結果

問題 No.1078 I love Matrix Construction
ユーザー aru aru
提出日時 2020-10-27 21:01:32
言語 Go
(1.23.4)
結果
AC  
実行時間 218 ms / 2,000 ms
コード長 5,824 bytes
コンパイル時間 15,186 ms
コンパイル使用メモリ 238,680 KB
実行使用メモリ 42,752 KB
最終ジャッジ日時 2024-07-21 22:03:15
合計ジャッジ時間 20,344 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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ファイルパターン 結果
other AC * 22
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ソースコード

diff #
プレゼンテーションモードにする

package main
import (
    "bufio"
    "fmt"
    "os"
    "sort"
    "strconv"
)
var sc = bufio.NewScanner(os.Stdin)
var wr = bufio.NewWriter(os.Stdout)
func out(x ...interface{}) {
    fmt.Fprintln(wr, x...)
}
func getI() int {
    sc.Scan()
    i, e := strconv.Atoi(sc.Text())
    if e != nil {
        panic(e)
    }
    return i
}
func getF() float64 {
    sc.Scan()
    i, e := strconv.ParseFloat(sc.Text(), 64)
    if e != nil {
        panic(e)
    }
    return i
}
func getInts(N int) []int {
    ret := make([]int, N)
    for i := 0; i < N; i++ {
        ret[i] = getI()
    }
    return ret
}
func getS() string {
    sc.Scan()
    return sc.Text()
}
// min, max, asub, absなど基本関数
func max(a, b int) int {
    if a > b {
        return a
    }
    return b
}
func min(a, b int) int {
    if a < b {
        return a
    }
    return b
}
func asub(a, b int) int {
    if a > b {
        return a - b
    }
    return b - a
}
func abs(a int) int {
    if a >= 0 {
        return a
    }
    return -a
}
func lowerBound(a []int, x int) int {
    idx := sort.Search(len(a), func(i int) bool {
        return a[i] >= x
    })
    return idx
}
func upperBound(a []int, x int) int {
    idx := sort.Search(len(a), func(i int) bool {
        return a[i] > x
    })
    return idx
}
func main() {
    defer wr.Flush()
    sc.Split(bufio.ScanWords)
    sc.Buffer([]byte{}, 1000000)
    // this template is new version.
    // use getI(), getS(), getInts(), getF()
    N := getI()
    S := getInts(N)
    T := getInts(N)
    U := getInts(N)
    for i := 0; i < N; i++ {
        S[i]--
        T[i]--
    }
    ts := New(N * N)
    var id = func(i, j int) int {
        return i*N + j
    }
    for i := 0; i < N; i++ {
        for j := 0; j < N; j++ {
            switch U[i] {
            case 0:
                ts.AddClause(id(S[i], j), true, id(j, T[i]), true)
            case 1:
                ts.AddClause(id(S[i], j), false, id(j, T[i]), true)
            case 2:
                ts.AddClause(id(S[i], j), true, id(j, T[i]), false)
            case 3:
                ts.AddClause(id(S[i], j), false, id(j, T[i]), false)
            }
        }
    }
    if !ts.Satisfiable() {
        out("-1")
        return
    }
    ans := ts.Answer()
    // test := make([][]int, N)
    for i := 0; i < N; i++ {
        // test[i] = make([]int, N)
        for j := 0; j < N; j++ {
            if ans[id(i, j)] {
                fmt.Fprint(wr, 1, " ")
                // test[i][j] = 1
            } else {
                fmt.Fprint(wr, 0, " ")
                // test[i][j] = 0
            }
        }
        fmt.Fprintln(wr)
    }
    // test = [][]int{{0, 0, 0}, {1, 0, 1}, {0, 0, 0}}
    // out(test)
    // for i := 0; i < N; i++ {
    //  for j := 0; j < N; j++ {
    //      x := test[S[i]][j] + 2*test[j][T[i]]
    //      if x == U[i] {
    //          out(i, j, x, U[i])
    //      }
    //  }
    // }
}
// TwoSat defines n, answer and scc
type TwoSat struct {
    n      int
    answer []bool
    scc    *SccGraph
}
// New creates a TwoSAT of n variables and 0 clauses
func New(n int) *TwoSat {
    ts := &TwoSat{
        n:      n,
        answer: make([]bool, n),
        scc:    NewGraph(n * 2),
    }
    return ts
}
