Sgu 190. Dominoes (Bipartite Graph Matching)

Time Limit: 0.25 s

Space limit: 4 m

Question:

Given an N * n board, some grids are removed, and some 1*2 dominoes are placed on the Board to determine whether they can be filled up and output any scheme.

 

 

 

 

 

 

 

 

Solution:

First, consider a lattice black and white Dyeing of the Board (not required in fact) to get something similar to the chess board. A card can be placed on an adjacent black and white lattice.

We consider connecting each black lattice to an edge of the adjacent white lattice, and then performing the maximum matching of the Bipartite Graph to determine whether it is a complete match. Then, we can output the solution.

The idea is simple and straightforward, and some simple skills and small processing are required for output.

 

Code

#include <iostream>#include <cstring>#include <fstream>#include <cmath>#include <cstdio>using namespace std;const int INF = 1700;struct node {    int u, v, next;} edge[100000];int pHead[INF], vis[INF], pr[INF];int dx[] = {0, 0, 1, -1}, dy[] = {1, -1, 0, 0};int n, m, x, y, nCnt, an;int exPath (int x) {    for (int k = pHead[x]; k != 0; k = edge[k].next) {        int x = edge[k].u, y = edge[k].v;        if (!vis[y]) {            vis[y] = 1;            if ( !pr[y] || exPath (pr[y]) ) return pr[y] = x;        }    }    return 0;}void addEdge (int u, int v) {    edge[++nCnt].u = u, edge[nCnt].v = v;    edge[nCnt].next = pHead[u];    pHead[u] = nCnt;}int g[50][50];int main() {       //ofstream cout("out.txt");    cin >> n >> m;    for (int i = 1; i <= n; i++)        for (int j = 1; j <= n; j++) g[i][j] = 1;    for (int i = 1; i <= m; i++) {        cin >> x >> y;        g[x][y] = 0;    }    for (int i = 1; i <= n; i++)        for (int j = 1; j <= n; j++) {            if (g[i][j])                for (int k = 0; k < 4; k++) {                    int x = i + dx[k], y = j + dy[k];                    if (g[x][y])                        addEdge ( (i - 1) *n + j, (x - 1) *n + y);                }        }    for (int i = 1; i <= n * n; i++) {        if (exPath (i) ) an++;        memset (vis, 0, sizeof vis);    }    int t1 = 0, t2 = 0;    int ans[2][INF];    for (int i = 1; i <= n * n; i++) {        if (pr[i] && !vis[i]) {            vis[i] = vis[pr[i]] = 1;            if (abs (pr[i] - i) == n)                ans[0][++t1] = min (i, pr[i]);            else                ans[1][++t2] = min (i, pr[i]);        }    }    if (an == (n * n - m) ) {        cout << "Yes" << endl;        cout << t1 << endl;        for (int i = 1; i <= t1; i++) {            int l, r;            if (ans[0][i] % n) l = ans[0][i] / n + 1, r = ans[0][i] % n;            else                l = ans[0][i] / n, r = n;            cout << l << ‘ ‘ << r << endl;        }        cout << t2 << endl;        for (int i = 1; i <= t2; i++) {            int l, r;            l = ans[1][i] / n + 1, r = ans[1][i] % n;            cout << l << ‘ ‘ << r << endl;        }    }    else        cout << "No";    return 0;}

View code

 

Sgu 190. Dominoes (Bipartite Graph Matching)