代码

• 时间复杂度：O(n+m)O(n+m)O(n+m)

#include 
#define IOS ios::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
using namespace std;
typedef long long ll;
void show(){std::cerr << endl;}templatevoid show(T x,Args... args){std::cerr << "[ " << x <<  " ] , ";show(args...);}const int MAX = 2e5+50;
const int MOD = 1e9+7;
const int INF = 0x3f3f3f3f;
const ll LINF = 0x3f3f3f3f3f3f3f3f;
const double EPS = 1e-5;ll qpow(ll a,ll n){/* */ll res = 1LL;while(n){if(n&1)res=res*a%MOD;a=a*a%MOD;n>>=1;}return res;}
ll qpow(ll a,ll n,ll p){a%=p;ll res = 1LL;while(n){if(n&1)res=res*a%p;a=a*a%p;n>>=1;}return res;}
ll npow(ll a,ll n){/* */ll res = 1LL;while(n){if(n&1)res=res*a;a=a*a;n>>=1;if(res<0||a<0)return 0;}return res;}
ll inv(ll a){/* */return qpow(a,MOD-2);}
ll inv(ll a,ll p){return qpow(a,p-2,p);}unordered_mapM[MAX];
int aa[MAX];
int cnt[MAX];
ll dp[MAX][2];int F(int n,int m){return n + m - 1;
}int main()
{int T;scanf("%d",&T);for(int kase = 1;kase <= T;++kase){ll ans = 0;int n,m,k;scanf("%d%d%d",&n,&m,&k);int min_nm = min(n,m);for(int i = 1;i <= n + m;++i){M[i].clear();}for(int i = 1;i <= min_nm;++i){cnt[i] = i;}for(int i = min_nm;i <= n + m - 1;++i){cnt[i] = min_nm;}for(int i = 1;i <= min_nm;++i){cnt[n + m - i] = i;}for(int i = 1;i <= n + m;++i){scanf("%d",&aa[i]);}bool cant = false;for(int i = 1;i <= k;++i){int x,y,h;scanf("%d%d%d",&x,&y,&h);int aim = F(x,y);M[aim][h] = 1;cnt[aim]--;if(h > aa[aim] || h > aa[aim+1]){cant = true;}}if(aa[1] > aa[2]){cant = true;}if(cnt[1] == 0 && !M[1][aa[1]]){cant = true;}if(!cant){// initdp[1][1] = dp[1][0] = 0;if(aa[1] == aa[2]) dp[1][1] = 1;else dp[1][0] = 1;for(int i = 2;i <= n + m - 1;++i){dp[i][0] = dp[i][1] = 0;int a = aa[i],b = aa[i+1];int k = min(a,b);bool ys = M[i][k];int ccnt = cnt[i];ll rem = (qpow(k,ccnt) - qpow(k-1,ccnt) + MOD) % MOD;// dp[i-1][1]if(b <= a){if(ys) dp[i][1] = (dp[i][1] + dp[i-1][1] * qpow(b,ccnt) % MOD) % MOD;else dp[i][1] = (dp[i][1] + dp[i-1][1] * rem % MOD) % MOD;}if(b <= a && !ys){dp[i][0] = (dp[i][0] + dp[i-1][1] * qpow(b-1,ccnt) % MOD) % MOD;}else if(a < b){dp[i][0] = (dp[i][0] + dp[i-1][1] * qpow(a,ccnt) % MOD) % MOD;}// dp[i-1][0]if(a > b){//no solution}else if(a < b){if(ys)  dp[i][0] = (dp[i][0] + dp[i-1][0] * qpow(a,ccnt) % MOD) % MOD;else dp[i][0] = (dp[i][0] + dp[i-1][0] * rem % MOD) % MOD;}else if(a == b){if(ys)  dp[i][1] = (dp[i][1] + dp[i-1][0] * qpow(a,ccnt) % MOD) % MOD;else dp[i][1] = (dp[i][1] + dp[i-1][0] * rem % MOD) % MOD;}
//                show(i,dp[i][0],dp[i][1]);}ans = dp[n+m-1][1];}printf("Case #%d: %lld\n",kase,ans);}return 0;
}
/***/