Created
August 14, 2017 07:11
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import java.util.*; | |
import java.io.*; | |
public class MikeandMatrixGame { | |
/************************ SOLUTION STARTS HERE ************************/ | |
static final int MAX = 1234; | |
static double logFact[]; | |
static { | |
logFact = new double[MAX]; | |
for(int i = 2; i < MAX; i++) | |
logFact[i] = Math.log(i) + logFact[i - 1]; | |
} | |
private static void solve() { | |
int N = nextInt(); | |
int K = nextInt(); | |
int X = nextInt(); | |
int arr[][] = new int[N][]; | |
int trans[][] = new int[N][N]; | |
for(int i = 0; i < N; i++) | |
arr[i] = nextIntArray(N); | |
for(int i = 0; i < N; i++) | |
for(int j = 0; j < N; j++) | |
trans[j][i] = arr[i][j]; | |
for(int i = 0; i < N; i++) | |
Arrays.sort(trans[i]); | |
double totalExpectation = 0; | |
for(int i = 0; i < N; i++) { | |
double colExpectation = 0; | |
for(int j = 1; j <= N - K + 1; j++) { | |
double logProb = Math.log(K) + logFact[N - K] + logFact[N - j] - logFact[N - K - (j - 1)] - logFact[N]; | |
double prob = Math.exp(logProb); | |
colExpectation += prob * (trans[i][N - j] + X); | |
} | |
totalExpectation += colExpectation; | |
} | |
println(String.format("%.15f", totalExpectation)); | |
} | |
/************************ SOLUTION ENDS HERE ************************/ | |
/************************ TEMPLATE STARTS HERE **********************/ | |
public static void main(String[] args) throws IOException { | |
reader = new BufferedReader(new InputStreamReader(System.in)); | |
writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)), false); | |
st = null; | |
solve(); | |
reader.close(); | |
writer.close(); | |
} | |
static BufferedReader reader; | |
static PrintWriter writer; | |
static StringTokenizer st; | |
static String next() | |
{while(st == null || !st.hasMoreTokens()){try{String line = reader.readLine();if(line == null){return null;} | |
st = new StringTokenizer(line);}catch (Exception e){throw new RuntimeException();}}return st.nextToken();} | |
static String nextLine() {String s=null;try{s=reader.readLine();}catch(IOException e){e.printStackTrace();}return s;} | |
static int nextInt() {return Integer.parseInt(next());} | |
static long nextLong() {return Long.parseLong(next());} | |
static double nextDouble(){return Double.parseDouble(next());} | |
static char nextChar() {return next().charAt(0);} | |
static int[] nextIntArray(int n) {int[] a= new int[n]; int i=0;while(i<n){a[i++]=nextInt();} return a;} | |
static long[] nextLongArray(int n) {long[]a= new long[n]; int i=0;while(i<n){a[i++]=nextLong();} return a;} | |
static int[] nextIntArrayOneBased(int n) {int[] a= new int[n+1]; int i=1;while(i<=n){a[i++]=nextInt();} return a;} | |
static long[] nextLongArrayOneBased(int n){long[]a= new long[n+1];int i=1;while(i<=n){a[i++]=nextLong();}return a;} | |
static void print(Object o) { writer.print(o); } | |
static void println(Object o){ writer.println(o);} | |
/************************ TEMPLATE ENDS HERE ************************/ | |
} |
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