結果

問題 No.1813 Magical Stones
ユーザー 草苺奶昔
提出日時 2023-12-24 02:41:33
言語 Go
(1.23.4)
結果
AC  
実行時間 306 ms / 2,000 ms
コード長 4,745 bytes
コンパイル時間 11,804 ms
コンパイル使用メモリ 237,748 KB
実行使用メモリ 43,088 KB
最終ジャッジ日時 2024-09-27 13:34:48
合計ジャッジ時間 19,492 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 40
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

// StronglyConnectedComponent-有向图SCC
package main
import (
    "bufio"
    "fmt"
    "os"
)
func main() {
    yuki1813()
    // yosupo()
    // yuki1293()
}
func yuki1813() {
    // https://yukicoder.me/problems/no/1813
    // 不等关系:有向边; 全部相等:强连通(环)
    // 给定一个DAG 求将DAG变为一个环(强连通分量)的最少需要添加的边数
    // !答案为 `max(入度为0的点的个数, 出度为0的点的个数)`
    in := bufio.NewReader(os.Stdin)
    out := bufio.NewWriter(os.Stdout)
    defer out.Flush()
    var n, m int
    fmt.Fscan(in, &n, &m)
    graph := make([][]int, n)
    for i := 0; i < m; i++ {
        var u, v int
        fmt.Fscan(in, &u, &v)
        u, v = u-1, v-1
        graph[u] = append(graph[u], v)
    }
    count, belong := StronglyConnectedComponent(graph)
    if count == 1 { // 缩成一个点了,说明是强连通的
        fmt.Fprintln(out, 0)
        return
    }
    dag := SCCDag(graph, count, belong)
    indeg, outDeg := make([]int, count), make([]int, count)
    for i := 0; i < count; i++ {
        for _, next := range dag[i] {
            indeg[next]++
            outDeg[i]++
        }
    }
    in0, out0 := 0, 0
    for i := 0; i < count; i++ {
        if indeg[i] == 0 {
            in0++
        }
        if outDeg[i] == 0 {
            out0++
        }
    }
    fmt.Fprintln(out, max(in0, out0))
}
func yosupo() {
    in := bufio.NewReader(os.Stdin)
    out := bufio.NewWriter(os.Stdout)
    defer out.Flush()
    var n, m int
    fmt.Fscan(in, &n, &m)
    graph := make([][]int, n)
    for i := 0; i < m; i++ {
        var u, v int
        fmt.Fscan(in, &u, &v)
        graph[u] = append(graph[u], v)
    }
    count, belong := StronglyConnectedComponent(graph)
    group := make([][]int, count)
    for i := 0; i < n; i++ {
        group[belong[i]] = append(group[belong[i]], i)
    }
    fmt.Fprintln(out, count)
    for _, p := range group {
        fmt.Fprint(out, len(p))
        for _, v := range p {
            fmt.Fprint(out, " ", v)
        }
        fmt.Fprintln(out)
    }
}
func yuki1293() {
    // https://yukicoder.me/problems/no/1293
    // No.1293 2種類の道路-SCC
    // 无向图中有两种路径,各有road1,road2条
    // 求有多少个二元组(a,b),满足从a到b经过 '若干条第一种路径+若干条第二种路径'
    // !每个点i拆成点2*i和点2*i+1,2*i->2*i+1
    // !第一种路径: 2*i<->2*j
    // !第二种路径: 2*i+1<->2*j+1
    // 然后对每个顶点求出有多少个可以到达自己
    in := bufio.NewReader(os.Stdin)
    out := bufio.NewWriter(os.Stdout)
    defer out.Flush()
    var n, road1, road2 int
    fmt.Fscan(in, &n, &road1, &road2)
    graph := make([][]int, 2*n)
    for i := 0; i < road1; i++ {
        var a, b int
        fmt.Fscan(in, &a, &b)
        a, b = a-1, b-1
        graph[2*a] = append(graph[2*a], 2*b)
        graph[2*b] = append(graph[2*b], 2*a)
    }
    for i := 0; i < road2; i++ {
        var a, b int
        fmt.Fscan(in, &a, &b)
        a, b = a-1, b-1
        graph[2*a+1] = append(graph[2*a+1], 2*b+1)
        graph[2*b+1] = append(graph[2*b+1], 2*a+1)
    }
    for i := 0; i < n; i++ {
        graph[2*i] = append(graph[2*i], 2*i+1)
    }
    count, belong := StronglyConnectedComponent(graph)
    dag := SCCDag(graph, count, belong)
    dp := make([]int, count)
    for i := 0; i < n; i++ {
        dp[belong[2*i]]++
    }
    for i := 0; i < count; i++ {
        for _, to := range dag[i] {
            dp[to] += dp[i]
        }
    }
    res := 0
    for i := 0; i < n; i++ {
        res += dp[belong[2*i+1]] - 1 // !减去自己到自己的路径1
    }
    fmt.Fprintln(out, res)
}
// 有向图强连通分量分解.
func StronglyConnectedComponent(graph [][]int) (count int, belong []int) {
    n := len(graph)
    belong = make([]int, n)
    low := make([]int, n)
    order := make([]int, n)
    for i := range order {
        order[i] = -1
    }
    now := 0
    path := []int{}
    var dfs func(int)
    dfs = func(v int) {
        low[v] = now
        order[v] = now
        now++
        path = append(path, v)
        for _, to := range graph[v] {
            if order[to] == -1 {
                dfs(to)
                low[v] = min(low[v], low[to])
            } else {
                low[v] = min(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 := 0; i < n; i++ {
        if order[i] == -1 {
            dfs(i)
        }
    }
    for i := 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 [][]int, count int, belong []int) (dag [][]int) {
    dag = make([][]int, count)
    adjSet := make([]map[int]struct{}, count)
    for i := 0; i < count; i++ {
        adjSet[i] = make(map[int]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 := 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
}
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