// 最小费用流/最小费用最大流 // "边权要求非负",或者"给出的图为dag且顶点编号为拓扑序". // https://kopricky.github.io/code/NetworkFlow/min_cost_flow_DAG.html // https://atcoder.jp/contests/tdpc/tasks/tdpc_graph // 时间复杂度O(|f|mlogn), |f|为流量 // // api: // NewMinCostFlow(n, source, sink int32) *MinCostFlow // NewMinCostFlowFromDag(n, source, sink int32) *MinCostFlow // AddEdge(from, to int32, cap, cost int) int32 // Flow() (flow, cost int) // FlowWithLimit(limit int) (flow, cost int) // Slope() [][2]int // SlopeWithLimit(limit int) [][2]int // PathDecomposition() [][]int32 // GetEdge(i int32) edge // Edges() []edge // Debug() package main import ( "bufio" "fmt" "os" ) func main() { // assignment() // judge() // abc214h() // abcGraph() // abcMinCostFlow() // yuki1288() // yuki1301() // yuki1324() // yuki1678() yuki2604() } // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_6_B func judge() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var n, m int32 var f int fmt.Fscan(in, &n, &m, &f) pd := NewMinCostFlow(n, 0, n-1) for i := int32(0); i < m; i++ { var from, to int32 var cap, cost int fmt.Fscan(in, &from, &to, &cap, &cost) pd.AddEdge(from, to, cap, cost) } flow, cost := pd.FlowWithLimit(f) if flow < f { fmt.Fprintln(out, -1) } else { fmt.Fprintln(out, cost) } } // https://judge.yosupo.jp/problem/assignment // 给定一个n*n的矩阵,每个元素表示从i到j的费用. // 选择n个元素,使得每行每列只有一个元素,求最小费用. // 输出每行选择的列. func assignment() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var n int32 fmt.Fscan(in, &n) grid := make([][]int, n) for i := int32(0); i < n; i++ { grid[i] = make([]int, n) for j := int32(0); j < n; j++ { fmt.Fscan(in, &grid[i][j]) } } source := int32(0) left := func(i int32) int32 { return 1 + i } right := func(i int32) int32 { return 1 + n + i } sink := right(n) M := NewMinCostFlowFromDag(n+n+2, source, sink) for i := int32(0); i < n; i++ { for j := int32(0); j < n; j++ { M.AddEdge(left(i), right(j), 1, grid[i][j]) } } for i := int32(0); i < n; i++ { M.AddEdge(source, left(i), 1, 0) M.AddEdge(right(i), sink, 1, 0) } _, minCost := M.Flow() edges := M.Edges() res := make([]int32, n) for _, e := range edges { if e.flow > 0 && 1 <= e.from && e.from <= n { res[e.from-1] = e.to - right(0) } } fmt.Fprintln(out, minCost) for i := int32(0); i < n; i++ { fmt.Fprint(out, res[i], " ") } } // H - Collecting // https://atcoder.jp/contests/abc214h/tasks/abc214_h // !有一张N个点M条边的有向图,每个点有一个点权ai. // !现在要找出k条经过点0的路径,使得这些路径的并集的点权和尽量大。 // dag路径覆盖最大点权和 // n,m<=2e5,k<=10. func abc214h() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var n, m int32 var k int fmt.Fscan(in, &n, &m, &k) graph := make([][]int32, n) for i := int32(0); i < m; i++ { var u, v int32 fmt.Fscan(in, &u, &v) u, v = u-1, v-1 graph[u] = append(graph[u], v) } weights := make([]int, n) for i := int32(0); i < n; i++ { fmt.Fscan(in, &weights[i]) } count, belong := StronglyConnectedComponent(graph) dag := SccDag(graph, count, belong) groupSum := make([]int, count) for i := int32(0); i < n; i++ { groupSum[belong[i]] += weights[i] } source := int32(0) left := func(i int32) int32 { return 1 + 2*i + 0 } right := func(i int32) int32 { return 1 + 2*i + 1 } sink := 1 + count + count M := NewMinCostFlowFromDag(count+count+2, source, sink) M.AddEdge(source, left(belong[0]), k, 0) // 经过0 for i := int32(0); i < count; i++ { M.AddEdge(left(i), right(i), 1, -groupSum[i]) M.AddEdge(left(i), right(i), k, 0) } for i := int32(0); i < count; i++ { M.AddEdge(right(i), sink, k, 0) } for from := int32(0); from < int32(len(dag)); from++ { nexts := dag[from] for _, to := range nexts { M.AddEdge(right(from), left(to), k, 0) } } _, minCost := M.Flow() fmt.Fprintln(out, -minCost) } // https://atcoder.jp/contests/tdpc/tasks/tdpc_graph // !有一张N个点M条边的有向图. // !现在要找出两条路径,使得这两条路径的并集的点的个数最多. // n<=300. func abcGraph() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var n int32 fmt.Fscan(in, &n) adjMatrix := make([][]bool, n) for i := int32(0); i < n; i++ { adjMatrix[i] = make([]bool, n) } for i := int32(0); i < n; i++ { for j := int32(0); j < n; j++ { var v int8 fmt.Fscan(in, &v) adjMatrix[i][j] = v == 1 } } k := 2 graph := make([][]int32, n) for i := int32(0); i < n; i++ { for j := int32(0); j < n; j++ { if adjMatrix[i][j] { graph[i] = append(graph[i], j) } } } weights := make([]int, n) for i := int32(0); i < n; i++ { weights[i] = 1 } count, belong := StronglyConnectedComponent(graph) dag := SccDag(graph, count, belong) groupSum := make([]int, count) for i := int32(0); i < n; i++ { groupSum[belong[i]] += weights[i] } source := int32(0) source2 := int32(1) left := func(i int32) int32 { return 2 + 2*i + 0 } right := func(i int32) int32 { return 2 + 2*i + 1 } sink := 2 + count + count M := NewMinCostFlowFromDag(count+count+3, source, sink) M.AddEdge(source, source2, k, 0) for i := int32(0); i < count; i++ { M.AddEdge(source2, left(i), k, 0) } for i := int32(0); i < count; i++ { M.AddEdge(left(i), right(i), 1, -groupSum[i]) M.AddEdge(left(i), right(i), k, 0) } for i := int32(0); i < count; i++ { M.AddEdge(right(i), sink, k, 0) } for from := int32(0); from < int32(len(dag)); from++ { nexts := dag[from] for _, to := range nexts { M.AddEdge(right(from), left(to), k, 0) } } _, minCost := M.Flow() fmt.Fprintln(out, -minCost) } // https://atcoder.jp/contests/practice2/tasks/practice2_e // 给定一个n*n的矩阵,选择若干个单元格使得和最大. // 但是不能同一行或者同一列选择个数不能超过k. // 输出方案. func abcMinCostFlow() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var n int32 var k int fmt.Fscan(in, &n, &k) grid := make([][]int, n) for i := int32(0); i < n; i++ { grid[i] = make([]int, n) for j := int32(0); j < n; j++ { fmt.Fscan(in, &grid[i][j]) } } ROW, COL := n, n S, T := ROW+COL, ROW+COL+1 BIG := int(1e9 + 10) /** * generate (s -> row -> column -> t) graph * i-th row correspond to vertex i * i-th col correspond to vertex n + i **/ M := NewMinCostFlow(ROW+COL+2, S, T) // we can "waste" the flow M.AddEdge(S, T, int(n)*k, BIG) for i := int32(0); i < n; i++ { M.AddEdge(S, i, k, 0) M.AddEdge(ROW+i, T, k, 0) } for i := int32(0); i < ROW; i++ { for j := int32(0); j < COL; j++ { M.AddEdge(i, ROW+j, 1, BIG-grid[i][j]) } } _, cost := M.FlowWithLimit(int(n) * k) fmt.Fprintln(out, -cost+BIG*int(n)*k) visited := make([][]bool, ROW) for i := int32(0); i < ROW; i++ { visited[i] = make([]bool, COL) } path := M.PathDecomposition() for _, p := range path { if len(p) == 4 { x, y := p[1], p[2]-ROW visited[x][y] = true } } for i := int32(0); i < ROW; i++ { for j := int32(0); j < COL; j++ { if visited[i][j] { fmt.Fprint(out, "X") } else { fmt.Fprint(out, ".") } } fmt.Fprintln(out) } } // yukiCollection // https://yukicoder.me/problems/no/1288 // 给定yuki组成的一个字符,每个字符有一个权值. // 不断删除子序列yuki,求获得的最大权值. // n<=2000. func yuki1288() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var n int32 fmt.Fscan(in, &n) var s string fmt.Fscan(in, &s) scores := make([]int, n) for i := int32(0); i < n; i++ { fmt.Fscan(in, &scores[i]) } fa := func(i int32) int32 { return i } fb := func(i int32) int32 { return n + 1 + i } fc := func(i int32) int32 { return 2*(n+1) + i } fd := func(i int32) int32 { return 3*(n+1) + i } fe := func(i int32) int32 { return 4*(n+1) + i } M := NewMinCostFlowFromDag(5*n+5, fa(0), fe(n)) for i := int32(0); i < n; i++ { M.AddEdge(fa(i), fa(i+1), int(n), 0) M.AddEdge(fb(i), fb(i+1), int(n), 0) M.AddEdge(fc(i), fc(i+1), int(n), 0) M.AddEdge(fd(i), fd(i+1), int(n), 0) M.AddEdge(fe(i), fe(i+1), int(n), 0) } for i := int32(0); i < n; i++ { switch s[i] { case 'y': M.AddEdge(fa(i), fb(i+1), 1, -scores[i]) case 'u': M.AddEdge(fb(i), fc(i+1), 1, -scores[i]) case 'k': M.AddEdge(fc(i), fd(i+1), 1, -scores[i]) case 'i': M.AddEdge(fd(i), fe(i+1), 1, -scores[i]) } } res := -INF slope := M.Slope() for _, p := range slope { res = max(res, -p[1]) } fmt.Fprintln(out, res) } // StrangeGraphShortestPath // https://yukicoder.me/problems/no/1301 // No.1301-奇怪图的最短路-拆点 // 每条无向边有一个边权 // 第一次经过这条边的时候,边权为w1 // 第二次经过这条边的时候,边权为w2 (w1<=w2) // 每条边最多经过两次 // !求1到n再回到1的最短路(折返) // O(f*ElogV) // !只能走两次:流量限定为2 // 去的时候: a->ein->eout->b // 回来的时候: b->ein->eout->a // 注意ein->eout有两条边,一条边的边权为w1,一条边的边权为w2,容量都为1 func yuki1301() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var n, m int32 fmt.Fscan(in, &n, &m) M := NewMinCostFlow(n+m+m, 0, n-1) for i := int32(0); i < m; i++ { var a, b int32 var w1, w2 int fmt.Fscan(in, &a, &b, &w1, &w2) a, b = a-1, b-1 ein, eout := n+2*i, n+2*i+1 M.AddEdge(a, ein, 2, 0) M.AddEdge(eout, a, 2, 0) M.AddEdge(b, ein, 2, 0) M.AddEdge(eout, b, 2, 0) M.AddEdge(ein, eout, 1, w1) M.AddEdge(ein, eout, 1, w2) } _, minCost := M.FlowWithLimit(2) fmt.Fprintln(out, minCost) } // No.1324 Approximate the Matrix (凸函数,增量) // https://yukicoder.me/problems/no/1324 // 构造一个n*n的矩阵,每个元素是一个非负整数. // 矩阵第i行的和是A[i],第j列的和是B[j]. // 再给定一个目标矩阵P,求一个矩阵Q,使得Q和P的距离之和最小. // 这里的距离是每个元素的平方差之和. func yuki1324() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var n, k int32 fmt.Fscan(in, &n, &k) A, B := make([]int, n), make([]int, n) for i := int32(0); i < n; i++ { fmt.Fscan(in, &A[i]) } for i := int32(0); i < n; i++ { fmt.Fscan(in, &B[i]) } P := make([][]int, n) for i := int32(0); i < n; i++ { P[i] = make([]int, n) for j := int32(0); j < n; j++ { fmt.Fscan(in, &P[i][j]) } } source := int32(0) left := func(i