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#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
const int MOD = (int)1e9 + 7;
int n,m,h[101],hnum[101],dh[101];
long long dp[101][101];
int pow_(int x,int y) {///快速幂求 x的y次方
long long ans = 1;
if(y > 0) {
while(y) {
if(y % 2)ans = ans * x % MOD;
x = (long long)x * x % MOD;
y /= 2;
}
}
return ans;
}
int main() {
scanf("%d",&n);
for(int i = 1;i <= n;i ++) {
scanf("%d",&h[i]);
dh[++ m] = h[i];
}
sort(dh + 1,dh + m + 1);///高度排序
m = unique(dh + 1,dh + m + 1) - dh - 1;///离散化 m是离散化后的长度
for(int i = 1;i <= n;i ++) {
hnum[i] = lower_bound(dh + 1,dh + m + 1,h[i]) - dh;
}
dp[0][0]=1;
for(int i = 1;i <= n;i ++) {
for(int j = hnum[i] + 1;j <= hnum[i - 1];j ++)
(dp[i][0] += dp[i - 1][j] * 2 % MOD) %= MOD;
(dp[i][0] += dp[i - 1][0] * 2 % MOD) %= MOD;///交叉或者不交叉
int d = pow_(2,h[i] - h[i - 1]);
for(int j = 1;j <= min(hnum[i - 1],hnum[i]);j ++) {
dp[i][j] = dp[i - 1][j] * d % MOD;
}
for(int j = hnum[i - 1] + 1;j <= hnum[i];j ++) {///比前一列高出的部分
if(j > 1)(dp[i][j] += dp[i - 1][0] * (pow_(2,dh[j] - dh[j - 1]) - 1) % MOD * 2 % MOD * pow_(2,h[i] - dh[j]) % MOD) %= MOD;
else (dp[i][1] += dp[i - 1][0] * (pow_(2,dh[1]) - 2) % MOD * pow_(2,h[i] - dh[1]) % MOD) %= MOD;///上一列中无重复相同的乘上化不超过上一列高度中有重复的
}
}
long long ans = 0;
for(int i = 0;i <= hnum[n];i++)
(ans += dp[n][i]) %= MOD;
printf("%lld",ans);
return 0;
}
|
#include "iostream"
#include "algorithm"
#include "cstring"
#include "cstdio"
#include "vector"
using namespace std;
#define MAXN 106
#define P 1000000007
int n;
int A[MAXN];
int Pow( int x , int a ) {
int cur = x % P , ans = 1;
while( a ) {
if( a & 1 ) ans = 1ll * ans * cur % P;
cur = 1ll * cur * cur % P , a >>= 1;
}
return ans;
}
pair<int,int> solve( int l , int r , int c ) {
// cout << l << ' ' << r << endl;
if( l > r ) return make_pair( 1 , 0 );
int h = 0x3f3f3f3f;
for( int i = l ; i <= r ; ++ i ) h = min( h , A[i] );
vector<int> pos;
pos.push_back( l - 1 );
for( int i = l ; i <= r ; ++ i ) if( A[i] == h ) pos.push_back( i );
pos.push_back( r + 1 );
int nm = pos.size() - 2;
int re = 1 , tot = 1;
for( int i = 0 ; i < pos.size() - 1 ; ++ i ) {
pair<int,int> ret = solve( pos[i] + 1, pos[i + 1] - 1, h );
re = 1ll * re * ret.first % P , tot = 1ll * tot * ( ret.first + ret.second ) % P;
// cout << l << ' ' << r << ' ' << pos[i] + 1 << ' ' << pos[i + 1] << ' ' << re << ' ' << tot << endl;
}
return make_pair( 1ll * re * Pow( 2 , h - c ) % P , ( 1ll * re * ( Pow( 2 , h - c ) - 2 ) % P + 1ll * Pow( 2 , nm ) * tot % P ) % P );
}
int main() {
cin >> n;
for( int i = 1 ; i <= n ; ++ i ) scanf("%d",&A[i]);
cout << solve( 1 , n , 0 ).second << endl;
} |
#include<bits/stdc++.h>
#define fo(i, x, y) for(int i = x, B = y; i <= B; i ++)
#define ff(i, x, y) for(int i = x, B = y; i < B; i ++)
#define fd(i, x, y) for(int i = x, B = y; i >= B; i --)
#define ll long long
#define pp printf
#define hh pp("\n")
using namespace std;
const int N = 105;
int n, a[N], b[N], m, na[N];
map<int, int> ba;
const int mo = 1e9 + 7;
ll ksm(ll x, ll y) {
ll s = 1;
for(; y; y /= 2, x = x * x % mo)
if(y & 1) s = s * x % mo;
return s;
}
ll qu(int x, int y) {
return (ksm(2, y + 1) - ksm(2, x) + mo) % mo;
}
ll a2[N];
ll f[N][N];
void add(ll &x, ll y) {
(x += y) %= mo;
}
int main() {
scanf("%d", &n);
fo(i, 1, n) scanf("%d", &a[i]), b[i] = a[i];
sort(b + 1, b + n + 1);
m = unique(b + 1, b + n + 1) - (b + 1);
fo(i, 1, m) ba[b[i]] = i;
fo(i, 1, n) na[i] = ba[a[i]];
b[m + 1] = 2e9; f[0][m + 1] = 1;
fo(i, 1, n) {
fo(j, 1, m + 1) if(f[i - 1][j]) {
if(a[i - 1] <= a[i]) {
if(b[j] <= a[i]) {
add(f[i][j], f[i - 1][j] * ksm(2, a[i] - a[i - 1]));
} else {
fo(k, na[i - 1] + 1, na[i]) {
int x = b[k - 1] + 1, y = b[k];
if(x == 1) x ++;
if(x <= y)
add(f[i][k], f[i - 1][j] * qu(a[i] - y + 1, a[i] - x + 1)) ;
}
add(f[i][m + 1], f[i - 1][j] * 2);
}
} else {
if(b[j] <= a[i]) {
add(f[i][j], f[i - 1][j]);
} else {
add(f[i][m + 1], f[i - 1][j] * 2);
}
}
}
}
ll ans = 0;
fo(j, 1, m + 1) ans = (ans + f[n][j]) % mo;
pp("%lld\n", ans);
}
|
#include<cstdio>
using namespace std;
const int N=100,mod=1e9+7;
int n,h[N+1];
int f[N+1][N+1];
int pow(int x,int times)
{
int ret=1;
while(times) {
if(times&1) {
ret=1ll*ret*x%mod;
}
times>>=1,x=1ll*x*x%mod;
}
return ret;
}
int main()
{
scanf("%d",&n);
for(int i=1;i<=n;++i) {
scanf("%d",&h[i]);
}
h[0]=1,f[0][0]=1;
for(int i=1;i<=n;++i) {
for(int j=0;j<=n;++j) {
if(h[j]>h[i]) {
continue;
}
if(h[j]<h[i-1]) {
if(h[i]<h[i-1]) {
f[i][j]=(f[i-1][j]+f[i-1][i])%mod;
} else {
f[i][j]=1ll*(f[i-1][j]+f[i-1][i-1])*pow(2,h[i]-h[i-1])%mod;
}
} else {
f[i][j]=2ll*f[i-1][i-1]*pow(2,h[i]-h[j])%mod;
}
}
}
printf("%d\n",f[n][0]);
return 0;
} |
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
const int mod = 1000000007;
int binpow(int a, int b) {
int ret = 1;
while (b) {
if (b & 1) ret = 1LL * ret * a % mod;
a = 1LL * a * a % mod;
b >>= 1;
}
return ret;
}
int main() {
int n;
cin >> n;
vector<int> h(n);
for (int i = 0; i < n; ++i) cin >> h[i];
vector<int> dp = { 2 };
int firstlow = (n == 1 ? 1 : h[1]);
dp[0] = 1LL * dp[0] * binpow(2, max(h[0] - firstlow, 0)) % mod;
for (int i = 1; i < n; ++i) {
vector<int> ndp(i + 1);
int low = (i == n - 1 ? 1 : h[i + 1]);
if (h[i] <= low) {
for (int j = 0; j < i; ++j) {
ndp[j] = dp[j];
ndp[i] = (ndp[i] + dp[j]) % mod;
}
}
else {
int mx = min(h[i - 1], h[i]);
int s = 0;
for (int j = i - 1; j >= 0; --j) {
mx = min(mx, (j == 0 ? 1 : h[j - 1]));
ndp[j] = 1LL * dp[j] * binpow(2, h[i] - max(low, mx)) % mod;
s = (s + dp[j]) % mod;
}
ndp[i] = 1LL * s * binpow(2, h[i] - max(min(h[i - 1], h[i]), low)) % mod;
}
dp = ndp;
}
int sum = 0;
for (int i = 0; i < n; ++i) {
sum = (sum + dp[i]) % mod;
}
cout << sum << '\n';
return 0;
} |
#include<algorithm>
#include<cstdio>
#define N 101
#define p 1000000007
#define ll long long
using namespace std;
inline int mod(int x){return x<p?x:x-p;}
inline int calc(int x,int y)
{
int z=1;
for(;y;x=(ll)x*x%p,y>>=1)if(y&1)z=(ll)x*z%p;
return z;
}
int a[N],b[N],d[N],e[N],f[2][N],g[N],h,i,j,n;
inline bool cmp(int u,int v){return a[u]<a[v];}
inline int mul(int u,int v){return(ll)d[v]*e[u]%p;}
int main()
{
scanf("%d",&n);
for(i=1;i<=n;i++)scanf("%d",a+i),b[i]=i;
sort(b+1,b+n+1,cmp);
for(i=1;i<=n;a[b[i++]]=h)if(a[b[i]]!=g[h])g[++h]=a[b[i]];
for(i=0;i<=n;i++)e[i]=calc(d[i]=calc(2,g[i]),p-2);
for(i=1,*f[0]=mod(p+d[a[1]]-mod(mul(1,a[1])<<1)),f[0][a[1]]=2;i<a[1];i++)f[0][i]=mod(mod(p+mul(i,a[1])-mul(i+1,a[1]))<<1);
for(i=2;i<=n;i++)
if(a[i-1]<a[i])
{
for(j=0;j<a[i-1];f[i&1][j++]=0)f[i&1^1][j]=(ll)f[i&1][j]*mul(a[i-1],a[i])%p;
for(f[i&1^1][a[i]]=h=mod(f[i&1][j=a[i-1]]<<1),f[i&1][j]=0;j<a[i];j++)f[i&1^1][j]=(ll)h*(p+mul(j,a[i])-mul(j+1,a[i]))%p;
}
else
{
for(j=0;j<a[i];f[i&1][j++]=0)f[i&1^1][j]=f[i&1][j];
for(j=a[i];j<=a[i-1];f[i&1][j++]=0)f[i&1^1][a[i]]=mod(f[i&1^1][a[i]]+mod(f[i&1][j]<<1));
}
for(i=j=0;i<=a[n];i++)j=mod(j+f[n&1^1][i]);
return 0&printf("%d\n",j);
} |
#include<cstdio>
#include<algorithm>
const int mod=1000000007;
int N,h[110];
int pw(int a,int n){
int b=1;
for(;n;n>>=1)n&1?b=1ll*b*a%mod:1,a=1ll*a*a%mod;
return b;
}
std::pair<int,int>dfs(int l,int r,int mn){
int m=l;
for(int i=l;i<r;i++)if(h[i]<h[m])m=i;
int s=pw(2,h[m]-mn);
if(r-l==1)return std::make_pair(s,s);
if(m==l){
std::pair<int,int>sr=dfs(m+1,r,h[m]);
