uva12105 Bigger is Better

更简单的做法：
定义状态dp[i][j]表示在已经用了i根火柴的情况下拼出来了剩余部分(是剩余部分，不是已经拼出来了的)为j(需要%m)的最大长度，一个辅助数组p[i][j]表示状态[i][j]的最高位
是往后添加k
dp[i][j]=max(dp[i][j],dp[i-c[k]][(j*10+k)%m]+1)
(这里应该要证明dp[i-c[k]][(j*10+k)%m]加了d%m=j，没证出来...
倒着枚举k，这样保证位数相同存更大的数

#include<cstdio>
#include<cstring>
#include<iostream>
using namespace std;

const int maxn = 105;
const int maxm = 3005;

// dp[i][j] is the maximal length of the integer whose remainder is j (with at most i matches)
// p[i][j] is the maximal digit for state (i,j)
int n, m, dp[maxn][maxm], p[maxn][maxm];

int needs[] = { 6, 2, 5, 5, 4, 5, 6, 3, 7, 6 };

int main(){
  int kase = 0;
  while(scanf("%d%d", &n, &m) == 2) {
    printf("Case %d: ", ++kase);

    for(int i = 0; i <= n; i++)          //dp[i][j]=max(dp[i][j],dp[i-c[k]][(j*10+k)%m]+1)
      for(int j = 0; j < m; j++){                   //注意枚举的是火柴数不是位数
        int& ans = dp[i][j];
        ans = p[i][j] = -1;
        if (j == 0) ans = 0;
        for(int d = 9; d >= 0; d--)
          if (i >= needs[d]){
            int t = dp[i - needs[d]][(j * 10 + d) % m];

            if (t >= 0 && t + 1 > ans){   //t exist
              ans = t + 1;
              p[i][j] = d;
            }
          }
      }

    if (p[n][0] < 0) printf("-1");
    else {
      int i = n, j = 0;
      for(int d = p[i][j]; d >= 0; d = p[i][j]){
        printf("%d", d);
        i -= needs[d];
        cout<<"x"<<j<<endl;
        j = (j * 10 + d) % m;
        //printf("%d", j);
      }
    }
    printf("\n");
  }
  return 0;
}