func (ts *TwoSat) internalJudge(f bool, a int, b int) int {
    if f {
        return a
    }
    return b
}
// AddClause adds a clause.
func (ts *TwoSat) AddClause(i int, f bool, j int, g bool) {
    if !(0 <= i && i < ts.n) {
        panic("")
    }
    if !(0 <= j && j < ts.n) {
        panic("")
    }
    ts.scc.AddEdge(2*i+ts.internalJudge(f, 0, 1), 2*j+ts.internalJudge(g, 1, 0))
    ts.scc.AddEdge(2*j+ts.internalJudge(g, 0, 1), 2*i+ts.internalJudge(f, 1, 0))
}
// Satisfiable returns True if there is a truth assignment that satisfies all clauses
func (ts *TwoSat) Satisfiable() bool {
    id := ts.scc.SccIds().Second
    for i := 0; i < ts.n; i++ {
        if id[2*i] == id[2*i+1] {
            return false
        }
        ts.answer[i] = id[2*i] < id[2*i+1]
    }
    return true
}
// Answer returns a truth assignment that satisfies all clauses of the last call of satisfiable
func (ts *TwoSat) Answer() []bool {
    return ts.answer
}
type sccFromToPair struct {
    first, second int
}
type sccIdPair struct {
    First  int
    Second []int
}
type csr struct {
    start []int
    elist []int
}
func initCsr(n int, edges []*sccFromToPair) *csr {
    var ret csr
    ret.start = make([]int, n+1)
    ret.elist = make([]int, len(edges))
    for _, e := range edges {
        ret.start[e.first+1]++
    }
    for i := 1; i <= n; i++ {
        ret.start[i] += ret.start[i-1]
    }
    counter := make([]int, len(ret.start))
    copy(counter, ret.start)
    for _, e := range edges {
        ret.elist[counter[e.first]] = e.second
        counter[e.first]++
    }
    return &ret
}
// SccGraph :
type SccGraph struct {
    n     int
    edges []*sccFromToPair
}
// NewGraph :
func NewGraph(n int) *SccGraph {
    var s SccGraph
    s.n = n
    return &s
}
// AddEdge :
func (s *SccGraph) AddEdge(from, to int) {
    s.edges = append(s.edges, &sccFromToPair{from, to})
}
func (s *SccGraph) min(a, b int) int {
    if a > b {
        return b
    }
    return a
}
// SccIds :
func (s *SccGraph) SccIds() sccIdPair {
    g := initCsr(s.n, s.edges)
    nowOrd, groupNum := 0, 0
    visited := make([]int, 0, s.n)
    low := make([]int, s.n)
    ord := make([]int, s.n)
    ids := make([]int, s.n)
    for i := 0; i < s.n; i++ {
        ord[i] = -1
    }
    var dfs func(v int)
    dfs = func(v int) {
        low[v] = nowOrd
        ord[v] = nowOrd
        nowOrd++
        visited = append(visited, v)
        for i := g.start[v]; i < g.start[v+1]; i++ {
            to := g.elist[i]
            if ord[to] == -1 {
                dfs(to)
                low[v] = s.min(low[v], low[to])
            } else {
                low[v] = s.min(low[v], ord[to])
            }
        }
        if low[v] == ord[v] {
            for {
                u := visited[len(visited)-1]
                visited = visited[:len(visited)-1]
                ord[u] = s.n
                ids[u] = groupNum
                if u == v {
                    break
                }
            }
            groupNum++
        }
    }
    for i := 0; i < s.n; i++ {
        if ord[i] == -1 {
            dfs(i)
        }
    }
    for i := 0; i < len(ids); i++ {
        ids[i] = groupNum - 1 - ids[i]
    }
    return sccIdPair{groupNum, ids}
}
// Scc :
func (s *SccGraph) Scc() [][]int {
    ids := s.SccIds()
    groupNum := ids.First
    counts := make([]int, groupNum)
    for _, x := range ids.Second {
        counts[x]++
    }
    groups := make([][]int, ids.First)
    for i := 0; i < groupNum; i++ {
        groups[i] = make([]int, 0, counts[i])
    }
    for i := 0; i < s.n; i++ {
        groups[ids.Second[i]] = append(groups[ids.Second[i]], i)
    }
    return groups
}
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