2020 Jiangsu Collegiate Programming Contest
阿新 • • 發佈:2020-11-29
8 / 45 Problem A CFGym 102875A Array !!!
1 / 3 Problem B CFGym 102875B Building Blocks !!!
70 / 90 Problem C CFGym 102875C Cats ---
64 / 125 Problem D CFGym 102875D Delete Prime ---
2 / 6 Problem E CFGym 102875E Eliminate the Virus ???
0 / 14 Problem F CFGym 102875F Flee from Maze ???
15 / 59 Problem G CFGym 102875G Grid Coloring !!!
首先打表觀察(預設n<=m)
1.n和m都大於等於5的輸出8
2.n等於4且m==4,輸出18,m>=5,輸出14
3.n=1,n=2,n=3都是和斐波那契有關的序列,直接大力bm
#include<stdio.h> #include<algorithm> using namespace std; #include <bits/stdc++.h> #define eps 1e-8 #define INF 0x3f3f3f3f #define PI acos(-1) #define lson l,mid,rt<<1 #define rson mid+1,r,(rt<<1)+1 #define CLR(x,y) memset((x),y,sizeof(x)) #define fuck(x) cerr << #x << "=" << x << endl using namespace std; typedef long long ll; typedef unsigned long long ull; const int seed = 131; const int maxn = 1e5 + 5; #define rep(i,a,n) for (int i=a;i<n;i++) #define pb push_back #define SZ(x) ((ll)(x).size()) typedef vector<ll> VI; typedef pair<ll, ll> PII; const ll mod = 1000000007; ll powmod(ll a, ll b) { ll res = 1; a %= mod; assert(b >= 0); for (; b; b >>= 1) { if (b & 1)res = res * a % mod; a = a * a % mod; } return res; } // head ll _; namespace linear_seq { const ll N = 10010; ll res[N], base[N], _c[N], _md[N]; vector<ll> Md; void mul(ll *a, ll *b, ll k) { rep(i, 0, k + k) _c[i] = 0; rep(i, 0, k) if (a[i]) rep(j, 0, k) _c[i + j] = (_c[i + j] + a[i] * b[j]) % mod; for (ll i = k + k - 1; i >= k; i--) if (_c[i]) rep(j, 0, SZ(Md)) _c[i - k + Md[j]] = (_c[i - k + Md[j]] - _c[i] * _md[Md[j]]) % mod; rep(i, 0, k) a[i] = _c[i]; } ll solve(ll n, VI a, VI b) { // a 係數 b 初值 b[n+1]=a[0]*b[n]+... // printf("%d\n",SZ(b)); ll ans = 0, pnt = 0; ll k = SZ(a); assert(SZ(a) == SZ(b)); rep(i, 0, k) _md[k - 1 - i] = -a[i]; _md[k] = 1; Md.clear(); rep(i, 0, k) if (_md[i] != 0) Md.push_back(i); rep(i, 0, k) res[i] = base[i] = 0; res[0] = 1; while ((1ll << pnt) <= n) pnt++; for (ll p = pnt; p >= 0; p--) { mul(res, res, k); if ((n >> p) & 1) { for (ll i = k - 1; i >= 0; i--) res[i + 1] = res[i]; res[0] = 0; rep(j, 0, SZ(Md)) res[Md[j]] = (res[Md[j]] - res[k] * _md[Md[j]]) % mod; } } rep(i, 0, k) ans = (ans + res[i] * b[i]) % mod; if (ans < 0) ans += mod; return ans; } VI BM(VI s) { VI C(1, 1), B(1, 1); ll L = 0, m = 1, b = 1; rep(n, 0, SZ(s)) { ll d = 0; rep(i, 0, L + 1) d = (d + (ll)C[i] * s[n - i]) % mod; if (d == 0) ++m; else if (2 * L <= n) { VI T = C; ll c = mod - d * powmod(b, mod - 2) % mod; while (SZ(C) < SZ(B) + m) C.pb(0); rep(i, 0, SZ(B)) C[i + m] = (C[i + m] + c * B[i]) % mod; L = n + 1 - L; B = T; b = d; m = 1; } else { ll c = mod - d * powmod(b, mod - 2) % mod; while (SZ(C) < SZ(B) + m) C.pb(0); rep(i, 0, SZ(B)) C[i + m] = (C[i + m] + c * B[i]) % mod; ++m; } } return C; } ll gao(VI a, ll n) { VI c = BM(a); c.erase(c.begin()); rep(i, 0, SZ(c)) c[i] = (mod - c[i]) % mod; return solve(n, c, VI(a.begin(), a.begin() + SZ(c))); } }; vector<ll>v; void init1() { v.clear(); v.push_back(2); v.push_back(4); v.push_back(6); v.push_back(10); v.push_back(16); v.push_back(26); v.push_back(42); v.push_back(68); } void init3() { v.clear(); v.push_back(44); v.push_back(64); v.push_back(104); v.push_back(164); v.push_back(264); v.push_back(424); v.push_back(684); } int a[100][100]; ll n,m; int cnt=0; void dfs(int now,int a[][100]){ if(now==n*m){ cnt++; return ; } int x=now/m; int y=now%m; a[x][y]=0; int flag=1; if(y>=2){ if(a[x][y-1]==a[x][y-2]&&a[x][y-1]==a[x][y])flag=0; } if(x>=2){ if(a[x-1][y]==a[x-2][y]&&a[x-1][y]==a[x][y])flag=0; } if(x>=2&&y>=2){ if(a[x-1][y-1]==a[x][y]&&a[x-2][y-2]==a[x][y])flag=0; } if(x>=2&&y<m-2){ if(a[x-1][y+1]==a[x][y]&&a[x-2][y+2]==a[x][y])flag=0; } if(flag==1)dfs(now+1,a); a[x][y]=1; flag=1; if(y>=2){ if(a[x][y-1]==a[x][y-2]&&a[x][y-1]==a[x][y])flag=0; } if(x>=2){ if(a[x-1][y]==a[x-2][y]&&a[x-1][y]==a[x][y])flag=0; } if(x>=2&&y>=2){ if(a[x-1][y-1]==a[x][y]&&a[x-2][y-2]==a[x][y])flag=0; } if(x>=2&&y<m-2){ if(a[x-1][y+1]==a[x][y]&&a[x-2][y+2]==a[x][y])flag=0; } if(flag==1)dfs(now+1,a); } int main(){ int t; scanf("%d",&t); while(t--){ scanf("%lld %lld",&n,&m);cnt=0; if(n>m)swap(n,m); if(n>=5){ printf("8\n"); continue; } if(n==4){ if(m>=5)printf("14\n"); else if(m==4) printf("18\n"); continue; } if(n==1) { init1(); printf("%lld\n",linear_seq::gao(v,m-1)); } if(n==2) { init1(); printf("%lld\n",linear_seq::gao(v,m-1)*linear_seq::gao(v,m-1)%mod); } if(n==3) { init3(); if(m==3) printf("32\n"); else printf("%lld\n",linear_seq::gao(v,m-4)); } //printf("8\n"); } }