7 August

P1021 postage stamp design

Violent search of each denomination.

• Pruning 1: nominal value is incremented, a new denomination \ (\ in [G_ {i -1} +1, n \ cdot sum] \) Why not on the boundary. \ (N-\ CDOT G_ {I-1} + 1'd \) it?
• Pruning 2: \ (= G_1. 1 \) .

dp seeking the maximum nominal value.

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

int n, k, f[5005], G[17], ans[17], MAX;

int calc(int dep, int sum) {
    memset(f, 0x3f, sizeof f);
    f[0]=0;
    for (int i=1; i<=dep; ++i) for (int j=G[i]; j<=sum*n; ++j)
        f[j]=min(f[j], f[j-G[i]]+1);
    for (int i=1; i<=sum*n; ++i) if (f[i]>n) return i-1;
    return sum*n;
}

void dfs(int dep, int m, int sum) {
    if (dep>k) {
        if (MAX<m) {MAX=m; for (int i=1; i<=k; ++i) ans[i]=G[i]; }
        return;
    }
    for (int i=G[dep-1]+1; i<=m+1; ++i) // *1
        G[dep]=i, dfs(dep+1, calc(dep, sum+i), sum+i);
}

int main() {
    scanf("%d%d", &n, &k);
    G[1]=1, dfs(2, n, 1); // *2
    for (int i=1; i<=k; ++i) printf("%d ", ans[i]);
    printf("\nMAX=%d\n", MAX);
    return 0;
}