#include <bits/stdc++.h>
using namespace std;
const int inf = 1e9 + 7;
int n, M;
vector<int> v, odp;
int dp[5005][5005];
int pref[5005][5005];
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin >> n;
v.resize(n);
for (int& i : v)
{
cin >> i;
M = M < i ? i : M;
}
sort(v.begin(), v.end());
if (v[0] != 1)
{
cout << "0\n";
return 0;
}
// dp[i][j] = ilosc dobrych podzbiorow [0, i] o sumie dokladnie j
dp[0][1] = 1;
for (int i = 1; i < n; i++)
for (int j = 1; j <= M; j++)
{
int tmp = dp[i - 1][j - v[i]] * (j >= 2 * v[i] - 1) + dp[i - 1][j] + (v[i] == (j == 1));
dp[i][j] = tmp >= inf ? tmp - inf : tmp;
}
// pref[i][j] = ilosc dobrych podzbiorow [0, i] o sumie <= j
for (int i = 0; i < n; i++)
for (int j = 1; j <= M; j++)
{
int tmp = pref[i][j - 1] + dp[i][j];
pref[i][j] = tmp >= inf ? tmp - inf : tmp;
}
// odp[i] = ilosc dobrych podzbiorow [0, i]
int odp = 1;
/*for (; i < n && v[i] == 1; i++)
{
odp = 2 * odp + 1;
odp = odp > inf ? odp - inf : odp;
} */
for (int i = 1; i < n; i++)
{
odp = 2 * odp - pref[i - 1][v[i] - 2] + (v[i] == 1);
if (odp < 0)
odp += inf;
else if (odp >= inf)
odp -= inf;
}
cout << odp << '\n';
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 | #include <bits/stdc++.h> using namespace std; const int inf = 1e9 + 7; int n, M; vector<int> v, odp; int dp[5005][5005]; int pref[5005][5005]; int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cin >> n; v.resize(n); for (int& i : v) { cin >> i; M = M < i ? i : M; } sort(v.begin(), v.end()); if (v[0] != 1) { cout << "0\n"; return 0; } // dp[i][j] = ilosc dobrych podzbiorow [0, i] o sumie dokladnie j dp[0][1] = 1; for (int i = 1; i < n; i++) for (int j = 1; j <= M; j++) { int tmp = dp[i - 1][j - v[i]] * (j >= 2 * v[i] - 1) + dp[i - 1][j] + (v[i] == (j == 1)); dp[i][j] = tmp >= inf ? tmp - inf : tmp; } // pref[i][j] = ilosc dobrych podzbiorow [0, i] o sumie <= j for (int i = 0; i < n; i++) for (int j = 1; j <= M; j++) { int tmp = pref[i][j - 1] + dp[i][j]; pref[i][j] = tmp >= inf ? tmp - inf : tmp; } // odp[i] = ilosc dobrych podzbiorow [0, i] int odp = 1; /*for (; i < n && v[i] == 1; i++) { odp = 2 * odp + 1; odp = odp > inf ? odp - inf : odp; } */ for (int i = 1; i < n; i++) { odp = 2 * odp - pref[i - 1][v[i] - 2] + (v[i] == 1); if (odp < 0) odp += inf; else if (odp >= inf) odp -= inf; } cout << odp << '\n'; } |
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