1; que.push(newp); }
            if (N - cnt.b >= cnt.c){ sit newp1 = { cnt.a, cnt.b + cnt.c, 0, cnt.step + 1 }; if (v[newp1.a][newp1.b][newp1.c] == 0){ v[newp1.a][newp1.b][newp1.c] = 1; que.push(newp1); } }
            else{ sit newp1 = { cnt.a, N, cnt.c - N + cnt.b, cnt.step + 1 }; if (v[newp1.a][newp1.b][newp1.c] == 0){ v[newp1.a][newp1.b][newp1.c] = 1; que.push(newp1); } }
        }
    }
    while (!que.empty()){ que.pop(); }
    return ans;
}

int main(){
    while (~scanf("%d%d%d",&S, &N, &M),S!=0){
        if (S % 2 != 0){ printf("NO\n"); }
        else{
            memset(v, 0, sizeof(v));
            v[S][0][0] = 1;
            sit beg = { S, 0, 0, 0 };
            que.push(beg);
            int ans = bfs();
            if (ans != -1)
                printf("%d\n", ans);
            else printf("NO\n");
        }
    }
    return 0;
}

N - Find a way

两个到某一个相同麦当劳的时间和最小值,一开始对每一个麦当劳广搜两个人,然后超时了,然后改成两个人搜索麦当劳最短路径,然后找最小和。

#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
using namespace std;
int N, M;
struct point{
    int x, y;
    int step;
};
vector ansa, ansb;
queue que;
char map[205][205];
bool v[205][205];

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

void bfs(bool yyy){
    while (!que.empty()){
        point cnt = que.front();
        que.pop();
        if (map[cnt.x][cnt.y] == '@'){ if (yyy) ansa.push_back(cnt); else ansb.push_back(cnt); }
        for (int i = 0; i < 4; i++){
            point newp = { cnt.x + dx[i], cnt.y + dy[i], cnt.step + 1 };
            if (newp.x >= 0 && newp.x < N&&newp.y >= 0 && newp.y < M&&map[newp.x][newp.y]!='#'&&v[newp.x][newp.y] == 0){
                v[newp.x][newp.y] = 1;
                que.push(newp);
            }
        }
    }
}

int main(){
    int ax, ay, bx, by;
    while (~scanf("%d%d", &N, &M)){
        ansa.clear(), ansb.clear();
        for (int i = 0; i < N; i++){
            scanf("%s", &map[i]);
        }
        point a = { 0, 0, 0 }, b = {0,0,0};
        for (int i = 0; i < N; i++){
            for (int j = 0; j < M; j++){
                if (map[i][j] == 'Y'){ a.x = i, a.y = j; }
                else if (map[i][j] == 'M'){ b.x = i, b.y = j; }
            }
        }
        memset(v, 0, sizeof(v));
        que.push(a);
        v[a.x][a.y] = 1;
        bfs(1);
        memset(v, 0, sizeof(v));
        que.push(b);
        v[b.x][b.y] = 1;
        bfs(0);
        int ans = 0x3f3f3f;
        int len = ansa.size();
        for (int i = 0; i < len; i++){
            for (int j = 0; j < len; j++){
                if (ansa[i].x == ansb[j].x&&ansa[i].y == ansb[j].y){
                    ans = min(ans, ansa[i].step + ansb[j].step);
                }
            }
        }
        printf("%d\n", ans * 11);
    }
    return 0;
}

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