In this HackerRank Jumping Rooks problem solution, You have Given the configuration of the chessboard and some k, help Nina place k jumping rooks in the chessboard's free cells such that the number of pairs of rooks that beat each other is minimal. Then print a single integer denoting the number of rooks that beat each other.

HackerRank Jumping Rooks problem solution


Problem solution in Java.

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.List;

public class C {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    
    void solve()
    {
        int n = ni(), K = ni();
        char[][] map = nm(n,n);
        int[][] ud = new int[n][n];
        int[][] lr = new int[n][n];
        int pud = 0, plr = 0;
        {
            int id = -1;
            for(int i = 0;i < n;i++){
                char pre = 0;
                for(int j = 0;j < n;j++){
                    if(map[j][i] == '.'){
                        if(pre != '.')id++; 
                        ud[j][i] = id;
                    }
                    pre = map[j][i];
                }
            }
            pud = id + 1;
        }
        {
            int id = -1;
            for(int i = 0;i < n;i++){
                char pre = 0;
                for(int j = 0;j < n;j++){
                    if(map[i][j] == '.'){
                        if(pre != '.')id++; 
                        lr[i][j] = id;
                    }
                    pre = map[i][j];
                }
            }
            plr = id + 1;
        }
        List<Edge> es = new ArrayList<>();
        for(int i = 0;i < n;i++){
            for(int j = 0;j < n;j++){
                if(map[i][j] == '.'){
                    es.add(new Edge(ud[i][j], lr[i][j]+pud, 1, 0));
                }
            }
        }
        int src = pud + plr, sink = src + 1;
        for(int i = 0;i < pud;i++){
            for(int j = 0;j <= n;j++){
                es.add(new Edge(src, i, 1, j));
            }
        }
        for(int i = 0;i < plr;i++){
            for(int j = 0;j <= n;j++){
                es.add(new Edge(i+pud, sink, 1, j));
            }
        }
        out.println(solveMinCostFlow(compileWD(sink+1, es), src, sink, K));
    }
    
    public static class Edge
    {
        public int from, to;
        public int capacity;
        public int cost;
        public int flow;
        public Edge complement;
        // public int iniflow;
        
        public Edge(int from, int to, int capacity, int cost) {
            this.from = from;
            this.to = to;
            this.capacity = capacity;
            this.cost = cost;
        }
    }
    
    public static Edge[][] compileWD(int n, List<Edge> edges)
    {
        Edge[][] g = new Edge[n][];
        // cloning
        for(int i = edges.size()-1;i >= 0;i--){
            Edge origin = edges.get(i);
            Edge clone = new Edge(origin.to, origin.from, origin.capacity, -origin.cost);
            clone.flow = origin.capacity;
            clone.complement = origin;
            origin.complement = clone;
            edges.add(clone);
        }
        
        int[] p = new int[n];
        for(Edge e : edges)p[e.from]++;
        for(int i = 0;i < n;i++)g[i] = new Edge[p[i]];
        for(Edge e : edges)g[e.from][--p[e.from]] = e;
        return g;
    }

    // NOT VERIFIED
    public static Edge[][] compileWU(int n, List<Edge> edges)
    {
        Edge[][] g = new Edge[n][];
        // cloning
        for(int i = edges.size()-1;i >= 0;i--){
            Edge origin = edges.get(i);
            Edge back = new Edge(origin.to, origin.from, origin.capacity, origin.cost);
            edges.add(back);
        }
        for(int i = edges.size()-1;i >= 0;i--){
            Edge origin = edges.get(i);
            Edge clone = new Edge(origin.to, origin.from, origin.capacity, -origin.cost);
            clone.flow = origin.capacity;
            clone.complement = origin;
            origin.complement = clone;
            edges.add(clone);
        }
        
        int[] p = new int[n];
        for(Edge e : edges)p[e.from]++;
        for(int i = 0;i < n;i++)g[i] = new Edge[p[i]];
        for(Edge e : edges)g[e.from][--p[e.from]] = e;
        return g;
    }    

    
    public static long solveMinCostFlow(Edge[][] g, int source, int sink, long all)
    {
        int n = g.length;
        long mincost = 0;
        int[] potential = new int[n];
        
