HDU - 2732 Leapin' Lizards(ISAP Dinic EK)

题目大意：给出两张地图，第一章地图代表的是每根柱子的高度，第二张地图代表的是每只蜥蜴所在的位置
每根柱子只能站一只蜥蜴，蜥蜴离开该柱子时，柱子的高度会下降一个单元，当柱子的高度为0时，该柱子将不可用
现在给出每只蜥蜴能跳跃的距离，问最少有多少只蜥蜴逃不出来

解题思路：将柱子拆成2个点，权值为柱子的高度
将每只蜥蜴所在的位置和超级源点连接，权值为1
将能通到外界的柱子连接到超级汇点，权值为INF
如果柱子间的距离满足蜥蜴跳跃的距离，连接起来，权值为INF
这样图就完成了

ISAP：

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
#define N 2010
#define INF 0x3f3f3f3f

struct Edge {
    int from, to, cap, flow;
    Edge() {}
    Edge(int from, int to, int cap, int flow): from(from), to(to), cap(cap), flow(flow) {}
};

struct ISAP {
    int p[N], num[N], cur[N], d[N];
    int t, s, n, m;
    bool vis[N];

    vector<int> G[N];
    vector<Edge> edges;

    void init(int n, int m) {
        this->n = n; this->m = m;
        for (int i = 0; i <= n; i++) {
            G[i].clear();
            d[i] = INF;
        }
        edges.clear();
    }

    void AddEdge(int from, int to, int cap) {
        edges.push_back(Edge(from, to, cap, 0));
        edges.push_back(Edge(to, from, 0, 0));
        int m = edges.size();
        G[from].push_back(m - 2);
        G[to].push_back(m - 1);
    }

    bool BFS() {
        memset(vis, 0, sizeof(vis));

        queue<int> Q;
        d[t] = 0;
        vis[t] = 1;
        Q.push(t);

        while (!Q.empty()) {
            int u = Q.front();
            Q.pop();

            for (int i = 0; i < G[u].size(); i++) {
                Edge &e = edges[G[u][i] ^ 1];
                if (!vis[e.from] && e.cap > e.flow) {
                    vis[e.from] = true;
                    d[e.from] = d[u] + 1;
                    Q.push(e.from);
                }
            }
        }
        return vis[s];
    }

    int Augment() {
        int u = t, flow = INF;
        while (u != s) {
            Edge &e = edges[p[u]];
            flow = min(flow, e.cap - e.flow);
            u = edges[p[u]].from;
        }

        u = t;
        while (u != s) {
            edges[p[u]].flow += flow;
            edges[p[u] ^ 1].flow -= flow;
            u = edges[p[u]].from;
        }
        return flow;
    }

    int Maxflow(int s, int t) {
        this->s = s; this->t = t;
        int flow = 0;
        BFS();
        if (d[s] > n)
            return 0;

        memset(num, 0, sizeof(num));
        memset(cur, 0, sizeof(cur));
        for (int i = 0; i < n; i++)
            if (d[i] < INF)
                num[d[i]]++;
        int u = s;

        while (d[s] <= n) {
            if (u == t) {
                flow += Augment();
                u = s;
            }
            bool ok = false;
            for (int i = cur[u]; i < G[u].size(); i++) {
                Edge &e = edges[G[u][i]];
                if (e.cap > e.flow && d[u] == d[e.to] + 1) {
                    ok = true;
                    p[e.to] = G[u][i]; 
                    cur[u] = i;
                    u = e.to;
                    break;
                }
            }

            if (!ok) {
                int Min = n;
                for (int i = 0; i < G[u].size(); i++) {
                    Edge &e = edges[G[u][i]];
                    if (e.cap > e.flow)
                        Min = min(Min, d[e.to]);
                }
                if (--num[d[u]] == 0)
                    break;
                num[d[u] = Min + 1]++;
                cur[u] = 0;
                if (u != s)
                    u = edges[p[u]].from;
            }
        }
        return flow;
    }
};

ISAP isap;
#define M 110
#define ABS(x) ((x) > 0 ? x : (-(x)))
#include <cstring>
char map1[25][M], map2[25][M];
int n, d, m, cas = 1;

void init() {
    scanf("%d%d", &n, &d);
    for (int i = 0; i < n; i++)
        scanf("%s", map1[i]);
    for (int i = 0; i < n; i++)
        scanf("%s", map2[i]);

    m = strlen(map1[0]);
    int s = n * m * 2, t = s + 1;
    isap.init(t, 0);

