CF1340B Nastya and Scoreboard (dp 确定可行方案)

Nastya and Scoreboard

思路：先确定每个位置上变成0~9需要额外点亮多少灯，因为需要用完k个灯，可以有前导零，我们从最后一位开始点亮灯，往前递推可行的方案。dp[当前位置][用了j个灯] = （可行，不可行）。

然后就判断能不能用完k个灯，可以得话从前往后以9~0顺序寻找最大数字。

#include <cstdio>
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <functional>
#include <set>
#include <vector>
#include <queue>
#include <cstring>
#include <stack>
 
using namespace std;
 
#define ll long long
#define pb push_back
#define fi first
#define se second

string digits[10] = { "1110111", "0010010", "1011101", "1011011", "0111010",
                   "1101011", "1101111", "1010010", "1111111", "1111011" };

void solve(){
    int n, k;
    cin >> n >> k;
    vector<string > s(n);
    for(auto& str : s) cin >> str;
    vector<vector<int > > dist(n + 1, vector<int>(10 ));
    for(int i = 0; i < n; ++i){
        for(int d = 0; d < 10; ++d){
            for(int j = 0; j < 7; ++j){
                char x = s[i][j];
                char y = digits[d][j];
                if(x == '1' && y == '0'){
                    dist[i][d] = -1;
                    break;
                }
                if(x == '0' && y == '1'){
                    ++dist[i][d];
                }
            }
        }
    }

    vector<vector<int > > dp(n + 1, vector<int >(k + 1));
    dp[n][0] = 1;
    for(int i = n; i > 0; --i){
        for(int j = 0; j <= k; ++j){
            if(dp[i][j]){
                for(int d = 0; d < 10; ++d){
                    if(dist[i - 1][d] != -1 && j + dist[i - 1][d] <= k){
                        dp[i - 1][j + dist[i - 1][d]] = 1;
                    }
                }
            }
        }
    }
    if(dp[0][k] == 0) cout << "-1" << endl;
    else{
        int now = -1;
        for(int i = 0; i < n; ++i){
            for(int d = 9; d >= 0; --d){
                if(dist[i][d] != -1 && k >= dist[i][d] && dp[i + 1][k - dist[i][d]]){
                    now = d;
                    k -= dist[i][d];
                    break;
                }
            }
            cout << now;
        }
        cout << endl;
    }
}
 
int main(){
    
    // freopen("C:\Users\admin\Desktop\input.txt", "r", stdin);
    // freopen("C:\Users\admin\Desktop\output.txt", "w", stdout);
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    solve();
    
    return 0;
}