return std::make_pair((2ll*sr.first+(s-1ll)*sr.second)%mod,1ll*s*sr.second%mod);
}
if(m==r-1){
std::pair<int,int>sl=dfs(l,m,h[m]);
return std::make_pair((2ll*sl.first+(s-1ll)*sl.second)%mod,1ll*s*sl.second%mod);
}
std::pair<int,int>sl=dfs(l,m,h[m]),sr=dfs(m+1,r,h[m]);
return std::make_pair(
(4ll*sl.first%mod*sr.first+(s-1ll)*sl.second%mod*sr.second)%mod,
1ll*s*sl.second%mod*sr.second%mod
);
}
int main(){
scanf("%d",&N);
for(int i=0;i<N;i++)scanf("%d",h+i),--h[i];
printf("%d\n",dfs(0,N,0).first*2%mod);
} |
#include<bits/stdc++.h>
#define MN 100
#define mod 1000000007
#define MK 32768
using namespace std;
inline int read()
{
int x=0,f=1;char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
while(ch>='0'&&ch<='9')x=x*10+ch-'0',ch=getchar();
return x*f;
}
int n,a[MN+5],L[MN+5],num,f[MN+5][MN+5],pw[MK+5],PW[MK+5],ans;
inline void R(int&x,int y){(x+=y)>=mod?x-=mod:0;}
inline int pw2(int x){return 1LL*PW[x>>15]*pw[x&32767]%mod;}
inline int Sum(int l,int r){return (pw2(r+1)-pw2(l)+mod)%mod;}
int main()
{
n=read();pw[0]=PW[0]=1;
for(int i=1;i<=MK;++i) pw[i]=2*pw[i-1]%mod;
for(int i=1;i<=MK;++i) PW[i]=1LL*PW[i-1]*pw[MK]%mod;
for(int i=1;i<=n;++i) a[i]=L[i]=read();
sort(L+1,L+n+1);num=unique(L+1,L+n+1)-L-1;L[++num]=2e9;
f[0][num]=1;
for(int i=1;i<=n;++i)
{
a[i]=lower_bound(L+1,L+num+1,a[i])-L;
for(int j=1;j<=a[i];++j) R(f[i][j],1LL*f[i-1][j]*pw2(max(0,L[a[i]]-L[a[i-1]]))%mod);
int res=0;
for(int j=a[i]+1;j<=num;++j) R(res,f[i-1][j]);
res=2*res%mod;
for(int j=a[i-1]+1;j<=a[i];++j)
{
int l=max(2,L[j-1]+1),r=L[j];if(l>r) continue;
R(f[i][j],1LL*res*Sum(L[a[i]]-r,L[a[i]]-l)%mod);
}
R(f[i][num],res);
}
for(int j=1;j<=num;++j) R(ans,f[n][j]);
cout<<ans;
return 0;
} |
#include<bits/stdc++.h>
#define fo(i,a,b)for(int i=a,_e=b;i<=_e;++i)
#define add(x,y)(x=((ll)y+x)%mo)
#define ll long long
using namespace std;
const int N=105,mo=1e9+7;
int n,nn,v,ans;
int h[N],w[N],h2[N],f[N][N];
int ksm(int x,int y){
int t=1;
for(;y;y>>=1,x=(ll)x*x%mo)if(y&1)t=(ll)t*x%mo;
return t;
}
int main(){
ios::sync_with_stdio(0);
cin>>n;
fo(i,1,n)cin>>h[i],h2[i]=h[i];
sort(h2+1,h2+n+1);
nn=unique(h2+1,h2+n+1)-h2-1;
f[0][0]=1;
fo(i,1,n){
w[i]=lower_bound(h2+1,h2+nn+1,h[i])-h2;
if(v=f[i-1][0]){
f[i][0]=(ll)v*2%mo;
if(h[i-1]<h[i]){
fo(j,w[i-1]+1,w[i]){
if(j==1)f[i][j]=(ll)2*ksm(2,h[i]-h2[1])%mo*(ksm(2,h2[1]-1)-1)%mo;
else f[i][j]=(ll)v*2*ksm(2,h[i]-h2[j])%mo*(ksm(2,h2[j]-h2[j-1])-1)%mo;
}
}
}
int p;
if(h[i-1]<h[i])p=ksm(2,h[i]-h[i-1]);
fo(j,1,nn)if(v=f[i-1][j]){
if(h[i-1]>=h[i]){
if(j<=w[i])add(f[i][j],v);
else add(f[i][0],v*2);
}else{
add(f[i][j],v*p);
}
}
}
fo(i,0,nn)add(ans,f[n][i]);
cout<<ans;
} |
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
#define fi first
#define sc second
const ll mod = 1000000007;
#define repn(i,n) for(int i=1;i<=n;i++)
#define rep(i,n) for(int i=0;i<n;i++)
#define mp make_pair
#define pb push_back
int n,a[105];
ll modpow(ll a,ll n){
ll ret = 1;
while(n){
if(n&1) ret = ret*a%mod;
a = a*a%mod;
n >>= 1;
}
return ret;
}
P rec(int l,int r,int dep){
int mn = mod;
for(int i=l;i<=r;i++) mn = min(mn,a[i]);
int cnt = 0;
vector<P>ret;
int sum = 0;
for(int i=l;i<=r;i++){
if(a[i] == mn){
if(cnt) ret.pb(rec(i-cnt,i-1,mn));
cnt = 0;
sum++;
}
else cnt++;
}
if(cnt) ret.pb(rec(r-cnt+1,r,mn));
//01010101....
ll val = 1;
rep(i,ret.size()) val = val * ret[i].fi % mod * 2LL % mod;
//all
ll val2 = modpow(2LL,sum);
rep(i,ret.size()) val2 = val2 * (ret[i].fi*4LL%mod+ret[i].sc) % mod;
val2 = (val2-2LL*val)%mod;
if(val2 < 0) val2 += mod;
val = val * modpow(2LL,mn-dep-1) % mod;
return mp(val,val2);
}
int main(){
cin >> n;
repn(i,n) cin >> a[i];
P ret = rec(1,n,0);
ll ans = ret.fi*2LL+ret.sc;
cout << (ans%mod+mod)%mod << endl;
} |
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const LL N=101;
const LL p=1e9+7;
const LL inf=0x3f3f3f3f;
LL n,h[N];
inline LL pw(LL x,LL y){
LL ans=1;
while(y){
if(y&1)ans=ans*x%p;
x=x*x%p; y>>=1;
}
return ans;
}
#define pii pair<LL,LL>
#define mp(x,y) make_pair((x),(y))
#define fi first
#define se second
inline pii solve(LL l,LL r,LL H){
LL mn=inf;
for(LL i=l; i<=r; ++i)mn=min(mn,h[i]-H);
bool flag=0; for(LL i=l; i<=r; ++i)if(h[i]>mn+H)flag=1;
if(!flag)return mp(pw(2,mn-1),(pw(2,r-l+1)-2+p)%p);
LL ans0=1,ans1=1,x=r-l+1,y=0;
for(LL i=l,pre=0; i<=r; ++i){
if(!pre&&h[i]>mn+H)pre=i;
if(pre&&h[i]==mn+H){
pii P=solve(pre,i-1,mn+H);
ans0=2*ans0%p*P.fi%p; ans1=ans1*(P.se+4*P.fi%p)%p;
++y; x-=i-pre; pre=0;
}else if(pre&&i==r){
pii P=solve(pre,r,mn+H);
ans0=2*ans0%p*P.fi%p; ans1=ans1*(P.se+4*P.fi%p)%p;
++y; x-=r-pre+1; pre=0;
}
}
ans1=(ans1-ans0+p)%p;
ans1=ans1*pw(2,x)%p;
ans1=(ans1+(pw(2,x)%p-2+p)%p*ans0%p)%p;
ans0=ans0*pw(2,mn-1)%p;
return mp(ans0,ans1);
}
int main(){
scanf("%lld",&n);
for(LL i=1; i<=n; ++i)scanf("%lld",&h[i]);
pii ans=solve(1,n,0);
printf("%lld",(2*ans.fi+ans.se)%p);
return 0;
} |
#include<bits/stdc++.h>
#define fi first
#define se second
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
using namespace std;
const int N=105,P=1e9+7;
int n,h[N];
int fpow(int k1,int k2){
int k3=1;
for(;k2;k2>>=1,k1=1LL*k1*k1%P)if(k2&1)k3=1LL*k3*k1%P;
return k3;
}
pair<int,int>sol(int l,int r,int bs){
int mn=*min_element(h+l,h+r+1),coef=1,all=1,num=0;
for(int i=l;i<=r;){
if(h[i]!=mn){
int j=i+1;
while(j<=r&&h[j]!=mn)++j;
pair<int,int>val(sol(i,j-1,mn));
coef=1LL*coef*val.fi%P;
all=1LL*all*(val.fi+val.se)%P;
i=j;
}else{
++num,++i;
}
}
return make_pair(1LL*coef*fpow(2,mn-bs)%P,(1LL*all*fpow(2,num)%P+1LL*coef*(fpow(2,mn-bs)+P-2)%P)%P);
}
int main(){
scanf("%d",&n);
rep(i,1,n)scanf("%d",h+i);
printf("%d\n",sol(1,n,0).se);
return 0;
} |
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
const int mod=1000000007;
int h[111];
int n;
int fpow2(int y)
{
if(y==0)
return 1;
int ret=fpow2(y>>1);
ret=(long long)ret*ret%mod;
if(y&1)
(ret<<=1)%=mod;
return ret;
}
pair<int,int> solve(int l,int r,int nh)
{
int mi=1010101010,cnt=0;
for(int i=l;i<=r;i++)
mi=min(mi,h[i]);
for(int i=l;i<=r;i++)
cnt+=(mi==h[i]);
int h1=1,h2=1,st=0;
pair<int,int> dp;
for(int i=l;i<=r+1;i++)
if(h[i]>mi)
{
if(st==0)
st=i;
}
else
{
if(st)
{
dp=solve(st,i-1,mi);
h1=(long long)dp.first*h1%mod;
h2=((long long)dp.first*2+dp.second)*h2%mod;
st=0;
}
}
return make_pair((long long)h1*fpow2(mi-nh)%mod,((long long)h2*fpow2(cnt)+mod+mod-h1-h1)%mod);
}
int main()
{
pair<int,int> dp;
scanf("%d",&n);
for(int i=1;i<=n;i++)
scanf("%d",&h[i]);
dp=solve(1,n,0);
printf("%d",(dp.first+dp.second)%mod);
return 0;
} |
#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
#define ll long long
using namespace std;
template <class T>
inline void rd(T &x) {
x=0; char c=getchar(); int f=1;
while(!isdigit(c)) { if(c=='-') f=-1; c=getchar(); }
while(isdigit(c)) x=x*10-'0'+c,c=getchar(); x*=f;
}
const int N=110,mod=1e9+7;
inline int Pow(int x,int y) { int res=1; for(;y;y>>=1,x=x*(ll)x%mod) if(y&1) res=res*(ll)x%mod; return res; }
int f[N][N][2],vis[N][N],h[N],minv[N][N],n;
void sol(int l,int r) {
if(vis[l][r]) return;
vis[l][r]=1;
minv[l][r]=1e9;
for(int i=l;i<=r;++i) minv[l][r]=min(minv[l][r],h[i]);
int lst=l-1,tot=0;
f[l][r][0]=f[l][r][1]=1;
for(int i=l;i<=r+1;++i) if(h[i]==minv[l][r]||i==r+1) {
int L=lst+1,R=i-1; lst=i;
if(L<=R) {
sol(L,R);
f[l][r][0]=f[l][r][0]*(ll)f[L][R][0]%mod*Pow(2,minv[L][R]-minv[l][r]-1)%mod;
f[l][r][1]=f[l][r][1]*(ll)(f[L][R][0]*(ll)Pow(2,minv[L][R]-minv[l][r])%mod+f[L][R][1])%mod;