    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++) 
            if (map1[i][j] - ‘0‘) {
                isap.AddEdge(i * m + j, n * m + i * m + j, map1[i][j] - ‘0‘);
            }

    int cnt = 0;
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
            if (map2[i][j] == ‘L‘) {
                isap.AddEdge(s, i * m + j, 1);
                cnt++;
            }

    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++) {
            if (i < d || j < d || j >= m - d || i >= n - d) {
                isap.AddEdge(i * m + j + n * m, t, INF);
            }
        }

    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 (!(i == k && l == m) && d >= ABS(i - k) + ABS(j - l))
                        isap.AddEdge(i * m + j + n * m, k * m + l, INF);
    int ans = isap.Maxflow(s, t);

    printf("Case #%d: ", cas++);
    if (ans == cnt) 
        printf("no lizard was left behind.\n");
    else if(ans + 1 == cnt)
        printf("1 lizard was left behind.\n");
    else 
        printf("%d lizards were left behind.\n", cnt - ans);
}

int main() {
    int test;
    scanf("%d", &test);
    while (test--) {
        init();

    }
    return 0;
}

EK

#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>
#include <vector>
using namespace std;
#define N 1010
#define INF 0x3f3f3f3f


struct Edge{
    int from, to, cap, flow;
    Edge() {}
    Edge(int from, int to, int cap, int flow): from(from), to(to), cap(cap), flow(flow){}
};

struct EK{
    vector<int> G[N];
    vector<Edge> edges;
    int s, t, n, m, p[N];
    bool vis[N];

    void init(int n, int m) {
        this->n = n; this->m = m;
        for (int i = 0; i <= n; i++)
            G[i].clear();
        edges.clear();
    }

    void AddEdge(int from, int to, int cap) {
        edges.push_back(Edge(from, to, cap, 0));
        edges.push_back(Edge(to, from, 0, 0));
        int m = edges.size();
        G[from].push_back(m - 2);
        G[to].push_back(m - 1);
    }

    bool BFS() {
        queue<int> q;
        memset(vis, 0, sizeof(vis));
        vis[s] = 1;
        q.push(s);

        while (!q.empty()) {
            int u = q.front();
            q.pop();

            for (int i = 0; i < G[u].size(); i++) {
                Edge &e = edges[G[u][i]];
                if (!vis[e.to] && e.cap > e.flow) {
                    vis[e.to] = true;
                    p[e.to] = G[u][i];
                    if (e.to == t)
                        return true;
                    q.push(e.to);
                }
            }
        }
        return false;
    }

    int Augment() {
        int flow = INF, u = t;
        while (u != s) {
            Edge &e = edges[p[u]];
            flow = min(flow, e.cap - e.flow);
            u = e.from;
        }

        u = t;
        while (u != s) {
            edges[p[u]].flow += flow;
            edges[p[u] ^ 1].flow -= flow;
            u = edges[p[u]].from;
        }
        return flow;
    }

    int Maxflow(int s, int t) {
        this->s = s; this->t = t;
        int flow = 0;

        while (BFS()) {
            flow += Augment();
        }
        return flow;
    }
};

EK ek;



#define M 110
#define ABS(x) ((x) > 0 ? x : (-(x)))
#include <cstring>
char map1[25][M], map2[25][M];
int n, d, m, cas = 1;

void init() {
    scanf("%d%d", &n, &d);
    for (int i = 0; i < n; i++)
        scanf("%s", map1[i]);
    for (int i = 0; i < n; i++)
        scanf("%s", map2[i]);

    m = strlen(map1[0]);
    int s = n * m * 2, t = s + 1;
    ek.init(t, 0);

    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++) 
            if (map1[i][j] - ‘0‘) {
                ek.AddEdge(i * m + j, n * m + i * m + j, map1[i][j] - ‘0‘);
            }

    int cnt = 0;
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
            if (map2[i][j] == ‘L‘) {
                ek.AddEdge(s, i * m + j, 1);
                cnt++;
            }

    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++) {
            if (i < d || j < d || j >= m - d || i >= n - d) {
                ek.AddEdge(i * m + j + n * m, t, INF);
            }
        }

