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#define PROBLEM "https://yukicoder.me/problems/no/957" #include <vector> #include <iostream> #include <queue> using namespace std; #include "../../lib/00-util/FastIO.cpp" #include "../../lib/40-graph/DinicMaxFlow.cpp" int main() { cin.tie(0);ios::sync_with_stdio(false); int H,W; read(H),read(W); vector<vector<long long>> grid(H,vector<long long>(W)); for(int i=0;i<H;++i) for(int j=0;j<W;++j) read(grid[i][j]); vector<long long> R(H),C(W); for(int i=0;i<H;++i) read(R[i]); for(int j=0;j<W;++j) read(C[j]); //行/列に対して「植える」:0, 「植えない」:1 ,と割り当てる //加えて、問題の性質的にi行目に関してはフローを流す前に貪欲に選んでしまう //そうすることで、辺の数が2乗オーダーから落ちる DinicMaxFlow<long long> di(H+W+2); int S = H+W, G = H+W+1; long long ans = 0; for(int i=0;i<H;++i) { //i行目を全部植えたときのコストを計算 long long cost = 0; for(int j=0;j<W;++j) cost += grid[i][j]; //差分が正のとき if(R[i]-cost >= 0) ans += R[i]-cost; //差分が負のとき→ iが0のとき|cost-R[i]|失う else di.make_edge(i,G,abs(R[i]-cost)); } for(int j=0;j<W;++j) { //j列目を全部植えたときのコスト long long cost = C[j]; //jが0のとき|cost|得る ans += cost, di.make_edge(S,j+H,cost); } for(int i=0;i<H;++i) for(int j=0;j<W;++j) { //iが1,jが0のとき、grid[i][j]失う di.make_edge(j+H,i,grid[i][j]); } cout << ans - di.flow(S,G) << endl; return 0; }
#line 1 "test/graph/DinicMaxFlow-2.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/957" #include <vector> #include <iostream> #include <queue> using namespace std; #line 1 "lib/00-util/FastIO.cpp" /* * @title FastIO * @docs md/util/FastIO.md */ class FastIO{ private: inline static constexpr int ch_0='0'; inline static constexpr int ch_9='9'; inline static constexpr int ch_n='-'; inline static constexpr int ch_s=' '; inline static constexpr int ch_l='\n'; inline static void endline_skip(char& ch) { while(ch==ch_l) ch=getchar(); } template<typename T> inline static void read_integer(T &x) { int neg=0; char ch; x=0; ch=getchar(); endline_skip(ch); if(ch==ch_n) neg=1,ch=getchar(); for(;(ch_0 <= ch && ch <= ch_9); ch = getchar()) x = x*10 + (ch-ch_0); if(neg) x*=-1; } template<typename T> inline static void read_unsigned_integer(T &x) { char ch; x=0; ch=getchar(); endline_skip(ch); for(;(ch_0 <= ch && ch <= ch_9); ch = getchar()) x = x*10 + (ch-ch_0); } inline static void read_string(string &x) { char ch; x=""; ch=getchar(); endline_skip(ch); for(;(ch != ch_s && ch!=ch_l); ch = getchar()) x.push_back(ch); } inline static char ar[40]; inline static char *ch_ar; template<typename T> inline static void write_integer(T x) { ch_ar=ar; if(x< 0) putchar(ch_n), x=-x; if(x==0) putchar(ch_0); for(;x;x/=10) *ch_ar++=(ch_0+x%10); while(ch_ar--!