        final int[] d = new int[n];
        MinHeap q = new MinHeap(n);
        while(all > 0){
            // shortest path src->sink
            Edge[] inedge = new Edge[n];
            Arrays.fill(d, Integer.MAX_VALUE / 2);
            d[source] = 0;
            q.add(source, 0);
            while(q.size() > 0){
                int cur = q.argmin();
                q.remove(cur);
                for(Edge ne : g[cur]){
                    if(ne.capacity - ne.flow > 0){
                        int nd = d[cur] + ne.cost + potential[cur] - potential[ne.to];
                        if(d[ne.to] > nd){
                            inedge[ne.to] = ne;
                            d[ne.to] = nd;
                            q.update(ne.to, nd);
                        }
                    }
                }
            }
            
            if(inedge[sink] == null)break;
            
            long minflow = all;
            long sumcost = 0;
            for(Edge e = inedge[sink];e != null;e = inedge[e.from]){
                if(e.capacity - e.flow < minflow)minflow = e.capacity - e.flow;
                sumcost += e.cost;
            }
            mincost += minflow * sumcost;
            for(Edge e = inedge[sink];e != null;e = inedge[e.from]){
                e.flow += minflow;
                e.complement.flow -= minflow;
            }
            
            all -= minflow;
            for(int i = 0;i < n;i++){
                potential[i] += d[i];
            }
        }
        return mincost;
    }
    

    public static class MinHeap {
        public int[] a;
        public int[] map;
        public int[] imap;
        public int n;
        public int pos;
        public static int INF = Integer.MAX_VALUE;
        
        public MinHeap(int m)
        {
            n = m+2;
            a = new int[n];
            map = new int[n];
            imap = new int[n];
            Arrays.fill(a, INF);
            Arrays.fill(map, -1);
            Arrays.fill(imap, -1);
            pos = 1;
        }
        
        public int add(int ind, int x)
        {
            int ret = imap[ind];
            if(imap[ind] < 0){
                a[pos] = x; map[pos] = ind; imap[ind] = pos;
                pos++;
                up(pos-1);
            }
            return ret != -1 ? a[ret] : x;
        }
        
        public int update(int ind, int x)
        {
            int ret = imap[ind];
            if(imap[ind] < 0){
                a[pos] = x; map[pos] = ind; imap[ind] = pos;
                pos++;
                up(pos-1);
            }else{
                int o = a[ret];
                a[ret] = x;
                up(ret);
                down(ret);
//                if(a[ret] > o){
//                    up(ret);
//                }else{
//                    down(ret);
//                }
            }
            return x;
        }
        
        public int remove(int ind)
        {
            if(pos == 1)return INF;
            if(imap[ind] == -1)return INF;
            
            pos--;
            int rem = imap[ind];
            int ret = a[rem];
            map[rem] = map[pos];
            imap[map[pos]] = rem;
            imap[ind] = -1;
            a[rem] = a[pos];
            a[pos] = INF;
            map[pos] = -1;
            
            up(rem);
            down(rem);
            return ret;
        }
        
        public int min() { return a[1]; }
        public int argmin() { return map[1]; }
        public int size() {    return pos-1; }
        
        private void up(int cur)
        {
            for(int c = cur, p = c>>>1;p >= 1 && a[p] > a[c];c>>>=1, p>>>=1){
                int d = a[p]; a[p] = a[c]; a[c] = d;
                int e = imap[map[p]]; imap[map[p]] = imap[map[c]]; imap[map[c]] = e;
                e = map[p]; map[p] = map[c]; map[c] = e;
            }
        }
        
        private void down(int cur)
        {
            for(int c = cur;2*c < pos;){
                int b = a[2*c] < a[2*c+1] ? 2*c : 2*c+1;
                if(a[b] < a[c]){
                    int d = a[c]; a[c] = a[b]; a[b] = d;
                    int e = imap[map[c]]; imap[map[c]] = imap[map[b]]; imap[map[b]] = e;
                    e = map[c]; map[c] = map[b]; map[b] = e;
                    c = b;
                }else{
                    break;
                }
            }
        }
    }

    
    void run() throws Exception
    {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception { new C().run(); }
    
    private byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}

{"mode":"full","isActive":false}


Problem solution in C++.