    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 (!(i == k && l == m) && d >= ABS(i - k) + ABS(j - l))
                        ek.AddEdge(i * m + j + n * m, k * m + l, INF);
    int ans = ek.Maxflow(s, t);

    printf("Case #%d: ", cas++);
    if (ans == cnt) 
        printf("no lizard was left behind.\n");
    else if(ans + 1 == cnt)
        printf("1 lizard was left behind.\n");
    else 
        printf("%d lizards were left behind.\n", cnt - ans);
}

int main() {
    int test;
    scanf("%d", &test);
    while (test--) {
        init();

    }
    return 0;
}

Dinic

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
#define N 1010
#define INF 0x3f3f3f3f

struct Edge{
    int from, to, cap, flow;
    Edge() {}
    Edge(int from, int to, int cap, int flow) : from(from), to(to), cap(cap), flow(flow) {}
};

struct Dinic{
    int n, m, s, t;
    vector<Edge> edges;
    vector<int> G[N];
    bool vis[N];
    int d[N], cur[N];

    void init(int n, int m) {
        this->n = n; this->m = m;
        for (int i = 0; i <= n; i++) {
            G[i].clear();
        }
        edges.clear();
    }

    void AddEdge(int from, int to, int cap) {
        edges.push_back(Edge(from, to, cap, 0));
        edges.push_back(Edge(to, from, 0, 0));
        int m = edges.size();
        G[from].push_back(m - 2);
        G[to].push_back(m - 1);
    } 

    bool BFS() {
        memset(vis, 0, sizeof(vis));
        queue<int> Q;
        Q.push(s);
        vis[s] = 1;
        d[s] = 0;

        while (!Q.empty()) {
            int u = Q.front();
            Q.pop();
            for (int i = 0; i < G[u].size(); i++) {
                Edge &e = edges[G[u][i]];
                if (!vis[e.to] && e.cap > e.flow) {
                    vis[e.to] = true;
                    d[e.to] = d[u] + 1;
                    Q.push(e.to);
                }
            }
        }
        return vis[t];
    }

    int DFS(int x, int a) {
        if (x == t || a == 0)
            return a;

        int flow = 0, f;
        for (int i = cur[x]; i < G[x].size(); i++) {
            Edge &e = edges[G[x][i]];
            if (d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap - e.flow))) > 0) {
                e.flow += f;
                edges[G[x][i] ^ 1].flow -= f;
                flow += f;
                a -= f;
                if (a == 0)
                    break;
            }
        }
        return flow;
    }

    int Maxflow(int s, int t) {
        this->s = s; this->t = t;
        int flow = 0;
        while (BFS()) {
            memset(cur, 0, sizeof(cur));
            flow += DFS(s, INF);
        }
        return flow;
    }
};

Dinic dinic;


#define M 110
#define ABS(x) ((x) > 0 ? x : (-(x)))
#include <cstring>
char map1[25][M], map2[25][M];
int n, d, m, cas = 1;

void init() {
    scanf("%d%d", &n, &d);
    for (int i = 0; i < n; i++)
        scanf("%s", map1[i]);
    for (int i = 0; i < n; i++)
        scanf("%s", map2[i]);

    m = strlen(map1[0]);
    int s = n * m * 2, t = s + 1;
    dinic.init(t, 0);

    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++) 
            if (map1[i][j] - ‘0‘) {
                dinic.AddEdge(i * m + j, n * m + i * m + j, map1[i][j] - ‘0‘);
            }

    int cnt = 0;
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
            if (map2[i][j] == ‘L‘) {
                dinic.AddEdge(s, i * m + j, 1);
                cnt++;
            }

    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++) {
            if (i < d || j < d || j >= m - d || i >= n - d) {
                dinic.AddEdge(i * m + j + n * m, t, INF);
            }
        }

    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 (!(i == k && l == m) && d >= ABS(i - k) + ABS(j - l))
                        dinic.AddEdge(i * m + j + n * m, k * m + l, INF);
    int ans = dinic.Maxflow(s, t);

    printf("Case #%d: ", cas++);
    if (ans == cnt) 
        printf("no lizard was left behind.\n");
    else if(ans + 1 == cnt)
        printf("1 lizard was left behind.\n");
    else 
        printf("%d lizards were left behind.\n", cnt - ans);
}

int main() {
    int test;
    scanf("%d", &test);
    while (test--) {
        init();

    }
    return 0;
}