=ar) putchar(*ch_ar); } public: inline static void read(int &x) {read_integer<int>(x);} inline static void read(long long &x) {read_integer<long long>(x);} inline static void read(unsigned int &x) {read_unsigned_integer<unsigned int>(x);} inline static void read(unsigned long long &x) {read_unsigned_integer<unsigned long long>(x);} inline static void read(string &x) {read_string(x);} inline static void read(__int128_t &x) {read_integer<__int128_t>(x);} inline static void write(__int128_t x) {write_integer<__int128_t>(x);} inline static void write(char x) {putchar(x);} }; #define read(arg) FastIO::read(arg) #define write(arg) FastIO::write(arg) #line 1 "lib/40-graph/DinicMaxFlow.cpp" /* * @title DinicMaxFlow - Dinicフロー * @docs md/graph/DinicMaxFlow.md */ template <class TypeFlow> class DinicMaxFlow { struct Edge { size_t to, rev; TypeFlow cap; }; vector<vector<Edge>> edge; vector<int> level, iter; TypeFlow inf_flow; inline void bfs(const size_t start) { for (int i = 0; i < level.size(); ++i) level[i] = -1; queue<size_t> q; level[start] = 0; q.push(start); while (q.size()) { auto from = q.front(); q.pop(); for (auto& e : edge[from]) { if (e.cap > 0 && level[e.to] < 0) { level[e.to] = level[from] + 1; q.push(e.to); } } } } inline TypeFlow dfs(size_t from, size_t goal, TypeFlow flow) { if (from == goal) return flow; for (int& i = iter[from]; i < edge[from].size(); ++i) { //TODO 参照が効いてなくて冗長 auto& e = edge[from][i]; if (e.cap <= 0 || level[from] >= level[e.to]) continue; TypeFlow dflow = dfs(e.to, goal, min(flow, e.cap)); if (dflow <= 0) continue; e.cap -= dflow; edge[e.to][e.rev].cap += dflow; return dflow; } return 0; } public: DinicMaxFlow(const size_t N) : edge(N), level(N), iter(N), inf_flow(0) { // do nothing } inline void make_edge(const size_t from,const size_t to, TypeFlow cap) { edge[from].push_back({ to, edge[to].size(), cap }); edge[to].push_back({ from, edge[from].size() - 1, 0}); inf_flow += cap; } inline TypeFlow flow(const size_t start,const size_t goal) { TypeFlow max_flow = 0; while (1) { bfs(start); if (level[goal] < 0) return max_flow; for (int i = 0; i < iter.size(); ++i) iter[i] = 0; TypeFlow flow; while ((flow = dfs(start, goal, inf_flow))>0) max_flow += flow; } } }; #line 9 "test/graph/DinicMaxFlow-2.test.cpp" int main() { cin.tie(0);ios::sync_with_stdio(false); int H,W; read(H),read(W); vector<vector<long long>> grid(H,vector<long long>(W)); for(int i=0;i<H;++i) for(int j=0;j<W;++j) read(grid[i][j]); vector<long long> R(H),C(W); for(int i=0;i<H;++i) read(R[i]); for(int j=0;j<W;++j) read(C[j]); //行/列に対して「植える」:0, 「植えない」:1 ,と割り当てる //加えて、問題の性質的にi行目に関してはフローを流す前に貪欲に選んでしまう //そうすることで、辺の数が2乗オーダーから落ちる DinicMaxFlow<long long> di(H+W+2); int S = H+W, G = H+W+1; long long ans = 0; for(int i=0;i<H;++i) { //i行目を全部植えたときのコストを計算 long long cost = 0; for(int j=0;j<W;++j) cost += grid[i][j]; //差分が正のとき if(R[i]-cost >= 0) ans += R[i]-cost; //差分が負のとき→ iが0のとき|cost-R[i]|失う else di.make_edge(i,G,abs(R[i]-cost)); } for(int j=0;j<W;++j) { //j列目を全部植えたときのコスト long long cost = C[j]; //jが0のとき|cost|得る ans += cost, di.make_edge(S,j+H,cost); } for(int i=0;i<H;++i) for(int j=0;j<W;++j) { //iが1,jが0のとき、grid[i][j]失う di.make_edge(j+H,i,grid[i][j]); } cout << ans - di.flow(S,G) << endl; return 0; }