tot+=R-L+1;
}
}
f[l][r][0]=f[l][r][0]*2ll%mod;
f[l][r][1]=(f[l][r][1]*(ll)Pow(2,r-l+1-tot)%mod-f[l][r][0])%mod;
}
int main() {
rd(n);
for(int i=1;i<=n;++i) rd(h[i]);
sol(1,n);
int ans=(f[1][n][0]*(ll)Pow(2,minv[1][n]-1)%mod+f[1][n][1])%mod;
printf("%d",(ans+mod)%mod);
return 0;
} |
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#define SF scanf
#define PF printf
#define MAXN 100010
#define MOD 1000000007
using namespace std;
int n;
typedef long long ll;
ll dp[MAXN],h[MAXN];
ll fsp(ll x,ll y){
ll res=1;
while(y){
if(y&1)
res=res*x%MOD;
x=x*x%MOD;
y>>=1;
}
return res;
}
int main(){
SF("%d",&n);
dp[n+1]=1;
for(int i=1;i<=n;i++){
SF("%lld",&h[i]);
if(h[i]==1){
h[i]--;
dp[n+1]=dp[n+1]*2ll%MOD;
}
}
for(int i=1;i<=n;i++)
if(h[i]>h[i-1]&&h[i]>h[i+1]){
int h1=max(h[i-1],h[i+1]);
dp[n+1]=dp[n+1]*fsp(2,h[i]-h1)%MOD;
h[i]=h1;
}
for(int i=n;i>0;i--){
//PF("{%d}",i);
if(h[i])
dp[i]=dp[i+1]*2ll%MOD;
else{
dp[i]=dp[i+1];
continue;
}
ll minh=h[i],q=i;
for(int j=i;h[j]==h[i];j++)
if(h[j+1]>h[i]){
q=j;
minh++;
}
ll res1=0;
ll end,sumh=0;
if(h[i]<h[i-1])
end=h[i];
else
end=h[i-1]+1;
//PF("{%d %d}\n",minh,end);
for(int j=q+1;minh>end;j++){
if(h[j]>h[j-1])
sumh+=h[j]-h[j-1];
if(h[j]<minh){
int minh1=max(end,h[j]);
//PF("{%d %d %d}\n",sumh+h[i]-minh,minh-minh1,-(minh==(h[i]+1)?0:1));
if(minh==h[i]+1)
res1+=dp[j]*(fsp(2,sumh+h[i]-minh+q-i+2)+fsp(2,sumh+h[i]-minh+2)*(fsp(2,minh-minh1-1)-1)%MOD)%MOD;
else
res1+=dp[j]*(fsp(2,sumh+h[i]-minh+1)*(fsp(2,minh-minh1)-1)%MOD)%MOD;
res1%=MOD;
minh=minh1;
}
}
dp[i]+=res1;
dp[i]%=MOD;
//PF("{%lld}\n",dp[i]);
}
PF("%lld",dp[1]);
}
|
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int mod=1000000007;
inline void add(int &x,int y){(x+=y)>=mod?x-=mod:0;}
inline int pl(int x,int y){return (x+=y)>=mod?x-mod:x;}
inline int kpow(int a,int b)
{
int s=1;
for(;b;b>>=1,a=1ll*a*a%mod)
if(b&1)s=1ll*s*a%mod;
return s;
}
int n,h[110],dp[110][110],d[110],m,ans;
int main()
{
scanf("%d",&n);
for(int i=1;i<=n;++i)scanf("%d",&h[i]),d[i]=h[i];
sort(d+1,d+1+n);
m=unique(d+1,d+1+n)-d-1;
for(int i=1;i<=n;++i)h[i]=lower_bound(d+1,d+1+m,h[i])-d;
dp[1][0]=kpow(2,d[h[1]]);
for(int i=1;i<=h[1];++i)dp[1][i]=2*kpow(2,d[h[1]]-d[i])%mod;
for(int i=0;i<h[1];++i)add(dp[1][i],mod-dp[1][i+1]);
for(int i=1;i<n;++i)
{
if(h[i]>=h[i+1])
{
for(int j=0;j<h[i+1];++j)dp[i+1][j]=dp[i][j];
for(int j=h[i+1];j<=h[i];++j)add(dp[i+1][h[i+1]],dp[i][j]);
(dp[i+1][h[i+1]]<<=1)%=mod;
}
else
{
int res=kpow(2,d[h[i+1]]-d[h[i]]);
for(int j=0;j<h[i];++j)dp[i+1][j]=1ll*dp[i][j]*res%mod;
for(int j=h[i];j<=h[i+1];++j)dp[i+1][j]=2ll*dp[i][h[i]]*kpow(2,d[h[i+1]]-d[j])%mod;
for(int j=h[i];j<h[i+1];++j)add(dp[i+1][j],mod-dp[i+1][j+1]);
}
}
for(int j=0;j<=h[n];++j)add(ans,dp[n][j]);
printf("%d",ans);
return 0;
}
|
#include<bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
const int MN = 111;
int exp(int x, int n) {
int ret = 1;
while(n) {
if(n & 1) ret = 1LL * ret * x % mod;
x = 1LL * x * x % mod;
n >>= 1;
}
return ret;
}
int N;
int H[MN], mnp[MN][MN];
int cc[MN][MN][MN][2];
int dp(int l, int r, int p, int t) {
if(l > r) return 1;
int &ret = cc[l][r][p][t];
if(ret != -1) return ret;
ret = 0;
int h = p == N? 1 : H[p];
int x = mnp[l][r];
int d = H[x] - h;
if(t) {
ret += 1LL * dp(l, x - 1, x, 1) * dp(x + 1, r, x, 1) % mod * 2 % mod;
ret %= mod;
ret += 1LL * dp(l, x - 1, x, 0) * dp(x + 1, r, x, 0) % mod * (exp(2, d) + mod - 1) % mod * 2 % mod;
ret %= mod;
}
else {
ret += 1LL * dp(l, x - 1, x, 0) * dp(x + 1, r, x, 0) % mod * exp(2, d) % mod;
ret %= mod;
}
//cout << l << ' ' << r << ' ' << p << ' ' << t << ' ' << ret << endl;
return ret;
}
int main() {
scanf("%d", &N);
for(int i = 0; i < N; i++) {
scanf("%d", &H[i]);
}
for(int i = 0; i < N; i++) {
int mn = 2e9, p = -1;
for(int j = i; j < N; j++) {
if(mn > H[j]) mn = H[j], p = j;
mnp[i][j] = p;
}
}
memset(cc, -1, sizeof(cc));
printf("%d", dp(0, N - 1, N, 1));
}
|
#include <cstdio>
#include <algorithm>
#include <utility>
#include <tuple>
using namespace std;
constexpr int mod = 1000000007;
int pow2(int n) {
// fprintf(stderr, "pow2(%d) = ", n);
long ans = 1, x = 2;
for (; n; n >>= 1, x = x * x % mod)
if (n & 1)
ans = ans * x % mod;
// fprintf(stderr, "%d\n", (int) ans);
return ans;
}
pair<int, int> solve(int *bg, int *ed) {
int m = *min_element(bg, ed);
for_each(bg, ed, [m](int &x) { x -= m; });
long f = 1, s = 2;
int n = 0;
for (int *p = bg; p != ed;) {
if (*p) {
int *q = find(p, ed, 0);
auto pa = solve(p, q);
f = f * (pa.first + pa.second) % mod;
s = s * pa.second % mod;
p = q;
} else {
n++;
p++;
}
}
f = f * pow2(n) % mod;
f = (f - s + mod) % mod;
s = s * pow2(m - 1) % mod;
f = (f + s) % mod;
return make_pair(f, s);
}
int h[100];
int main() {
int n;
scanf("%d", &n);
for (int i = 0; i < n; i++)
scanf("%d", h + i);
printf("%d\n", solve(h, h + n).first);
}
|
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;
const int N = 105;
const int INF = 0x3f3f3f3f;
typedef long long ll;
#define lson l, m, rt<<1
#define rson m+1, r, rt<<1|1
const int MOD = 1e9+7;
int h[N];
int Has[N]; int tot;
ll dp[N][N];
ll Pow(ll x, ll y) {
if(y <= 0) return 1;
ll result = 1;
while(y) {
if(y & 1)
result = result * x % MOD;
y >>= 1;
x = x*x % MOD;
}
return result;
}
int main() {
int n;
while(~scanf("%d", &n)) {
tot = 0;
memset(dp, 0, sizeof(dp));
h[0] = 0;
dp[0][0] = 1;
for(int i = 1; i <= n; ++i) {
scanf("%d", &h[i]);
Has[++tot] = h[i];
}
sort(Has + 1, Has + tot + 1);
tot = unique(Has+1, Has + tot + 1) - Has - 1;
for(int i = 1; i <= n; ++i) {
h[i] = lower_bound(Has + 1, Has + tot + 1, h[i]) - Has;
}
for(int i = 1; i <= n; ++i) {
dp[i][0] = dp[i-1][0] * 2 % MOD;
for(int j = h[i] + 1; j <= h[i-1]; ++j) dp[i][0] = (dp[i][0] + dp[i-1][j] * 2 % MOD) % MOD;
ll tmpPow = Pow(2, Has[h[i]] - Has[h[i-1]]);
for(int j = 1; j <= h[i]; ++j) {
dp[i][j] = dp[i-1][j] * tmpPow % MOD;
}
for(int j = h[i-1] + 1; j <= h[i]; ++j) {
dp[i][j] = (dp[i][j] + j==1? ( dp[i-1][0] * ( Pow(2, Has[j]) - 2) % MOD * Pow(2, Has[h[i]] - Has[j]) % MOD ) :
( dp[i-1][0] * ( Pow(2, Has[j]-Has[j-1]) - 1) % MOD * 2 % MOD * Pow(2, Has[h[i]]-Has[j]) % MOD )
) %MOD;
}
}
ll result = 0;
for(int i = 0; i <= tot; ++i) {
result = (result + dp[n][i]) % MOD;
}
printf("%lld\n", result);
}
return 0;
} |
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int mod=1e9+7;
inline int addmod(int x)
{
return x>=mod?x-mod:x;
}
inline int submod(int x)
{
return x<0?x+mod:x;
}
int fpow(int x,int y)
{
int ans=1;
while(y)
{
if(y&1) ans=1ll*ans*x%mod;
x=1ll*x*x%mod;
y/=2;
}
return ans;
}
int n,a[1005],f[1005][2],st[100005],tp,ls[100005],rs[100005],inv2;
void dfs(int u,int fa)
{
if(!u) return;
dfs(ls[u],u),dfs(rs[u],u);
int v=a[u]-a[fa];
if(!ls[u]&&!rs[u])
{
f[u][1]=fpow(2,v);
// printf("u=%d,f=%d,%d\n",u,f[u][0],f[u][1]);
return;
}
if(!ls[u]||!rs[u])
{
int s=ls[u]+rs[u];
f[u][0]=2ll*addmod(f[s][0]+f[s][1])%mod;
// f[u][0]=submod(f[u][0]-f[s][1]);
f[u][1]=1ll*fpow(2,v)*f[s][1]%mod;
// printf("u=%d,f=%d,%d\n",u,f[u][0],f[u][1]);
return;
}
f[u][0]=2ll*addmod(f[ls[u]][0]+2*f[ls[u]][1]%mod)*addmod(f[rs[u]][0]+2*f[rs[u]][1]%mod)%mod;
f[u][0]=submod(f[u][0]-2ll*f[ls[u]][1]*f[rs[u]][1]%mod);
f[u][1]=1ll*fpow(2,v)*f[ls[u]][1]%mod*f[rs[u]][1]%mod;
//printf("u=%d,f=%d,%d\n",u,f[u][0],f[u][1]);
}
int main()
{
inv2=fpow(2,mod-2);
