The Blacklist

Problem Statement :

A new gangster is trying to take control of the city. He makes a list of his N adversaries (e.g. gangster 1, gangster 2, ... gangster N-1, gangster N) and plans to get rid of them.

K mercenaries are willing to do the job. The gangster can use any number of these mercenaries. But he has to honor one condition set by them: they have to be assigned in such a way that they eliminate a consecutive group of gangsters in the list, e.g. gangster i, gangster i+1, ..., gangster j-1, gangster j, where the following is true: 1 <= i <= j <= N.

While our new gangster wants to kill all of them, he also wants to pay the least amount of money. All mercenaries charge a different amount to kill different people. So he asks you to help him minimize his expenses.

Input Format

The first line contains two space-separated integers, N and K. Then K lines follow, each containing N integers as follows:
The jth number on the ith line is the amount charged by the ith mercenary for killing the jth gangster on the list.

1 <= N <= 20
1 <= K <= 10
0 <= amount charged <= 10000
Output Format

Just one line, the minimum cost for killing the N gangsters on the list.

Solution :


                            Solution in C :

In C++ :

#include <cstdio>
#include <cmath>
#include <iostream>
#include <set>
#include <algorithm>
#include <vector>
#include <map>
#include <cassert>
#include <string>
#include <cstring>

using namespace std;

#define rep(i,a,b) for(int i = a; i < b; i++)
#define S(x) scanf("%d",&x)
#define P(x) printf("%d\n",x)

typedef long long int LL;
const int INF = 100000000;
int C[10][20];
int memo[1<<10][11][21];
int n,k;

int solve(int mask, int last, int idx) {
	// printf("%d %d %d\n",mask,last,idx);
	if(last == -1) {
		int res = INF;
		rep(i,0,k) res = min(res, C[i][idx] + solve(mask|(1<<i), i, idx+1));

		return res;
	if(idx == n) return 0;

	int &res = memo[mask][last][idx];
	if(memo[mask][last][idx] != INF) 
		return memo[mask][last][idx];

	res = C[last][idx] + min(res, solve(mask, last, idx+1));

	rep(i,0,k) if(!((mask>>i)&1)) {
		res = min(res, C[i][idx] + solve(mask|(1<<i) , i, idx+1) );

	return res;

int main() {

	rep(i,0,1<<k) rep(j,0,k) rep(l,0,n) memo[i][j][l] = INF;

	rep(i,0,k) rep(j,0,n) S(C[i][j]);

	printf("%d\n",solve(0, -1, 0));

	return 0;


In Java :

import java.util.Scanner;

public class Solution {

    public static void main(String[] args) {
        Scanner input = new Scanner(;
        int N = input.nextInt();
        int K = input.nextInt();
        int[][] price = new int[K][N];
        for (int k=0; k<K; k++) {
            for (int n=0; n<N; n++) {
                price[k][n] = input.nextInt();
        int limit = 1<<K;
        int[][] dp = new int[N+1][limit+1];
        for (int n=0; n<=N; n++) {
            for (int x=0; x<=limit; x++) {
                dp[n][x] = 1000000;
        dp[0][0] = 0;
        for (int n=1; n<=N; n++) {
            for (int k=0; k<K; k++) {
                int mask = 1 << k;
                for (int from=1; from<=n; from++) {
                    for (int x=0; x<limit; x++) {
                        if ((x&mask) == 0) {
                            int newMask = x|mask;
                            int newValue = dp[from-1][x];
                            for (int i=from; i<=n; i++) {
                                newValue += price[k][i-1];
                            if (dp[n][newMask] > newValue) {
                                dp[n][newMask] = newValue;
        int min = Integer.MAX_VALUE;
        for (int value : dp[N]) {
            min = Math.min(min, value);

In C :

#define MIN(x,y) x<y?x:y
int res,n,k,a[15][25]={0};
void find(int curr,int d[],int i,int sumsofar)

        //printf("here %d %d %d %d\n",curr,i,sumsofar,res);
    int p[25],x=0;

    int j,l;
        if(sumsofar+a[p[j]][l]<sumsofar+a[i][l] && sumsofar+a[p[j]][l]<res)
           // printf("here also %d %d\n",p[j],i);
int main()
    int i,j;
      //  printf("%d ",b[i][j]);
   // printf("\n");
    //int min=INT_MAX;
    int d[25]={0};
    return 0;

In Python3 :

G, M = [int(s) for s in input().split()]

costs = list()
cache = dict()

for i in range(M):
    costs.append([int(s) for s in input().split()])

def kill(gn, imercs):
    key = str(gn)+str(imercs)
    if key in cache:
        return cache[key]

    mercs = imercs[:]
    if gn == 0:
        return 0

    temp = list()
    for m in mercs:
        tempm = mercs[:]
        if len(tempm) == 0:
            for c in range(gn - 1, -1, -1):
                temp.append(sum(costs[m][c:gn]) + kill(c, tempm))
    cache[key] = min(temp)
    return min(temp)

print(str(kill(G, [i for i in range(M)])))

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