int32) int32 { return 1 + i } right := func(i int32) int32 { return 1 + n + i } sink := 1 + n + n M := NewMinCostFlowFromDag(n+n+2, source, sink) for i := int32(0); i < n; i++ { M.AddEdge(source, left(i), A[i], 0) M.AddEdge(right(i), sink, B[i], 0) } base := 0 for i := int32(0); i < n; i++ { for j := int32(0); j < n; j++ { v := P[i][j] base += v * v for k := 0; k <= min(A[i], B[j]); k++ { a := (v - k) * (v - k) b := (v - k - 1) * (v - k - 1) M.AddEdge(left(i), right(j), 1, b-a) // !每一条流的增量 } } } _, cost := M.Flow() fmt.Fprintln(out, base+cost) } // No.1678 CoinTrade (Multiple) // https://yukicoder.me/problems/no/1678 // https://yukicoder.me/problems/no/1678/editorial // 从国家0开始,有n个国家,每个国家有一个货币. // !A[i]表示国家i的货币单价. // !B[i]表示在国家i,可以用哪些国家的货币兑换国家i得货币(注意,最多兑换一枚). // 由于钱包的容量有限,货币个数不能超过k个. // 如果您采取最佳行动,您的日元在旅行开始前和旅行结束后会上涨多少? 求出其最大值。 // n<=5e4,k<=50. func yuki1678() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var n int32 var k int fmt.Fscan(in, &n, &k) A, B := make([]int, n), make([][]int32, n) for i := int32(0); i < n; i++ { var a, m int fmt.Fscan(in, &a, &m) A[i] = a B[i] = make([]int32, m) for j := 0; j < m; j++ { fmt.Fscan(in, &B[i][j]) B[i][j]-- } } source := int32(0) idx := func(v int32) int32 { return 1 + v } sink := n + 1 M := NewMinCostFlowFromDag(n+2, source, sink) for i := int32(0); i < n+1; i++ { M.AddEdge(i, i+1, k, 0) } for to := int32(0); to < n; to++ { for _, from := range B[to] { cost := A[to] - A[from] M.AddEdge(idx(from), idx(to), 1, -cost) } } _, cost := M.Flow() fmt.Fprintln(out, -cost) } // No.2604 Initial Motion // https://yukicoder.me/problems/no/2604 // 给定一张无向带权图. // 开始时,有K个人,每个人在顶点A[i]. // 每个顶点有B[i]个道具. // 求所有人捡到道具的最小移动距离和. func yuki2604() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var k, n, m int32 fmt.Fscan(in, &k, &n, &m) A, B := make([]int32, k), make([]int, n) for i := int32(0); i < k; i++ { fmt.Fscan(in, &A[i]) A[i]-- } for i := int32(0); i < n; i++ { fmt.Fscan(in, &B[i]) } type edge struct { from, to int32 weight int } edges := make([]edge, m) for i := int32(0); i < m; i++ { var a, b int32 var c int fmt.Fscan(in, &a, &b, &c) a, b = a-1, b-1 edges[i] = edge{from: a, to: b, weight: c} } source, sink := n, n+1 M := NewMinCostFlow(n+2, source, sink) for _, p := range A { M.AddEdge(source, p, 1, 0) } for i := int32(0); i < n; i++ { M.AddEdge(i, sink, B[i], 0) } for _, e := range edges { M.AddEdge(e.from, e.to, int(k), e.weight) M.AddEdge(e.to, e.from, int(k), e.weight) } _, cost := M.Flow() fmt.Fprintln(out, cost) } // 100401. 放三个车的价值之和最大 II // https://leetcode.cn/problems/maximum-value-sum-by-placing-three-rooks-ii/ func maximumValueSum(board [][]int) int64 { ROW, COL := int32(len(board)), int32(len(board[0])) S, T := ROW+COL, ROW+COL+1 BIG := int(1e9 + 10) M := NewMinCostFlow(ROW+COL+2, S, T) for r := int32(0); r < ROW; r++ { M.AddEdge(S, r, 1, 0) } for r := int32(0); r < ROW; r++ { for c := int32(0); c < COL; c++ { M.AddEdge(r, ROW+c, 1, BIG-board[r][c]) // 求最大值,取负数 } } for c := int32(0); c < COL; c++ { M.AddEdge(ROW+c, T, 1, 0) } _, cost := M.FlowWithLimit(3) // !