#include <cstdio>
#include <vector>
#include <queue>
#include <cstring>

using namespace std;

#define INF 1000000000
#define maxn 10002

struct Edge
{
    int from, to, cap, flow, cost;
    Edge(int u, int v, int c, int f, int w) : from(u), to(v), cap(c), flow(f), cost(w) {}
};

struct MCMF
{
    int n, m;
    vector<Edge> edges;
    vector<int> G[maxn];
    int inq[maxn];
    int d[maxn];
    int p[maxn];
    int a[maxn];

    void init(int n)
    {
        this->n = n;
        for (int i = 0; i < n; ++i)
        {
            G[i].clear();
        }
        edges.clear();
    }

    void AddEdge(int from, int to, int cap, int cost)
    {
        edges.push_back(Edge(from, to, cap, 0, cost));
        edges.push_back(Edge(to, from, 0, 0, -cost));
        m = edges.size();
        G[from].push_back(m - 2);
        G[to].push_back(m - 1);
    }

    bool BellmanFord(int s, int t, int & cost)
    {
        for (int i = 0; i < n; ++i)
        {
            d[i] = INF;
        }
        memset(inq, 0, sizeof(inq));
        d[s] = 0;
        inq[s] = 1;
        p[s] = 0;
        a[s] = INF;
        queue<int> Q;
        Q.push(s);
        while (!Q.empty())
        {
            int u = Q.front();
            Q.pop();
            inq[u] = 0;
            for (int i = 0; i < G[u].size(); ++i)
            {
                Edge & e = edges[G[u][i]];
                if (e.cap > e.flow && d[e.to] > d[u] + e.cost)
                {
                    d[e.to] = d[u] + e.cost;
                    p[e.to] = G[u][i];
                    a[e.to] = min(a[u], e.cap - e.flow);
                    if (!inq[e.to])
                    {
                        Q.push(e.to);
                        inq[e.to] = 1;
                    }
                }
            }
        }
        if (d[t] == INF)
        {
            return false;
        }
        cost += d[t] * a[t];
        for (int u = t; u != s; u = edges[p[u]].from)
        {
            edges[p[u]].flow += a[t];
            edges[p[u] ^ 1].flow -= a[t];
        }
        return true;
    }

    int MincostMaxflow(int s, int t)
    {
        int cost = 0;
        while (BellmanFord(s, t, cost));
        return cost;
    }
};

char s[50][51];
int rid[50][50];
int cid[50][50];
int rcnt, ccnt;
int r[2500], c[2500];

int main()
{
    int n, k;
    scanf("%d %d", &n, &k);
    for (int i = 0; i < n; ++i)
        scanf("%s", s[i]);
    for (int i = 0; i < n; ++i)
        for (int j = 0; j < n; ++j)
        {
            if (s[i][j] == '#')
                continue;
            if (!rid[i][j])
            {
                ++rcnt;
                int t = j;
                while (t < n && s[i][t] == '.')
                {
                    rid[i][t] = rcnt;
                    ++r[rcnt];
                    ++t;
                }
            }
            if (!cid[i][j])
            {
                ++ccnt;
                int t = i;
                while (t < n && s[t][j] == '.')
                {
                    cid[t][j] = ccnt;
                    ++c[ccnt];
                    ++t;
                }
            }
        }
    MCMF mcmf;
    mcmf.init(rcnt + ccnt + 3);
    for (int i = 1; i <= rcnt; ++i)
        for (int j = 0; j < r[i]; ++j)
            mcmf.AddEdge(0, i, 1, j);
    for (int i = 1; i <= ccnt; ++i)
        for (int j = 0; j < c[i]; ++j)
            mcmf.AddEdge(rcnt + i, rcnt + ccnt + 1, 1, j);
    for (int i = 0; i < n; ++i)
        for (int j = 0; j < n; ++j)
        {
            if (s[i][j] == '#')
                continue;
            mcmf.AddEdge(rid[i][j], rcnt + cid[i][j], 1, 0);
        }
    mcmf.AddEdge(rcnt + ccnt + 2, 0, k, 0);
    printf("%d\n", mcmf.MincostMaxflow(rcnt + ccnt + 2, rcnt + ccnt + 1));
    return 0;
}

{"mode":"full","isActive":false}


Problem solution in C.