scanf("%d",&n);
for(int i=1;i<=n;i++)
scanf("%d",&a[i]);
for(int i=1;i<=n;i++)
{
while(tp>1&&a[st[tp-1]]>a[i])
{
rs[st[tp-1]]=st[tp];
tp--;
}
if(tp&&a[st[tp]]>a[i]) ls[i]=st[tp],tp--;
st[++tp]=i;
}
//for(int i=1;i<=n;i++)
// printf("i=%d,ls=%d,rs=%d\n",i,ls[i],rs[i]);
while(tp>1)
{
rs[st[tp-1]]=st[tp];
tp--;
}
dfs(st[tp],0);
printf("%d",addmod(f[st[tp]][0]+f[st[tp]][1]));
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> ii;
const int mod = 1000000007;
int n;
int a[105];
ll exp(ll a, ll x){
if (x == 0) return 1ll;
ll p = exp(a,x/2);
p = (p*p)%mod;
if (x & 1){
p = (p*a)%mod;
}
return p;
}
ii solve(int l, int r, int s){
if (l > r) return ii(1ll,0ll);
int pos = l;
for (int i = l; i <= r; i++){
if (a[i] < a[pos]) pos = i;
}
ii L = solve(l,pos-1,a[pos]);
ii R = solve(pos+1,r,a[pos]);
ll prod1 = (ll)(L.first)*(R.first)%mod;
ll prod2 = (ll)(L.first+L.second)*(R.first+R.second)%mod;
ll ex = exp(2,a[pos]-s);
ll dp1 = (ex*prod1)%mod;
ll dp2 = (2*prod2 + (ex-2)*prod1)%mod;
//printf("%d %d %lld %lld\n",l,r,dp1,dp2);
return ii(dp1,dp2);
}
int main(){
scanf("%d",&n);
for (int i = 0; i < n; i++) scanf("%d",&a[i]);
printf("%lld",solve(0,n-1,0).second);
}
|
#include<iostream>
#include<cstdio>
using namespace std;const int mod=1000000007;typedef pair<long long,long long> pii;int h[105];
inline int qpow(int a,int b) {int rtv=1;for (;b;b>>=1,a=1LL*a*a%mod) if (b&1) rtv=1LL*rtv*a%mod;return rtv;}
inline pii dac(int l,int r,int bnd) {long long mn=1e18,cnt=0,rem=r-l+1,ans0=1,ans1=1;pii _;
for (int i=l;i<=r;++i) if (h[i]<mn) mn=h[i],cnt=1;else if (h[i]==mn) ++cnt;
if (cnt==r-l+1) return make_pair((qpow(2,r-l+1)+mod-2)%mod,qpow(2,mn-bnd-1));
for (int i=l,j=0;i<=r+1;++i) if (!j&&h[i]>mn) j=i;
else if (j&&(h[i]==mn||i>r)) {rem-=i-j,_=dac(j,i-1,mn),j=0;
ans0=1LL*ans0*(_.first+(4LL*_.second%mod)%mod)%mod,ans1=1LL*ans1*(_.second<<1)%mod;
}ans0=(ans0-ans1+mod)%mod;
return make_pair((1LL*ans0*qpow(2,rem)%mod+1LL*ans1*(qpow(2,rem)+mod-2)%mod)%mod,1LL*ans1*qpow(2,mn-bnd-1)%mod);
}int main() {int n,prod=1;pii _;scanf("%d",&n);for (int i=1;i<=n;++i) scanf("%d",h+i);
if (n<2) return 0*printf("%d",qpow(2,h[1]));
for (int i=1;i<=n;++i) if (h[i]>h[i-1]&&h[i]>h[i+1])
prod=1LL*prod*qpow(2,h[i]-max(h[i-1],h[i+1]))%mod,h[i]=max(h[i-1],h[i+1]);
_=dac(1,n,0);printf("%lld",1LL*prod*((_.first+_.second+_.second)%mod)%mod);return 0;
} |
#include <cstdio>
#include <algorithm>
typedef long long LL;
const int Mod = 1000000007;
const int MN = 100005;
inline int qPow(int b, LL e) {
e = (e % (Mod - 1) + Mod - 1) % (Mod - 1);
int a = 1;
for (; e; e >>= 1, b = (LL)b * b % Mod)
if (e & 1) a = (LL)a * b % Mod;
return a;
}
int N, A[MN];
LL B[MN];
int stk[MN], val[MN], top;
inline bool cmp(int i, int j) { return A[i] < A[j]; }
int f[MN];
int main() {
scanf("%d", &N);
for (int i = 1; i <= N; ++i) scanf("%d", &A[i]);
A[0] = A[N + 1] = 1;
for (int i = 1; i <= N; ++i) B[i] = A[i - 1] < A[i] ? A[i] - A[i - 1] : 0;
for (int i = 1; i <= N; ++i) B[i] += B[i - 1];
f[0] = 1;
stk[top = 1] = 0;
for (int i = 1; i <= N + 1; ++i) {
f[i] = f[i - 1] * 2 % Mod;
if (A[i - 1] > A[i]) {
int p = std::lower_bound(stk + 1, stk + top + 1, i, cmp) - stk;
f[i] = (f[i] + (LL)qPow(2, B[i - 1] + 1) * (val[top] - val[p] + Mod)) % Mod;
if (p > 1 && A[i] < A[stk[p]]) f[i] = (f[i] + (LL)qPow(2, B[i - 1] - B[stk[p - 1] + 1] + A[stk[p - 1] + 1] + 1) * (qPow(2, -A[i] + 1) - qPow(2, -A[stk[p]] + 1) + Mod) % Mod * f[stk[p - 1]]) % Mod;
}
while (top && A[stk[top]] >= A[i]) --top;
stk[++top] = i;
if (top > 1) val[top] = (val[top - 1] + (LL)qPow(2, A[stk[top - 1] + 1] - B[stk[top - 1] + 1] + 1) * (qPow(2, -A[stk[top - 1]]) - qPow(2, -A[stk[top]]) + Mod) % Mod * f[stk[top - 1]]) % Mod;
}
printf("%lld\n", (LL)qPow(2, -1) * f[N + 1] % Mod);
return 0;
} |
#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#define Mod 1000000007
using namespace std;
int fpow(int a,int b)
{
int ans=1,t=a;
while(b)
{
if(b&1)ans=(long long)ans*t%Mod;
t=(long long)t*t%Mod;
b>>=1;
}
return ans;
}
//2^a+...+2^{b-1}
int solve(int a,int b)
{
return (fpow(2,b)-fpow(2,a)+Mod)%Mod;
}
int h[110],H[110];
int f[110][110];
void add(int& x,int y)
{
x+=y;
if(x>=Mod)x-=Mod;
return ;
}
int main()
{
int n;scanf("%d",&n);
for(int i=1;i<=n;i++)
{
scanf("%d",&h[i]);
H[i]=h[i];
}
H[0]=1;
sort(H,H+n+1);int N=unique(H,H+n+1)-H;
for(int i=1;i<=n;i++)
h[i]=lower_bound(H,H+N,h[i])-H;
f[0][1]=1;
for(int i=1;i<=n;i++)
{
if(h[i]<=h[i-1]){
for(int j=1;j<=h[i-1]+1;j++)
if(j>h[i])add(f[i][h[i]+1],f[i-1][j]*2%Mod);
else add(f[i][j],f[i-1][j]);
}
else{
for(int j=1;j<=h[i-1];j++)
add(f[i][j],(long long)f[i-1][j]*fpow(2,H[h[i]]-H[h[i-1]])%Mod);
for(int j=h[i-1]+1;j<=h[i];j++)
add(f[i][j],(long long)f[i-1][h[i-1]+1]*solve(H[h[i]]-H[j],H[h[i]]-H[j-1])*2%Mod);
add(f[i][h[i]+1],f[i-1][h[i-1]+1]*2%Mod);
}
// printf("%d:",i);
// for(int j=1;j<=h[i]+1;j++)
// printf("%d ",f[i][j]);
// printf("\n");
}
int ans=0;
for(int i=1;i<=h[n]+1;i++)
add(ans,f[n][i]);
printf("%d\n",ans);
return 0;
} |
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
typedef long long LL;
const int N = 105;
const int MOD = 1000000007;
int n,f[N][N],h[N],w[N],m;
int ksm(int x,int y) {
if(y < 0)return 1;
int ans = 1;
while(y) {
if(y & 1)ans = (LL)ans * x % MOD;
x = (LL)x * x % MOD;
y /= 2;
}
return ans;
}
int main() {
scanf("%d",&n);
for(int i = 1;i <= n;i ++) {
scanf("%d",&h[i]);
w[++ m] = h[i];
}
sort(w + 1,w + m + 1);
m = unique(w + 1,w + m + 1) - w - 1;
for(int i = 1;i <= n;i ++) {
h[i] = lower_bound(w + 1,w + m + 1,h[i]) - w;
}
f[0][0]=1;
for(int i = 1;i <= n;i ++) {
for(int j = h[i] + 1;j <= h[i-1];j ++)
(f[i][0] += f[i - 1][j] * 2 % MOD) %= MOD;
(f[i][0] += f[i - 1][0] * 2 % MOD) %= MOD;
for(int j = 1;j <= h[i];j ++) {
f[i][j]=(LL)f[i - 1][j] * ksm(2,w[h[i]] - w[h[i-1]]) % MOD;
if(h[i - 1] >= j)continue;
if(j > 1)(f[i][j] += (LL)f[i - 1][0] * (ksm(2,w[j] - w[j - 1]) - 1) % MOD * 2 % MOD * ksm(2,w[h[i]] - w[j]) % MOD) %= MOD;
else (f[i][j] += (LL)f[i - 1][0] * (ksm(2,w[j]) - 2) % MOD * ksm(2,w[h[i]] - w[j]) % MOD) %= MOD;
}
}
int ans = 0;
for(int i = 0;i <= m;i++)
(ans += f[n][i]) %= MOD;
printf("%d",ans);
return 0;
}
|
// new day,new strength,new thougts
#include<bits/stdc++.h>
#define MP make_pair
#define PB push_back
#define PF push_front
#define POB pop_back
#define POF pop_front
#define F first
#define S second
#define sz(c) int((c).size())
#define REP(i,n) for(int i=0;i<int(n);i++)
#define REPD(i,n) for(int i=int(n)-1;i>=0;i--)
#define FOR(i,a,b) for(int i=int(a);i<=int(b);i++)
#define FORD(i,a,b) for(int i=int(a);i>=int(b);i--)
#define all(s) (s).begin(),(s).end()
#define bit(num,i) ((num>>i)&1)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> pll;
const ll inf=4e18;
const ll maxn=110;
const ll mod=1e9+7;
ll dp[maxn][maxn],a[maxn];
ll tavan(ll a,ll b){
ll an=1;
while(b>0){
if(b%2) an=(an*a)%mod;
a=(a*a)%mod;
b/=2;
}
return an;
}
int main(){
ll n;cin>>n;
FOR(i,1,n){
cin>>a[i];
}
a[0]=1;
dp[0][0]=1;
FOR(i,1,n){
FOR(j,0,n){
if(a[j]<=a[i]){
if(a[j]>=a[i-1]){
dp[i][j]=((2*dp[i-1][i-1])*tavan(2,max(ll(0),a[i]-a[j])))%mod;
}
else{
dp[i][j]=((dp[i-1][j]+dp[i-1][((a[i]>=a[i-1])?(i-1):(i))])*tavan(2,max(ll(0),a[i]-a[i-1])))%mod;
}
}
}
}
cout<<dp[n][0];
}
|
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
typedef long long LL;
const int N = 105;
