#include <bits/stdc++.h>
#define ll long long
#define str string
#define pii pair<int, int>
#define pll pair<ll, ll>
#define fi first
#define se second
#define vc vector<char>
#define vvc vector<vc>
#define vi vector<int>
#define vll vector<ll>
#define vvi vector<vi>
#define vvll vector<vll>
#define vvvll vector<vvll>
#define vs vector<str>
#define vvs vector<vs>
#define vpii vector<pii>
#define vvpii vector<vpii>
#define vpll vector<pll>
#define vvpll vector<vpll>
#define vb vector<bool>
#define vvb vector<vb>
#define rep(i, a, b) for (int i = (a); i < int(b); i++)
#define repi(i, a, b) for (int i = (a); i <= int(b); i++)
using namespace std;
ll INF = LONG_LONG_MAX;
template <typename T, typename L>
void read(vector<T> & _data, L & _size, bool _shift) {
_data.resize(_size + (ll)_shift);
for (ll i = (ll)_shift; i < _size + (ll)_shift; i++)
cin >> _data[i];
}
template <typename T, typename L>
void read(vector<vector<T>> & _data, L & _rows, L & _cols, bool _shiftRows, bool _shiftCols) {
_data.resize(_rows + (ll)_shiftRows);
for (ll i = 0; i < _rows + (ll)_shiftRows; i++)
_data[i].resize(_cols + (ll)_shiftCols);
for (ll i = (ll)_shiftRows; i < _rows + (ll)_shiftRows; i++)
for (ll j = (ll)_shiftCols; j < _cols + (ll)_shiftCols; j++)
cin >> _data[i][j];
}
template <typename T>
void write(vector<T> & _data, bool _shift) {
for (ll i = (ll)_shift; i < _data.size(); i++)
cout << _data[i] << " ";
cout << endl;
}
//TODO: SOLUTION
void solve() {
ll n, m, p; cin >> n >> m >> p;
vvll dp(n, vll(m, 0)); // dp[i][j] = kolorowania, t.że sztacheta i ma j pokolorowany najwyżej
vvll presums(n, vll(m, 0));
dp[0][0] = 1;
presums[0][0] = 1;
for (ll j = 1; j < m; j++) {
dp[0][j] = dp[0][j - 1] + 1;
dp[0][j] = dp[0][j] % p;
presums[0][j] = dp[0][j] + presums[0][j-1];
presums[0][j] = presums[0][j] % p;
}
for (int i = 1; i < n; i++) {
dp[i][0] = dp[i-1][m-1]; // symetria
presums[i][0] = dp[i][0];
for (int j = 1; j < m; j++) {
dp[i][j] = dp[i][j - 1]; // jestesmy polaczeni od lewej ponizej j
dp[i][j] += j * dp[i-1][m-j-1]; // mamy spod i jestesmy polaczeni powyzej j-1 (symetria)
dp[i][j] = dp[i][j] % p;
// case gdy i,j jest jedyny pomalowany
ll powy = presums[i-1][m-1] - presums[i-1][j-1]; // koncza sie powyzej j
while (powy < 0)
powy += p;
ll poni;
if (j == m-1)
poni = 0;
else
poni = presums[i-1][m-j-2];
ll sposy = powy - poni;
while (sposy < 0)
sposy += p;
dp[i][j] += sposy;
dp[i][j] = dp[i][j] % p;
presums[i][j] = presums[i][j-1] + dp[i][j];
presums[i][j] = presums[i][j] % p;
}
}
cout << presums[n-1][m-1] << endl;
}
int main() {
ios::sync_with_stdio(false);
// TODO: Set value of this variable manually
bool _multipleTestCases = false;
if (_multipleTestCases) {
ll t; cin >> t;
while (t--)
solve();
}
else {
solve();
}
return 0;
}
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 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 | #include <bits/stdc++.h> #define ll long long #define str string #define pii pair<int, int> #define pll pair<ll, ll> #define fi first #define se second #define vc vector<char> #define vvc vector<vc> #define vi vector<int> #define vll vector<ll> #define vvi vector<vi> #define vvll vector<vll> #define vvvll vector<vvll> #define vs vector<str> #define vvs vector<vs> #define vpii vector<pii> #define vvpii vector<vpii> #define vpll vector<pll> #define vvpll vector<vpll> #define vb vector<bool> #define vvb vector<vb> #define rep(i, a, b) for (int i = (a); i < int(b); i++) #define repi(i, a, b) for (int i = (a); i <= int(b); i++) using namespace std; ll INF = LONG_LONG_MAX; template <typename T, typename L> void read(vector<T> & _data, L & _size, bool _shift) { _data.resize(_size + (ll)_shift); for (ll i = (ll)_shift; i < _size + (ll)_shift; i++) cin >> _data[i]; } template <typename T, typename L> void read(vector<vector<T>> & _data, L & _rows, L & _cols, bool _shiftRows, bool _shiftCols) { _data.resize(_rows + (ll)_shiftRows); for (ll i = 0; i < _rows + (ll)_shiftRows; i++) _data[i].resize(_cols + (ll)_shiftCols); for (ll i = (ll)_shiftRows; i < _rows + (ll)_shiftRows; i++) for (ll j = (ll)_shiftCols; j < _cols + (ll)_shiftCols; j++) cin >> _data[i][j]; } template <typename T> void write(vector<T> & _data, bool _shift) { for (ll i = (ll)_shift; i < _data.size(); i++) cout << _data[i] << " "; cout << endl; } //TODO: SOLUTION void solve() { ll n, m, p; cin >> n >> m >> p; vvll dp(n, vll(m, 0)); // dp[i][j] = kolorowania, t.że sztacheta i ma j pokolorowany najwyżej vvll presums(n, vll(m, 0)); dp[0][0] = 1; presums[0][0] = 1; for (ll j = 1; j < m; j++) { dp[0][j] = dp[0][j - 1] + 1; dp[0][j] = dp[0][j] % p; presums[0][j] = dp[0][j] + presums[0][j-1]; presums[0][j] = presums[0][j] % p; } for (int i = 1; i < n; i++) { dp[i][0] = dp[i-1][m-1]; // symetria presums[i][0] = dp[i][0]; for (int j = 1; j < m; j++) { dp[i][j] = dp[i][j - 1]; // jestesmy polaczeni od lewej ponizej j dp[i][j] += j * dp[i-1][m-j-1]; // mamy spod i jestesmy polaczeni powyzej j-1 (symetria) dp[i][j] = dp[i][j] % p; // case gdy i,j jest jedyny pomalowany ll powy = presums[i-1][m-1] - presums[i-1][j-1]; // koncza sie powyzej j while (powy < 0) powy += p; ll poni; if (j == m-1) poni = 0; else poni = presums[i-1][m-j-2]; ll sposy = powy - poni; while (sposy < 0) sposy += p; dp[i][j] += sposy; dp[i][j] = dp[i][j] % p; presums[i][j] = presums[i][j-1] + dp[i][j]; presums[i][j] = presums[i][j] % p; } } cout << presums[n-1][m-1] << endl; } int main() { ios::sync_with_stdio(false); // TODO: Set value of this variable manually bool _multipleTestCases = false; if (_multipleTestCases) { ll t; cin >> t; while (t--) solve(); } else { solve(); } return 0; } |
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