#include<stdio.h>
#include<stdbool.h>
#define maxn 155
#define maxV 24035
#define maxE 96110
bool area[maxn][maxn];
int hnum[maxn][maxn], vnum[maxn][maxn], vdeg[maxn*maxn], hdeg[maxn*maxn], first[maxV], next[maxE], to[maxE], from[maxE], cap[maxE], cost[maxE], ecnt;
void add_edge(int u, int v, int _cap, int _cost)
{
    next[ecnt] = first[u];
    to[ecnt] = v;
    from[ecnt] = u;
    cap[ecnt] = _cap;
    cost[ecnt] = _cost;
    first[u] = ecnt;
    ecnt++;
    next[ecnt] = first[v];
    to[ecnt] = u;
    from[ecnt] = v;
    cap[ecnt] = 0;
    cost[ecnt] = -_cost;
    first[v] = ecnt;
    ecnt++;
}
bool inq[maxV];
int q[maxV], dist[maxV], h[maxV];
int push_flow(int S, int T)
{
    for( int i = 0 ; i <= T ; i++ )
    {
        inq[i] = 0, dist[i] = (int)1e9, h[i] = -1;
    }
    int ql = 0, qr = 0;
    dist[S] = 0;
    h[S] = -1;
    q[qr++] = S;
    inq[S] = 1;
    while( ql != qr )
    {
        int cur = q[ql];
        inq[cur] = 0;
        ql++; 
        if( ql == maxV )
        {
            ql = 0;
        }
        for( int i = first[cur] ; i != -1 ; i = next[i] )
        {
            if( cap[i] > 0 && dist[to[i]] > dist[cur] + cost[i] )
            {
                dist[to[i]] = dist[cur] + cost[i];
                h[to[i]] = i;
                if(!inq[to[i]])
                {
                    q[qr] = to[i];
                    inq[to[i]] = 1;
                    qr++;
                    if( qr == maxV )
                    {
                        qr = 0;
                    }
                }
            }
        }
    }
    if( dist[T] == (int)1e9 )
    {
        return -1;
    }
    int cur = T, pcost = 0;
    while( h[cur] != -1 )
    {
        cap[h[cur]]--;
        cap[h[cur]^1]++;
        pcost += cost[h[cur]];
        cur = from[h[cur]];
    }
    return pcost;
}
int main()
{
    int n, k;
    scanf("%d%d", &n, &k);
    for( int i = 0 ; i < n ; i++ )
    {
        for( int j = 0 ; j < n ; j++ )
        {
            char u[3];
            scanf("%1s", u);
            if( u[0] == '#' )
            {
                area[i][j] = 0;
            }
            else
            {
                area[i][j] = 1;
            }
        }
    }
    int hcnt = 0, vcnt = 0;
    for( int i = 0 ; i < n ; i++ )
    {
        for( int j = 0 ; j < n ; j++ )
        {
            if(area[i][j])
            {
                if( j == 0 || !area[i][j-1] )
                {
                    hnum[i][j] = hcnt++;
                }
                else
                {
                    hnum[i][j] = hnum[i][j-1];
                }
            }
        }
    }
    for( int j = 0 ; j < n ; j++ )
    {
        for( int i = 0 ; i < n ; i++ )
        {
            if(area[i][j])
            {
                if( i == 0 || !area[i-1][j] )
                {
                    vnum[i][j] = vcnt++;
                }
                else
                {
                    vnum[i][j] = vnum[i-1][j];
                }
            }
        }
    }
    int S = hcnt + vcnt, T = hcnt + vcnt + 1;
    ecnt = 0;
    for( int i = 0 ; i < hcnt ; i++ )
    {
        hdeg[i] = 0;
    }
    for( int i = 0 ; i < vcnt ; i++ )
    {
        vdeg[i] = 0;
    }
    for( int i = 0 ; i < n ; i++ )
    {
        for( int j = 0 ; j < n ; j++ )
        {
            if(area[i][j])
            {
                hdeg[hnum[i][j]]++, vdeg[vnum[i][j]]++;
            }
        }
    }
    for( int i = 0 ; i <= T ; i++ )
    {
        first[i] = -1;
    }
    for( int i = 0 ; i < hcnt ; i++ )
    {
        for( int j = 0 ; j < hdeg[i] ; j++ )
        {
            add_edge(S, i, 1, j);
        }
    }
    for( int i = 0 ; i < vcnt ; i++ )
    {
        for( int j = 0 ; j < vdeg[i] ; j++ )
        {
            add_edge(i+hcnt, T, 1, j);
        }
    }
    for( int i = 0 ; i < n ; i++ )
    {
        for( int j = 0 ; j < n ; j++ )
        {
            if(area[i][j])
            {
                add_edge(hnum[i][j], vnum[i][j] + hcnt, 1, 0);
            }
        }
    }
    int res = 0;
    for( int i = 0 ; i < k ; i++ )
    {
        int z = push_flow(S, T);
        res += z;
    }
    printf("%d", res);
    return 0;
}

{"mode":"full","isActive":false}