const int MOD = 1000000007;
int n,m,h[N],w[N];
LL dp[N][N];
int pow_(int x,int y) {///快速幂求 x的y次方
int ans = 1;
if(y > 0) {
while(y) {
if(y % 2)ans = (LL)ans * x % MOD;
x = (LL)x * x % MOD;
y /= 2;
}
}
return ans;
}
int main() {
scanf("%d",&n);
for(int i = 1;i <= n;i ++) {
scanf("%d",&h[i]);
w[++ m] = h[i];
}
sort(w + 1,w + m + 1);///高度排序
m = unique(w + 1,w + m + 1) - w - 1;///离散化 m是离散化后的长度
for(int i = 1;i <= n;i ++) {
h[i] = lower_bound(w + 1,w + m + 1,h[i]) - w;
}
dp[0][0]=1;
for(int i = 1;i <= n;i ++) {
for(int j = h[i] + 1;j <= h[i - 1];j ++)
(dp[i][0] += dp[i - 1][j] * 2 % MOD) %= MOD;
(dp[i][0] += dp[i - 1][0] * 2 % MOD) %= MOD;///交叉或者不交叉
int d = pow_(2,w[h[i]] - w[h[i-1]]);
for(int j = 1;j <= h[i];j ++) {
dp[i][j] = dp[i - 1][j] * d % MOD;
}
for(int j = h[i - 1] + 1;j <= h[i];j ++) {///比前一列高出的部分
if(j > 1)(dp[i][j] += dp[i - 1][0] * (pow_(2,w[j] - w[j - 1]) - 1) % MOD * 2 % MOD * pow_(2,w[h[i]] - w[j]) % MOD) %= MOD;
else (dp[i][1] += dp[i - 1][0] * (pow_(2,w[1]) - 2) % MOD * pow_(2,w[h[i]] - w[1]) % MOD) %= MOD;///上一列中无重复的乘上化不超过上一列高度中有重复的
}
}
LL ans = 0;
for(int i = 0;i <= m;i++)
(ans += dp[n][i]) %= MOD;
printf("%lld",ans);
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef long long ll;
typedef pair<int,int> 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;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
// head
map<pair<VI,int>,ll> hs;
int n,h[110];
ll solve(VI x,int ty) {
if (x.empty()) return 1;
if (hs.count(mp(x,ty))) return hs[mp(x,ty)];
int v=*min_element(all(x));
if (ty==0) {
ll ans=1;
if (v==1) {
VI c;
for (auto p:x) {
if (p==1) {
ans=ans*2%mod;
ans=ans*solve(c,0)%mod;
c.clear();
} else {
c.pb(p);
}
}
ans=ans*solve(c,0)%mod;
return hs[mp(x,ty)]=ans;
} else {
VI y=x;
rep(i,0,SZ(y)) y[i]-=v-1;
ll all=solve(y,0);
ll dif=solve(y,1)*2%mod;
all=(all-dif+mod)%mod;
return hs[mp(x,ty)]=(all+dif*powmod(2,v-1))%mod;
}
} else {
// RBRB
ll ans=1;
if (v==1) {
VI c;
for (auto p:x) {
if (p==1) {
ans=ans*solve(c,1)%mod;
c.clear();
} else {
c.pb(p);
}
}
ans=ans*solve(c,1)%mod;
return hs[mp(x,ty)]=ans;
} else {
VI y=x;
rep(i,0,SZ(y)) y[i]-=v-1;
ll dif=solve(y,1);
return hs[mp(x,ty)]=dif*powmod(2,v-1)%mod;
}
}
}
int main() {
scanf("%d",&n);
rep(i,0,n) scanf("%d",h+i);
printf("%lld\n",solve(VI(h,h+n),0));
}
|
#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
int fast_pow(int x, int y, int z = mod) {
long long ret = 1;
for (; y; y >>= 1, x = (long long)x * x % z) {
if (y & 1)
ret = ret * x % z;
}
return ret;
}
int main(int argc, char *argv[]) {
std::ios_base::sync_with_stdio(false);
map<int, map<int, long long>> f;
set<int> se;
int n;
cin >> n;
vector<int> a(n, 0);
for (int i = 0; i < n; i++) {
cin >> a[i];
se.insert(a[i]);
}
for (auto x : se) {
if (x <= a[0]) {
f[0][x] = fast_pow(2, a[0] - x + 1);
}
}
f[0][0] = fast_pow(2, a[0]);
se.insert(0);
for (int i = 1; i < n; i++) {
for (auto x : se) {
if (x <= a[i]) {
if (x > a[i - 1]) {
f[i][x] = f[i - 1][a[i - 1]] * fast_pow(2, a[i] - x + 1) % mod;
} else {
if (a[i] > a[i - 1]) {
f[i][x] = (f[i - 1][x] + f[i - 1][a[i - 1]]) * fast_pow(2, a[i] - a[i - 1]) % mod;
} else {
f[i][x] = (f[i - 1][x] + f[i - 1][a[i]]) % mod;
}
}
}
}
}
cout << f[n - 1][0] << endl;
return 0;
}
|
#include <cstdio>
#include <iostream>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <queue>
using namespace std;
typedef long long ll;
const int mod=(int)1e9+7,N=105;
int a[N],p[N],f[N][N];
void upd(int &x,int y){x=(x+y)%mod;}
int ksm(int x,int y){
int tmp=x,ans=1;
while(y){
if(y&1) ans=(ll)ans*tmp%mod;
tmp=(ll)tmp*tmp%mod;
y>>=1;
}
return ans;
}
int main(){
int n,i,len,j,k,ans=0;
scanf("%d",&n);
for(i=1;i<=n;i++)
scanf("%d",&a[i]),p[i]=a[i];
p[n+1]=1;
sort(p+1,p+n+2);
len=unique(p+1,p+n+2)-p-1;
for(i=1;i<=n;i++) a[i]=lower_bound(p+1,p+len+1,a[i])-p;
j=1;
for(j=1;j<a[1];j++)
f[1][j]=(ll)(ksm(2,p[j+1]-p[j])-1)*ksm(2,p[a[1]]-p[j+1])%mod*2%mod;
f[1][a[1]]=2;
for(i=1;i<n;i++)
for(j=1;j<=a[i];j++){
if(a[i+1]<=a[i]){
if(j>=a[i+1]) upd(f[i+1][a[i+1]],f[i][j]*2%mod);
else upd(f[i+1][j],f[i][j]);
}
else{
if(j==a[i]){
for(k=a[i];k<a[i+1];k++)
upd(f[i+1][k],(ll)f[i][j]*2*(ksm(2,p[k+1]-p[k])-1)%mod*ksm(2,p[a[i+1]]-p[k+1])%mod);
upd(f[i+1][a[i+1]],f[i][j]*2%mod);
}
else upd(f[i+1][j],(ll)f[i][j]*ksm(2,p[a[i+1]]-p[a[i]])%mod);
}
}
for(j=1;j<=a[n];j++) upd(ans,f[n][j]);
printf("%d",ans);
return 0;
}
|
#include<bits/stdc++.h>
#define ll long long
#define ull unsigned ll
#define uint unsigned
#define pii pair<int,int>
#define pll pair<ll,ll>
#define PB push_back
#define fi first
#define se second
#define For(i,j,k) for (int i=(int)(j);i<=(int)(k);i++)
#define Rep(i,j,k) for (int i=(int)(j);i>=(int)(k);i--)
#define CLR(a,v) memset(a,v,sizeof(a));
#define CPY(a,b) memcpy(a,b,sizeof(a));
using namespace std;
const int mo=1000000007;
int n,a[105];
int power(int x,int y){
int s=1;
for (;y;y/=2,x=1ll*x*x%mo)
if (y&1) s=1ll*s*x%mo;
return s;
}
pii operator *(const pii &a,const pii &b){
int sum=2ll*(a.fi+a.se)*(b.fi+b.se)%mo;
return pii(2ll*a.fi*b.fi%mo,sum);
}
pii F(int l,int r,int v){
if (l==r)
return pii(power(2,a[l]-v-1),0);
int mnv=1<<30,las=l;
pii vf;
For(i,l,r) mnv=min(mnv,a[i]);
For(i,l,r+1)
if (a[i]==mnv||i==r+1){
if (las!=i){
pii vson=F(las,i-1,mnv);
int v1=vf.fi,v2=vf.se;
int v3=2ll*vson.fi%mo,v4=vson.se;
if (las==l) vf=pii(v3,v4);
else{
vf.fi=1ll*v1*v3%mo;
vf.se=(2ll*(v1+v2)*(v3+v4)+mo-vf.fi)%mo;
}
}
if (i!=r+1){
if (i==l) vf=pii(1,0);
else{
int v1=vf.fi,v2=vf.se;
vf=pii(v1,(v1+2ll*v2)%mo);
}
}
las=i+1;
}
vf.fi=1ll*vf.fi*power(2,mnv-v-1)%mo;
return vf;
}
int main(){
scanf("%d",&n);
For(i,1,n) scanf("%d",&a[i]);
pii ans=F(1,n,0);
printf("%d",2ll*(ans.fi+ans.se)%mo);
} |
#include <iostream>
#include <algorithm>
#include <cstdio>
#define mod 1000000007
#define MN 110
int f[MN][MN], g[MN];
int h[MN], b[MN];
int c[MN];
int qpow(int x, int p)
{
int ans = 1;
while(p)
{
if(p & 1) ans = 1ll * ans * x % mod;
x = 1ll * x * x % mod; p >>= 1;
}
return ans;
}
int main()
{
int n; scanf("%d", &n);
for(int i = 1; i <= n; i++) scanf("%d", &h[i]), b[i] = h[i];
std::sort(b + 1, b + n + 1); int N = std::unique(b + 1, b + n + 1) - b - 1;
for(int i = 1; i <= n; i++) h[i] = std::lower_bound(b + 1, b + N + 1, h[i]) - b;
b[0] = 1; for(int i = 1; i <= N; i++) c[i] = qpow(2, b[i] - b[i - 1]) - 1;
g[0] = 1;
for(int i = 1; i <= n; i++)
{
if(h[i - 1] < h[i])
{
for(int j = 1; j <= h[i - 1]; j++)
f[i][j] = f[i - 1][j];
for(int j = h[i - 1] + 1; j <= h[i]; j++)
f[i][j] = 2 * g[i - 1] % mod;
g[i] = 2 * g[i - 1] % mod;
}
else
{
for(int j = 1; j <= h[i]; j++)
f[i][j] = 1ll * f[i - 1][j] * qpow(2, b[h[i - 1]] - b[h[i]]) % mod;
g[i] = 2 * g[i - 1] % mod;
for(int j = h[i] + 1; j <= h[i - 1]; j++)
g[i] = (g[i] + 2ll * c[j] * f[i - 1][j] % mod * qpow(2, b[h[i - 1]] - b[j])) % mod;
}
}
int ans = g[n];
for(int i = 1; i <= h[n]; i++) ans = (ans + 1ll * c[i] * f[n][i] % mod * qpow(2, b[h[n]] - b[i])) % mod;
printf("%d\n", ans);
} |
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <set>
#include <vector>
#include <map>
#include <cstdio>
#include <utility>
#include <algorithm>
#include <cmath>
#include <queue>
#include <stack>
#include <cassert>
#include <climits>
#include <numeric>
#include <sstream>
using namespace std;
typedef long long ll;
#define DEBUG
#ifdef DEBUG
#define debug printf
#else
#define debug(...)