放三个车,流量为3 return int64(-cost + 3*BIG) } const INF int = 1e18 type MinCostFlow struct { dag bool n, source, sink int32 edges []edge } type edge struct { from, to int32 cap, flow int cost int } type _edge struct { to, rev int32 cap, cost int } func NewMinCostFlow(n, source, sink int32) *MinCostFlow { checkArguments(n, source, sink) return &MinCostFlow{n: n, source: source, sink: sink} } func NewMinCostFlowFromDag(n, source, sink int32) *MinCostFlow { checkArguments(n, source, sink) return &MinCostFlow{dag: true, n: n, source: source, sink: sink} } func (mcf *MinCostFlow) AddEdge(from, to int32, cap, cost int) int32 { if from < 0 || from >= mcf.n { panic("from out of range") } if to < 0 || to >= mcf.n { panic("to out of range") } if cap < 0 { panic("cap is negative") } if !mcf.dag && cost < 0 { panic("cost is negative in non-dag") } if mcf.dag && from >= to { panic("from >= to in dag") } m := int32(len(mcf.edges)) mcf.edges = append(mcf.edges, edge{from: from, to: to, cap: cap, cost: cost}) return m } func (mcf *MinCostFlow) Flow() (flow, cost int) { return mcf.FlowWithLimit(INF) } func (mcf *MinCostFlow) FlowWithLimit(limit int) (flow, cost int) { res := mcf.SlopeWithLimit(limit) return res[len(res)-1][0], res[len(res)-1][1] } func (mcf *MinCostFlow) Slope() [][2]int { return mcf.SlopeWithLimit(INF) } func (mcf *MinCostFlow) SlopeWithLimit(limit int) [][2]int { m := int32(len(mcf.edges)) edgeIndex := make([]int32, m) g := func() *csr { degree, redgeIndex := make([]int32, mcf.n), make([]int32, m) elist := make([]elistPair, 0, 2*m) for i := int32(0); i < m; i++ { e := mcf.edges[i] edgeIndex[i] = degree[e.from] degree[e.from]++ redgeIndex[i] = degree[e.to] degree[e.to]++ elist = append(elist, elistPair{first: e.from, second: _edge{to: e.to, rev: -1, cap: e.cap - e.flow, cost: e.cost}}) elist = append(elist, elistPair{first: e.to, second: _edge{to: e.from, rev: -1, cap: e.flow, cost: -e.cost}}) } csr := newCsr(mcf.n, elist) for i := int32(0); i < m; i++ { e := mcf.edges[i] edgeIndex[i] += csr.start[e.from] redgeIndex[i] += csr.start[e.to] csr.elist[edgeIndex[i]].rev = redgeIndex[i] csr.elist[redgeIndex[i]].rev = edgeIndex[i] } return csr }() res := mcf._slope(g, limit) for i := int32(0); i < m; i++ { e := g.elist[edgeIndex[i]] mcf.edges[i].flow = mcf.edges[i].cap - e.cap } return res } // 路径还原, O(f*(n+m)). func (mcf *MinCostFlow) PathDecomposition() [][]int32 { to := make([][]int32, mcf.n) for _, e := range mcf.edges { for i := 0; i < e.flow; i++ { to[e.from] = append(to[e.from], e.to) } } var res [][]int32 visited := make([]bool, mcf.n) for len(to[mcf.source]) > 0 { path := []int32{mcf.source} visited[mcf.source] = true for path[len(path)-1] != mcf.sink { last := &to[path[len(path)-1]] tmp := (*last)[len(*last)-1] *last = (*last)[:len(*last)-1] for visited[tmp] { visited[path[len(path)-1]] = false path = path[:len(path)-1] } path = append(path, tmp) visited[tmp] = true } for _, v := range path { visited[v] = false } res = append(res, path) } return res } func (mcf *MinCostFlow) _slope(g *csr, flowLimit int) [][2]int { if mcf.dag { if mcf.source != 0 || mcf.sink != mcf.n-1 { panic("source and sink must be 0 and n-1 in dag") } } dualDist := make([][2]int, mcf.n) prevE := make([]int32, mcf.n) visited := make([]bool, mcf.n) queMin := make([]int32, 0) pq := make([]pqPair, 0) pqLess := func(i, j int32) bool { return pq[i].key < pq[j].key } dualRef := func() bool { for i := int32(0); i < mcf.n; i++ { dualDist[i][1] = INF } for i := int32(0); i < mcf.n; i++ { visited[i] = false } queMin = queMin[:0] pq = pq[:0] heapR := int32(0) dualDist[mcf.source][1] = 0 queMin = append(queMin, mcf.source) for len(queMin) > 0 || len(pq) > 0 { var v int32 if len(queMin) > 0 { v = queMin[len(queMin)-1] queMin = queMin[:len(queMin)-1] } else { for heapR < int32(len(pq)) { heapR++ heapUp(pq, heapR-1, pqLess) } v = pq[0].to pq[0], pq[heapR-1] = pq[heapR-1], pq[0] heapDown(pq, 0, heapR-1, pqLess) pq = pq[:len(pq)-1] heapR-- } if visited[v] { continue } visited[v] = true if v == mcf.sink { break } dualV, distV := dualDist[v][0], dualDist[v][1] for i := g.start[v]; i < g.start[v+1]; i++ { e := &g.elist[i] if e.cap == 0 { continue } cost := e.cost - dualDist[e.to][0] + dualV if dualDist[e.to][1] > distV+cost { distTo := distV + cost dualDist[e.to][1] = distTo prevE[e.to] = e.rev if distTo == distV { queMin = append(queMin, e.to) } else { pq = append(pq, pqPair{to: e.to, key: distTo}) } } } } if !visited[mcf.sink] { return false } for i := int32(0); i < mcf.n; i++ { if !visited[i] { continue } dualDist[i][0] -= dualDist[mcf.sink][1] - dualDist[i][1] } return true } dualRefDag := func() bool { for i := int32(0); i < mcf.n; i++ { dualDist[i][1] = INF } dualDist[mcf.source][1] = 0 for i := int32(0); i < mcf.n; i++ { visited[i] = false } visited[mcf.source] = true for v := int32(0); v < mcf.n; v++ { if !visited[v] { continue } dualV, distV := dualDist[v][0], dualDist[v][1] for i := g.start[v]; i < g.start[v+1]; i++ { e := &g.elist[i] if e.cap == 0 { continue } cost := e.cost - dualDist[e.to][0] + dualV if dualDist[e.to][1] > distV+cost { visited[e.to] = true distTo := distV + cost dualDist[e.to][1] = distTo prevE[e.to] = e.rev } } } if !visited[mcf.sink] { return false } for i := int32(0); i < mcf.n; i++ { if !visited[i] { continue } dualDist[i][0] -= dualDist[mcf.sink][1] - dualDist[i][1] } return true } flow, cost := 0, 0 prevCostPerFlow := -1 res := [][2]int{{0, 0}} for flow < flowLimit { if mcf.dag && flow == 0 { if !dualRefDag() { break } } else { if !dualRef() { break } } c := flowLimit - flow for v := mcf.sink; v != mcf.source; v = g.elist[prevE[v]].to { c = min(c, g.elist[g.elist[prevE[v]].rev].cap) } for v := mcf.sink; v != mcf.source; v = g.elist[prevE[v]].to { e := &g.elist[prevE[v]] e.cap += c g.elist[e.rev].cap -= c } d := -dualDist[mcf.source][0] flow += c cost += c * d if prevCostPerFlow == d { res = res[:len(res)-1] } res = append(res, [2]int{flow, cost}) prevCostPerFlow = d } return res } func (mcf *MinCostFlow) GetEdge(i int32) edge { return mcf.edges[i] } func (mcf *MinCostFlow) Edges() []edge { return mcf.edges } func (mcf *MinCostFlow) Debug() { fmt.Println("flow graph") fmt.Println("from, to, cap, cost") for _, e := range mcf.edges { fmt.Println(e.from, e.to, e.cap, e.cost) } } func checkArguments(n int32, source int32, sink int32) { if source < 0 || source >= n { panic("source out of range") } if sink < 0 || sink >= n { panic("sink out of range") } if source == sink { panic("source equals to sink") } } type elistPair struct { first int32 second _edge } type csr struct { start []int32 elist []_edge } func newCsr(n int32, edges []elistPair) *csr { start := make([]int32, n+1) elist := make([]_edge, len(edges)) for i := int32(0); i < int32(len(edges)); i++ { start[edges[i].first+1]++ } for i := int32(1); i <= n; i++ { start[i] += start[i-1] } counter := append(start[:0:0], start...) for _, e := range edges { elist[counter[e.first]] = e.second counter[e.first]++ } return &csr{start: start, elist: elist} } // heapUtils type pqPair = struct { to int32 key int } func heapUp(data []pqPair, i0 int32, less func(a, b int32) bool) { for { i := (i0 - 1) / 2 if i == i0 || !less(i0, i) { break } data[i], data[i0] = data[i0], data[i] i0 = i } } func heapDown(data []pqPair, i0, n int32, less func(a, b int32) bool) { i := i0 for { j1 := (i << 1) | 1 if j1 >= n || j1 < 0 { // j1 < 0 after int overflow break } j := j1 // left child if j2 := j1 + 1; j2 < n && less(j2, j1) { j = j2 // = 2*i + 2 // right child } if !less(j, i) { break } data[i], data[j] = data[j], data[i] i = j } } // 有向图强连通分量分解. func StronglyConnectedComponent(graph [][]int32) (count int32, belong []int32) { n := int32(len(graph)) belong = make([]int32, n) low := make([]int32, n) order := make([]int32, n) for i := range order { order[i] = -1 } now := int32(0) path := []int32{} var dfs func(int32) dfs = func(v int32) { low[v] = now order[v] = now now++ path = append(path, v) for _, to := range graph[v] { if order[to] == -1 { dfs(to) low[v] = min32(low[v], low[to]) } else { low[v] = min32(low[v], order[to]) } } if low[v] == order[v] { for { u := path[len(path)-1] path = path[:len(path)-1] order[u] = n belong[u] = count if u == v { break } } count++ } } for i := int32(0); i < n; i++ { if order[i] == -1 { dfs(i) } } for i := int32(0); i < n; i++ { belong[i] = count - 1 - belong[i] } return } // 有向图的强连通分量缩点. func SccDag(graph [][]int32, count int32, belong []int32) (dag [][]int32) { dag = make([][]int32, count) adjSet := make([]map[int32]struct{}, count) for i := int32(0); i < count; i++ { adjSet[i] = make(map[int32]struct{}) } for cur, nexts := range graph { for _, next := range nexts { if bid1, bid2 := belong[cur], belong[next]; bid1 != bid2 { adjSet[bid1][bid2] = struct{}{} } } } for i := int32(0); i < count; i++ { for next := range adjSet[i] { dag[i] = append(dag[i], next) } } return } func min(a, b int) int { if a < b { return a } return b } func max(a, b int) int { if a > b { return a } return b } func min32(a, b int32) int32 { if a < b { return a } return b } func max32(a, b int32) int32 { if a > b { return a } return b }