UVA 11082 - Matrix Decompressing(网络流+行列模型）

UVA 11082 - Matrix Decompressing

题目链接

题意：给定一个矩阵每行每列的和，要求现在构造一个矩阵满足元素在1-20之间，行列和满足条件

思路：行列建图，源点连到每个行，容量为和，每列连到汇点，容量为和，每行连到每列，容量20，注意这题要求的是1-20，所以可以先把所有位置-1，最后输出的时候+1即可

代码：

#include <cstdio>#include <cstring>#include <queue>#include <algorithm>using namespace std;const int MAXNODE = 105 * 2;const int MAXEDGE = 100005;typedef int Type;const Type INF = 0x3f3f3f3f;struct Edge {int u, v;Type cap, flow;Edge() {}Edge(int u, int v, Type cap, Type flow) {this->u = u;this->v = v;this->cap = cap;this->flow = flow;}};struct Dinic {int n, m, s, t;Edge edges[MAXEDGE];int first[MAXNODE];int next[MAXEDGE];bool vis[MAXNODE];Type d[MAXNODE];int cur[MAXNODE];void init(int n) {this->n = n;memset(first, -1, sizeof(first));m = 0;}void add_Edge(int u, int v, Type cap) {edges[m] = Edge(u, v, cap, 0);next[m] = first[u];first[u] = m++;edges[m] = Edge(v, u, 0, 0);next[m] = first[v];first[v] = m++;}bool bfs() {memset(vis, false, sizeof(vis));queue<int> Q;Q.push(s);d[s] = 0;vis[s] = true;while (!Q.empty()) {int u = Q.front(); Q.pop();for (int i = first[u]; i != -1; i = next[i]) {Edge& e = edges[i];if (!vis[e.v] && e.cap > e.flow) {vis[e.v] = true;d[e.v] = d[u] + 1;Q.push(e.v);}}}return vis[t];}Type dfs(int u, Type a) {if (u == t || a == 0) return a;Type flow = 0, f;for (int &i = cur[u]; i != -1; i = next[i]) {Edge& e = edges[i];if (d[u] + 1 == d[e.v] && (f = dfs(e.v, min(a, e.cap - e.flow))) > 0) {e.flow += f;edges[i^1].flow -= f;flow += f;a -= f;if (a == 0) break;}}return flow;}Type Maxflow(int s, int t) {this->s = s; this->t = t;Type flow = 0;while (bfs()) {for (int i = 0; i < n; i++)cur[i] = first[i];flow += dfs(s, INF);}return flow;}} gao;const int N = 105;int t, n, m, ans[N][N];int main() {int cas = 0;scanf("%d", &t);while (t--) {scanf("%d%d", &n, &m);gao.init(n + m + 2);int pre = 0, tmp;for (int i = 1; i <= n; i++) {scanf("%d", &tmp);gao.add_Edge(0, i, tmp - pre - m);pre = tmp;}pre = 0;for (int i = 1; i <= m; i++) {scanf("%d", &tmp);gao.add_Edge(i + n, n + m + 1, tmp - pre - n);pre = tmp;}for (int i = 1; i <= n; i++)for (int j = 1; j <= m; j++)gao.add_Edge(i, j + n, 19);gao.Maxflow(0, n + m + 1);printf("Matrix %d\n", ++cas);for (int i = 1; i <= n; i++) {for (int j = gao.first[i]; j != -1; j = gao.next[j]) {Edge e = gao.edges[j]; if (e.v > n && e.v <= n + m)ans[i][e.v - n] = e.flow;}}for (int i = 1; i <= n; i++) {for (int j = 1; j <= m; j++)printf("%d%c", ans[i][j] + 1, j == m ? '\n' : ' ');}}return 0;}