#endif
const int maxn = 103;
const int mod = 1e9 + 7;
int n,m,a[maxn],b[maxn],f[maxn][maxn],tp;
int i,j;
ll mypow(ll a,ll b)
{
if(b <= 0)
{
return 1;
}
ll res = 1;
for(;b;b >>= 1,a = a * a % mod)
{
if(b & 1)
{
res = res * a % mod;
}
}
return res;
}
void trans(int d)
{
d = min(d,a[i + 1]);
f[i + 1][d] = (f[i + 1][d] + mypow(2,b[a[i]] - b[max(j,a[i + 1])]) * tp) % mod;
}
int main(int argc, char const *argv[])
{
scanf("%d",&n);
for(int i = 0;i < n; ++i)
{
scanf("%d",&a[i]);
b[i] = --a[i];
}
sort(b,b + n + 1);
m = unique(b,b + n + 1) - b;
for(int i = 0;i < n; ++i)
{
a[i] = lower_bound(b,b + m,a[i]) - b;
}
f[0][0] = 1;
for(i = 0;i < n; ++i)
{
for(j = 0;j <= a[i]; ++j)
{
if((tp = f[i][j]))
{
trans(j),trans(a[i]);
}
}
}
printf("%d\n",f[n][0]);
return 0;
} |
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
using namespace std;
#define LL long long
const int N=105;
const LL mod=1000000007;
int a[N];
LL sqrr(LL x){return x*x%mod;}
LL mi2(int x){
if (!x) return 1;if (x==1) return 2;
LL ans=sqrr(mi2(x>>1));
if (x&1) ans=ans*2%mod;
return ans;
}
LL dp(int l,int r,int h,int ff){
if (l>r) return 1ll;
if (l==r) return mi2(a[l]-h);
int i,mini=0;
for (i=l;i<=r;i++) if (a[i]<a[mini]) mini=i;
if (ff) return dp(l,mini-1,a[mini],ff)*dp(mini+1,r,a[mini],ff)%mod*mi2(a[mini]-h)%mod;
else{
LL ans1=dp(l,mini-1,a[mini]-1,0)*dp(mini+1,r,a[mini]-1,0)%mod*2ll%mod;
LL ans2=dp(l,mini-1,a[mini],1)*dp(mini+1,r,a[mini],1)%mod*(mi2(a[mini]-h)+mod-2)%mod;
return (ans1+ans2)%mod;
}
}
int main(){
//freopen("in.txt","r",stdin);
//freopen("out.txt","w",stdout);
int i,n;
scanf("%d",&n);
for (i=1;i<=n;i++) scanf("%d",&a[i]);
a[0]=0x7fffffff;
printf("%lld\n",dp(1,n,0,0));
return 0;
}
|
#include<bits/stdc++.h>
#define ll long long
const ll mod=1e9+7;
using namespace std;
ll N;
ll f[1100][1100],g[1100];
ll a[1100],H[1100],lisan[1100],lcnt;
ll &ml=lcnt;
ll ans;
ll qpow(ll a,ll b) {
ll ans=1;
for(;b;b>>=1,a=(a*a)%mod) if(b&1) ans=(ans*a)%mod;
return ans;
}
int main() {
//cerr<<qpow(2,0)<<endl;
scanf("%lld",&N);
for(int i=1;i<=N;++i) scanf("%lld",a+i),lisan[i]=a[i];
sort(lisan+1,lisan+N+1);
lcnt=unique(lisan+1,lisan+N+1)-lisan-1;
for(int i=1;i<=N;++i) H[i]=lower_bound(lisan+1,lisan+lcnt+1,a[i])-lisan;
//for(int i=1;i<=N;++i) printf("H[%d]=%lld\n",i,H[i]);
g[1]=2;
for(int i=1;i<=H[1];++i) f[1][i]=qpow(2,a[1]-lisan[i])*(qpow(2,lisan[i])-2);//,tt(1,i);
for(int i=H[1]+1;i<=ml;++i) f[1][i]=f[1][i-1];//,tt(1,i);
for(int i=2;i<=N;++i) {
for(int j=1;j<=H[i];++j) {
f[i][j]+=f[i-1][j]%mod*qpow(2,max(0ll,a[i]-a[i-1]))%mod;
f[i][j]%=mod;
if(j>H[i-1]) {
f[i][j]+=2*g[i-1]%mod*qpow(2,a[i]-lisan[j])%mod*(qpow(2,lisan[j]-a[i-1])-1)%mod;
f[i][j]%=mod;
}
//tt(i,j);
}
for(int j=H[i]+1;j<=ml;++j) f[i][j]=f[i][j-1];
if(H[i-1]<=H[i]) g[i]=g[i-1]*2%mod;
else g[i]=(g[i-1]*2%mod+(f[i-1][H[i-1]]-f[i-1][H[i]]+mod)*2%mod)%mod;
g[i]=(g[i]%mod+mod)%mod;
//printf("g[%d]=%lld\n",i,g[i]);
}
ans=(g[N]+f[N][ml])%mod;
//printf("ans=%lld\n",ans);
printf("%lld\n",ans%mod);
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
#define fi first
#define se second
#define mp make_pair
const int MOD = (int)1e9 + 7;
int pow(int x, int k){
if(k==0) return 1;
int p = pow(x,k/2);
p = (p * 1ll * p) % MOD;
if(k % 2) p = (p * 1ll * x) % MOD;
return p;
}
pii solve(vector<int> hh){
int low = (int)1e9;
for(auto x : hh)
low = min(low, x);
vector<int> cur;
vector<pii> sols;
int emp = 0;
for(int i = 0 ; i < hh.size(); i ++ ){
hh[i] -= low;
emp += (hh[i] == 0);
if(hh[i] != 0) cur.push_back(hh[i]);
if(hh[i] == 0 || i + 1 == hh.size()){
if(!cur.empty()) sols.push_back(solve(cur));
cur.clear();
}
}
ll a1 = 1;
for(auto x : sols)
a1 = (a1 * 1ll * x.fi) % MOD;
a1 = (a1 * 1ll * pow(2,low)) % MOD;
ll a2 = pow(2,emp);
ll a3 = (pow(2,low) - 2);
for(auto x : sols){
a2 = (a2 * 1ll * (x.fi + x.se)) % MOD;
a3 = (a3 * 1ll * x.fi) % MOD;
}
return mp(a1, (a2+a3)%MOD);
}
int main(){
int n;
cin >> n;
vector<int> sol;
int a;
for(int i = 1; i <= n; i ++ ){
cin >> a;
sol.push_back(a);
}
pii res = solve(sol);
cout << res.se << "\n";
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
int N, K, H[100];
vector<int> L;
long long P[30];
long long D[101][101];
#define MOD 1000000007LL
long long R;
long long pow(int x) {
long long r = 1;
for(int b = 0; b < 30; ++b) {
if((1 << b) & x) (r *= P[b]) %= MOD;
}
return r;
}
int main() {
P[0] = 2LL;
for(int i = 1; i < 30; ++i) {
P[i] = P[i - 1] * P[i - 1] % MOD;
}
cin >> N;
L.push_back(0);
for(int i = 0; i < N; ++i) {
cin >> H[i]; L.push_back(H[i]);
}
sort(L.begin(), L.end());
L.erase(unique(L.begin(), L.end()), L.end());
K = L.size();
long long prev_l = 0; D[0][0] = 1;
for(int i = 0; i < N; ++i) {
long long l = lower_bound(L.begin(), L.end(), H[i]) - L.begin();
if(prev_l >= l) {
(D[i + 1][0] += 2 * D[i][0] % MOD) %= MOD;
for(int k = 1; k <= l; ++k) {
(D[i + 1][k] += D[i][k]) %= MOD;
}
for(int k = l + 1; k <= prev_l; ++k) {
(D[i + 1][0] += 2 * D[i][k] % MOD) %= MOD;
}
} else {
(D[i + 1][0] += 2 * D[i][0] % MOD) %= MOD;
for(int k = prev_l + 1; k <= l; ++k) {
(D[i + 1][k] +=
2
* (pow(L[k] - L[k - 1] - (k - 1 == 0 ? 1 : 0)) + MOD - 1) % MOD
* pow(L[l] - L[k]) % MOD
* D[i][0]) %= MOD;
}
long long C = pow(L[l] - L[prev_l]);
for(int k = 1; k <= prev_l; ++k) {
(D[i + 1][k] += C * D[i][k] % MOD) %= MOD;
}
}
prev_l = l;
}
for(int k = 0; k < K; ++k) {
(R += D[N][k]) %= MOD;
}
cout << R << endl;
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
constexpr int P = 1E9 + 7;
int power(int base, int exp) {
int result = 1;
while (exp > 0) {
if (exp & 1)
result = 1LL * result * base % P;
base = 1LL * base * base % P;
exp >>= 1;
}
return result;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n;
cin >> n;
vector<int> h(n);
for (int i = 0; i < n; ++i)
cin >> h[i];
function<array<int, 2>(int, int, int)> calc = [&](int l, int r, int low) {
if (l == r)
return array<int, 2>{1, 0};
int mn = 1E9;
array<int, 2> dp {1, 1};
for (int i = l; i < r; ++i)
mn = min(mn, h[i]);
int x = l, cnt = 0;
for (int i = l; i < r; ++i) {
if (h[i] == mn) {
auto f = calc(x, i, mn);
x = i + 1;
++cnt;
dp[0] = 1LL * dp[0] * f[0] % P;
dp[1] = 1LL * dp[1] * (f[0] + f[1]) % P;
}
}
auto f = calc(x, r, mn);
dp[0] = 1LL * dp[0] * f[0] % P;
dp[1] = 1LL * dp[1] * (f[0] + f[1]) % P;
int tmp = power(2, mn - low);
dp[1] = (1LL * power(2, cnt) * dp[1] + 1LL * (tmp - 2 + P) * dp[0]) % P;
dp[0] = 1LL * tmp * dp[0] % P;
return dp;
};
cout << calc(0, n, 0)[1] << endl;
return 0;
} |
#include <cstdio>
#include <iostream>
typedef long long ll;
inline int Max(const int a,const int b){return a>b?a:b;}
#define pii pair<int,int>
#define fi first
#define se second
int n,h[105];
const int Mod=1000000007,Inf=0x3f3f3f3f;
ll Pow(ll a,ll b)
{
ll s=1;
for(;b;b>>=1,a=a*a%Mod)
if(b&1)s=s*a%Mod;
return s%Mod;
}
std::pair<int,int> Solve(int l,int r,int Lim)
{
int Minh=Inf,Cnt=0;
for(int i=l;i<=r;++i)
if(h[i]<Minh)Minh=h[i],Cnt=1;
else if(h[i]==Minh)++Cnt;
if(Cnt==r-l+1)return std::make_pair(int((Pow(2,r-l+1)+Mod-2)%Mod),(int)Pow(2,Minh-Lim-1));
int Rem=r-l+1,s0=1,s1=1,Las=0;
for(int i=l;i<=r+1;++i)
if(!Las&&h[i]!=Minh)Las=i;
else if(Las&&(h[i]==Minh||i>r))
{
std::pair<int,int> Tmp=Solve(Las,i-1,Minh);
s0=(ll)s0*(Tmp.first+4ll*Tmp.second%Mod)%Mod;
s1=(ll)s1*2ll*Tmp.second%Mod,Rem-=i-Las,Las=0;
}
s0=(s0+Mod-s1)%Mod;
return std::make_pair(int((s0*Pow(2,Rem)%Mod+s1*(Pow(2,Rem)+Mod-2))%Mod),int(s1*Pow(2,Minh-Lim-1)%Mod));
}
int main()
{
scanf("%d",&n);
for(int i=1;i<=n;++i)scanf("%d",&h[i]);
if(n==1)return printf("%d\n",int(Pow(2,h[1]))),0;
int Ex=1;
for(int i=1;i<=n;++i)
if(h[i]>h[i-1]&&h[i]>h[i+1])
{
Ex=(Ex*Pow(2,h[i]-Max(h[i-1],h[i+1])))%Mod;
h[i]=Max(h[i-1],h[i+1]);
}
std::pair<int,int> Ans=Solve(1,n,0);
printf("%d\n",int(Ex*(Ans.first+2ll*Ans.second)%Mod));
return 0;
}
|
#include<bits/stdc++.h>
#define P pair<int,int>
#define fir first
#define sec second
using namespace std;
typedef long long ll;
const int mod=1e9+7;
const int inf=0x3f3f3f3f;
const int N=105;
int a[N],n;
int ksm(int x,int y)
{
int res=1;
while (y){if (y&1) res=(ll)res*x%mod;x=(ll)x*x%mod;y>>=1;}
return res;
}
void up(int &x,int y){x=x-mod+y;x=(x<0)?x+mod:x;}
P dfs(int l,int r,int h)//笛卡尔树,s1表示存在相同相邻，s2表示010101相邻不同
{
int Min=inf,cnt=0;
for (int i=l;i<=r;i++) Min=min(Min,a[i]);
for (int i=l;i<=r;i++) if (Min==a[i]) cnt++;
if (cnt==r-l+1)//边界，矩形
return P(((ll)ksm(2,r-l+1)-2+mod)%mod,ksm(2,Min-h));
int s1=1,s2=1,blo=0;cnt=0;
for (int i=l,L=l,R=l-1;i<=r;i++)
{
if (a[i]!=Min) R=i;else cnt++;
if (a[i]==Min||i==r)
{
if (L<=R)
{
blo++;
P now=dfs(L,R,Min);
s1=(ll)s1*(now.fir+(ll)now.sec*2%mod)%mod;//全集
s2=(ll)s2*now.sec%mod;//01交替
}
L=i+1,R=i;
}
}
s1=((ll)s1-(ll)s2*ksm(2,blo)%mod+mod)%mod;//存在相同相邻
P ans;
ans.fir=(ll)s1*ksm(2,cnt)%mod;
ans.fir=((ll)ans.fir+((ll)ksm(2,cnt)*ksm(2,blo)%mod-2+mod)%mod*s2%mod)%mod;
ans.sec=(ll)s2*ksm(2,Min-h)%mod;
return ans;
}
int main()
{
scanf("%d",&n);
for (int i=1;i<=n;i++) scanf("%d",&a[i]);
P now=dfs(1,n,0);//[1,n]当前底层高度
printf("%d\n",((ll)now.fir+now.sec)%mod);
return 0;
} |
//#pragma GCC optimize("Ofast,no-stack-protector")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx")
//#pragma GCC target("avx,tune=native")
#include<bits/stdc++.h>
#define int long long
//#include<ext/pb_ds/assoc_container.hpp>
using namespace std;
//using namespace __gnu_pbds;
const int inf=0x3f3f3f3f;
const double eps=1e-6;
const int mod=1000000007;
typedef long long ll;
#define eprintf(...) fprintf(stderr, __VA_ARGS__)
inline string getstr(string &s,int l,int r){string ret="";for(int i=l;i<=r;i++)ret.push_back(s[i]);return ret;}
int modpow(int x,int y,int md=mod){if(y<=0)return 1;int ret=modpow(x,y>>1,md);ret=(ll)ret*ret%md;if(y&1)ret=(ll)ret*x%md;return ret;}
int n;
int h[105],g[105];
inline int add(int x,int y){
return (x+y)%mod;
}
inline int mul(int x,int y){
return x*y%mod;
}
inline int sub(int x,int y){
return (x-y+mod)%mod;
}
pair<int,int>operator*(pair<int,int>a,pair<int,int>b){
a.first=mul(a.first,add(b.first,b.second));
a.second=mul(a.second,b.second);
return a;
}
pair<int,int>solve(int l,int r){
int low=*min_element(h+l,h+r+1);
int cnt=0;
for(int i=l;i<=r;i++)h[i]-=low;
for(int i=l;i<=r;i++)if(!h[i])cnt++;
int L=l,R=l;h[r+1]=0;
pair<int,int>ret(modpow(2,cnt),2);
for(int i=l;i<=r+1;i++){
R=i-1;
if(h[i]==0){
if(L<=R)ret=ret*solve(L,R);
L=i+1;
}
}
ret.first=sub(ret.first,ret.second);
ret.second=mul(ret.second,modpow(2,low-1));
ret.first=add(ret.first,ret.second);
return ret;
}
signed main(){
cin>>n;
for(int i=1;i<=n;i++)cin>>h[i];
cout<<solve(1,n).first<<endl;
return 0;
} |
#include<bits/stdc++.h>
#define ll long long
#define ull unsigned ll
#define uint unsigned
#define pii pair<int,int>
#define pll pair<ll,ll>
#define PB push_back
#define fi first
#define se second
#define For(i,j,k) for (int i=(int)(j);i<=(int)(k);i++)
#define Rep(i,j,k) for (int i=(int)(j);i>=(int)(k);i--)
#define CLR(a,v) memset(a,v,sizeof(a));
#define CPY(a,b) memcpy(a,b,sizeof(a));
using namespace std;
const int mo=1000000007;
int n,a[105];
int power(int x,int y){
int s=1;
for (;y;y/=2,x=1ll*x*x%mo)
if (y&1) s=1ll*s*x%mo;
return s;
}
pii F(int l,int r,int v){
if (l==r)
return pii(power(2,a[l]-v-1),0);
int mnv=1<<30,las=l;
pii vf;
For(i,l,r) mnv=min(mnv,a[i]);
For(i,l,r+1)
if (a[i]==mnv||i==r+1){
if (las!=i){
pii vson=F(las,i-1,mnv);
int v1=vf.fi,v2=vf.se;
int v3=2ll*vson.fi%mo,v4=vson.se;
if (las==l) vf=pii(v3,v4);
else{
vf.fi=1ll*v1*v3%mo;
vf.se=(2ll*(v1+v2)*(v3+v4)+mo-vf.fi)%mo;
}
}
if (i!=r+1){
if (i==l) vf=pii(1,0);
else vf.se=(2ll*vf.se+vf.fi)%mo;
}
las=i+1;
}
vf.fi=1ll*vf.fi*power(2,mnv-v-1)%mo;
return vf;
}
int main(){
scanf("%d",&n);
For(i,1,n) scanf("%d",&a[i]);
pii ans=F(1,n,0);
printf("%d",2ll*(ans.fi+ans.se)%mo);
} |
#include <bits/stdc++.h>
const int N = 105, mod = 1000000007;
typedef long long LL;
int pow(int x, int y, int ans = 1) {
for (; y; y >>= 1, x = (LL) x * x % mod)
if (y & 1) ans = (LL) ans * x % mod;
return ans;
}
int n, p, h[N];
std::pair<int, int> solve(int l, int r, int base) {
int x = h[l], w = 0;
for (int i = l; i <= r; ++i)
x = std::min(x, h[i]);
for (int i = l; i <= r; ++i)
if (h[i] == x) ++w;
int prod0 = 1, prod1 = 1, lst = l - 1;
for (int i = l; i <= r + 1; ++i)
if (i > r || h[i] == x) {
if (i - 1 > lst) {
auto t = solve(lst + 1, i - 1, x);
prod0 = (LL) prod0 * (t.first + t.second) % mod;
prod1 = (LL) prod1 * t.second % mod;
}
lst = i;
}
int t = pow(2, x - base);
prod0 = (pow(2, w, prod0) + (LL) (t + mod - 2) * prod1) % mod;
prod1 = (LL) t * prod1 % mod;
return {prod0, prod1};
}
int main() {
std::ios::sync_with_stdio(0), std::cin.tie(0);
std::cin >> n;
for (int i = 1; i <= n; ++i) std::cin >> h[i];
std::cout << solve(1, n, 0).first << '\n';
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 105, mod = 1000000007;
int n, h[N];
inline int qpow(int b, int p) {
int r = 1;
for (; p; p >>= 1) {
if (p & 1) r = (ll) r * b % mod;
b = (ll) b * b % mod;
}
return r;
}
pair<int, int> solve(int l, int r, int x) {
int mn = mod;
for (int i = l; i <= r; i++) {
mn = min(mn, h[i]);
}
pair<int, int> p = make_pair(2, 1);
for (int i = l; i <= r; i++) {
if (h[i] == mn) {
p.second = p.second * 2 % mod;
} else {
int j = i;
for (; j < r && h[j + 1] > mn; j++);
auto q = solve(i, j, mn);
p.first = (ll) p.first * q.first % mod;
p.second = (ll) p.second * (q.first * 2 % mod + q.second) % mod;
i = j;
}
}
p.second = (p.second + mod - p.first) % mod;
p.first = (ll) p.first * qpow(2, mn - x - 1) % mod;
return p;
}
int main() {
scanf("%d", &n);
for (int i = 1; i <= n; i++) {
scanf("%d", &h[i]);
}
auto p = solve(1, n, 0);
printf("%d\n", (p.first + p.second) % mod);
}
|
#include <bits/stdc++.h>
#define int long long
using namespace std;
int H[105];
int dp[105][105];
int all[105];
int mod = 1000000007;
long long qexp(long long b, long long p){
long long res = 1;
while(p){
if(p&1) res = (res * b) % mod;
b = (b * b) % mod;
p >>= 1;
}
return res;
}
vector<int> dis = {1};
int get(int x){ return lower_bound(dis.begin(),dis.end(),x) - dis.begin(); }
void c(int &x){
x %= mod;
if(x < 0) x += mod;
}
signed main(){
ios_base::sync_with_stdio(false); cin.tie(0);
int n; cin >> n;
for(int i = 1;i <= n;i++){
cin >> H[i];
dis.push_back(H[i]);
}
sort(dis.begin(),dis.end());
dis.erase(unique(dis.begin(), dis.end()), dis.end());
int m = dis.size();
all[0] = 1;
for(int i = 1;i <= n;i++){
if(H[i] > H[i-1]){
for(int j = m-1;j >= 0;j--){
if(dis[j] >= H[i]) dp[i][j] = 0;
else if(dis[j] >= H[i-1]){
dp[i][j] = all[i-1] * (qexp(2, H[i] - dis[j]) - 1) * 2;
c(dp[i][j]);
}
else{
dp[i][j] = dp[i-1][j] * qexp(2,H[i] - H[i-1]);
c(dp[i][j]);
dp[i][j] += all[i-1] * (qexp(2, H[i] - H[i-1]) - 1) * 2;
c(dp[i][j]);
}
}
all[i] = all[i-1] * 2;
c(all[i]);
}
else{
for(int j = 0;j < m;j++){
if(dis[j] >= H[i]) dp[i][j] = 0;
else{
dp[i][j] = dp[i-1][j] - dp[i-1][get(H[i])];
c(dp[i][j]);
}
}
all[i] = (all[i-1] + dp[i-1][get(H[i])]) * 2;
c(all[i]);
}
}
int ans = all[n] + dp[n][0];
c(ans);
cout << ans;
}
|
#include<stdio.h>
int mt(int a,int b)
{
if(b==0)
{
return 1;
}
int c=mt(a,b>>1);
c=(long long)c*c%1000000007;
if(b&1)
{
c=(long long)c*a%1000000007;
}
return c;
}
int h[128];
void sol(int l,int r,int& dp1,int& dp2)
{
int mn=1000000007;
for(int i=l;i<=r;i++)
{
if(h[i]<mn)
{
mn=h[i];
}
}
for(int i=l;i<=r;i++)
{
h[i]-=mn;
}
dp1=2;
dp2=1;
int pre=0;
for(int i=l;i<=r;i++)
{
if(h[i])
{
if(!pre)
{
pre=i;
}
}
else
{
if(pre)
{
int tmp1,tmp2;
sol(pre,i-1,tmp1,tmp2);
dp1=(long long)dp1*tmp1%1000000007;
dp2=(long long)dp2*(tmp1+tmp2)%1000000007;
pre=0;
}
dp2<<=1;
if(dp2>=1000000007)
{
dp2-=1000000007;
}
}
}
if(pre)
{
int tmp1,tmp2;
sol(pre,r,tmp1,tmp2);
dp1=(long long)dp1*tmp1%1000000007;
dp2=(long long)dp2*(tmp1+tmp2)%1000000007;
pre=0;
}
dp2-=dp1;
if(dp2<0)
{
dp2+=1000000007;
}
dp1=(long long)dp1*mt(2,mn-1)%1000000007;
dp2+=dp1;
if(dp2>=1000000007)
{
dp2-=1000000007;
}
}
int main()
{
int n;
scanf("%d",&n);
for(int i=1;i<=n;i++)
{
scanf("%d",&h[i]);
}
int dp1,dp2;
sol(1,n,dp1,dp2);
printf("%d\n",dp2);
return 0;
} |
//Love and Freedom.
#include<cstdio>
#include<cmath>
#include<algorithm>
#include<cstring>
#define ll long long
#define inf 20021225
#define N 110
#define pa pair<int,int>
#define mdn 1000000007
using namespace std;
int read()
{
int s=0,t=1; char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-') t=-1; ch=getchar();}
while(ch>='0' && ch<='9') s=s*10+ch-'0',ch=getchar();
return s*t;
}
int a[N],n;
int ksm(int bs,int mi)
{
int ans=1;
while(mi)
{
if(mi&1) ans=1ll*ans*bs%mdn;
bs=1ll*bs*bs%mdn; mi>>=1;
}
return ans;
}
pa solve(int l,int r,int lim)
{
int mn=a[min_element(a+l,a+r+1)-a],w1=1,w2=1,num=0;
for(int i=l,j;i<=r;i++)
{
if(a[i]!=mn)
{
j=i; while(j+1<=r&&a[j+1]!=mn) j++;
pa cur=solve(i,j,mn); i=j;
w1=1ll*cur.first*w1%mdn;
w2=1ll*(cur.first+cur.second)%mdn*w2%mdn;
}
else num++;
}
return make_pair(1ll*w1*ksm(2,mn-lim)%mdn,(1ll*w2*ksm(2,num)%mdn+1ll*w1*(ksm(2,mn-lim)-2)%mdn)%mdn);
}
int main()
{
n=read();
for(int i=1;i<=n;i++) a[i]=read();
printf("%d\n",solve(1,n,0).second);
return 0;
}
|
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const int mod=1e9+7;
inline int add(int x,int y){
return (x+y)%mod;
}
inline int mul(int x,int y){
return (ll)x*y%mod;
}
inline int qpow(int base,int pw){
if(pw<0) return 1;
int res=1;
while(pw>0){
if(pw&1) res=mul(res,base);
base=mul(base,base);
pw>>=1;
}
return res;
}
int h[110],dp[110][110];
vector<int> hs;
int main(){
int n;
scanf("%d",&n);
for(int i=1;i<=n;i++){
scanf("%d",h+i);
hs.push_back(h[i]);
}
hs.push_back(0);
sort(hs.begin(),hs.end());
hs.erase(unique(hs.begin(),hs.end()),hs.end());
for(int i=1;i<=n;i++)
h[i]=lower_bound(hs.begin(),hs.end(),h[i])-hs.begin();
dp[0][0]=1;
for(int i=1;i<=n;i++){
for(int j=h[i]+1;j<=h[i-1];j++)
dp[i][0]=add(dp[i][0],add(dp[i-1][j],dp[i-1][j]));
dp[i][0]=add(dp[i][0],add(dp[i-1][0],dp[i-1][0]));
for(int j=1;j<=h[i];j++){
dp[i][j]=mul(dp[i-1][j],qpow(2,hs[h[i]]-hs[h[i-1]]));
if(h[i-1]>=j) continue;
if(j>1) dp[i][j]=add(dp[i][j],mul(add(dp[i-1][0],dp[i-1][0]),mul(add(qpow(2,hs[j]-hs[j-1])-1,mod),qpow(2,hs[h[i]]-hs[j]))));
else dp[i][j]=add(dp[i][j],mul(dp[i-1][0],mul(add(qpow(2,hs[j])-2,mod),qpow(2,hs[h[i]]-hs[j]))));
}
}
int ans=0;
for(int i=0;i<(int)hs.size();i++)
ans=add(ans,dp[n][i]);
printf("%d\n",ans);
return 0;
} |
#include<iostream>
#include<algorithm>
#include<cstdio>
#include<string>
#include<cstring>
#include<cassert>
#include<cmath>
#include<sstream>
#include<fstream>
#include<map>
#include<set>
#include<vector>
#include<queue>
#include<stack>
#include<bitset>
using namespace std;
const long long MOD=1e9+7;
long long quipow(int i,long long x){
long long res=1;
while(i>0){
if(i&1) res=res*x%MOD;
x=x*x%MOD;
i>>=1;
}
return res;
}
long long dp1[105],dp2[105],ndp1[105],ndp2[105]; //dp2[i]:到第i行为止依然有序的情况
int h[105];
vector<int> v;
map<int,int> mp;
int main(){
int n;
cin>>n;
for(int i=0;i<n;i++){
cin>>h[i];
v.push_back(h[i]);
}
sort(v.begin(),v.end());
v.erase(unique(v.begin(),v.end()),v.end());
for(int i=0;i<v.size();i++) mp[v[i]]=i;
for(int i=0;v[i]<=h[0]&&i<v.size();i++){
dp2[i]=2*quipow(h[0]-v[i],2)%MOD;
dp1[i]=(quipow(h[0],2)-dp2[i]+MOD)%MOD;
}
for(int i=1;i<n;i++){
for(int j=0;v[j]<=min(h[i],h[i-1])&&j<v.size();j++) {
ndp1[j]=dp1[j]%MOD;
ndp2[j]=(dp2[j]+dp2[min(mp[h[i-1]],mp[h[i]])])%MOD;
dp1[j]=ndp1[j]*quipow(h[i]-h[i-1],2)%MOD;
dp2[j]=ndp2[j]*quipow(h[i]-h[i-1],2)%MOD;
}
int idx=mp[h[i-1]];
if(h[i]>h[i-1]){
for(int j=idx+1;v[j]<=h[i]&&j<v.size();j++){
ndp1[j]=((ndp1[j-1]+ndp2[j-1])%MOD*quipow(v[j]-v[j-1],2)%MOD-ndp2[j-1]+MOD)%MOD;
ndp2[j]=ndp2[j-1]%MOD;
dp1[j]=ndp1[j]*quipow(h[i]-v[j],2)%MOD;
dp2[j]=ndp2[j]*quipow(h[i]-v[j],2)%MOD;
}
}
}
long long res=0;
res=(dp1[mp[h[n-1]]]+dp2[mp[h[n-1]]])%MOD;
cout<<res;
} |
#include<iostream>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<cmath>
#include<vector>
#define mk make_pair
#define fi first
#define se second
using namespace std;
const int maxn=1e5+100;
const int mod=1e9+7;
const int inf=1e9+1000;
int h[maxn],n;
typedef long long ll;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
inline ll ksm(ll num,ll t) {
ll res=1;num%=mod;
for(;t;t>>=1,num=num*num%mod) {
if(t&1)res=res*num%mod;
}
return res%mod;
}
pll solve(int l,int r,int c) {
if(l>r)return mk(1,0);
vi tmp;tmp.clear();int mi=inf,w=0;
pll ans=mk(1,1);
for(int i=l;i<=r;i++)mi=min(mi,h[i]);
tmp.push_back(l-1);for(int i=l;i<=r;i++)if(h[i]==mi)tmp.push_back(i),w++;tmp.push_back(r+1);
for(int i=1;i<tmp.size();i++) {
int le=tmp[i-1]+1,re=tmp[i]-1;
pll tmp_ans=solve(le,re,mi);
ans.fi*=tmp_ans.fi;ans.fi%=mod;
ans.se*=tmp_ans.fi+tmp_ans.se;ans.se%=mod;
}
ans.se=ans.se*ksm(2,w)%mod+(ksm(2,mi-c)-2)*ans.fi%mod;ans.se%=mod;
ans.fi*=ksm(2,mi-c);ans.fi%=mod;
return ans;
}
int main() {
ios::sync_with_stdio(0);
cin>>n;
for(int i=1;i<=n;i++)cin>>h[i];
pll ans=solve(1,n,0);
cout<<ans.se;
} |
#include <cstdio>
#include <vector>
#include <cstring>
#include <algorithm>
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define fd(i,a,b) for(int i=a;i>=b;i--)
#define pb(a) push_back(a)
using namespace std;
typedef long long ll;
const int N=1e4+5,Mo=1e9+7;
int pwr(int x,int y) {
int z=1;
for(;y;y>>=1,x=(ll)x*x%Mo)
if (y&1) z=(ll)z*x%Mo;
return z;
}
int n,h[N],row[N],column[N],tot;
vector<int> son[N];
int build(int l,int r,int d) {
int mn=1e9,cnt=0,v=++tot;
fo(i,l,r) mn=min(mn,h[i]);
column[v]=r-l+1;row[v]=mn-d;
fo(i,l,r) cnt+=h[i]==mn;
if (cnt==r-l+1) return v;
int la=l-1;
fo(i,l,r)
if (h[i]==mn) {
if (la!=i-1) son[v].pb(build(la+1,i-1,mn));
la=i;
}
if (la!=r) son[v].pb(build(la+1,r,mn));
return v;
}
ll f[N],g[N];
void dfs(int x) {
f[x]=1;g[x]=0;int c=column[x]-1;
for(int y:son[x]) {
dfs(y);
g[x]=(g[x]*(f[y]+g[y])+f[x]*g[y])%Mo;
f[x]=f[x]*f[y]%Mo;
c-=column[y]-1;
}
g[x]=(g[x]*pwr(2,c)+f[x]*(pwr(2,c)-1))%Mo;
f[x]=f[x]*pwr(2,row[x]-(x==1))%Mo;
}
int main() {
scanf("%d",&n);
fo(i,1,n) scanf("%d",&h[i]);
int ans=1;
fo(i,2,n-1)
if (h[i]>h[i-1]&&h[i]>h[i+1]) {
ans=(ll)ans*pwr(2,h[i]-max(h[i-1],h[i+1]))%Mo;
h[i]=max(h[i-1],h[i+1]);
}
build(1,n,0);dfs(1);
ans=(ll)ans*(f[1]+g[1])%Mo;
printf("%d\n",ans*2%Mo);
return 0;
} |
#include<bits/stdc++.h>
#define ll long long
using namespace std;
template<typename tn> void read(tn &a){
tn x=0,f=1; char c=' ';
for(;!isdigit(c);c=getchar()) if(c=='-') f=-1;
for(;isdigit(c);c=getchar()) x=x*10+c-'0';
a=x*f;
}
const int mod = 1e9+7;
int n,h[110],cnt,b[110];
ll f[110][110];
ll fp(ll a,ll k){
ll ans=1;
for(;k;k>>=1,a=a*a%mod)
if(k&1) ans=a*ans%mod;
return ans;
}
int main(){
read(n);
for(int i=1;i<=n;i++)
read(h[i]),b[++cnt]=h[i];
sort(b+1,b+cnt+1);
cnt=unique(b+1,b+cnt+1)-b-1;
for(int i=1;i<=n;i++)
h[i]=lower_bound(b+1,b+cnt+1,h[i])-b;
f[0][0]=1;
for(int i=1;i<=n;i++){
f[i][0]=f[i-1][0]*2%mod;
for(int j=h[i]+1;j<=h[i-1];j++) f[i][0]=(f[i][0]+f[i-1][j]*2)%mod;
for(int j=1;j<=h[i];j++)
if(h[i]>=h[i-1]) f[i][j]=f[i-1][j]*fp(2,b[h[i]]-b[h[i-1]])%mod;
else f[i][j]=f[i-1][j];
for(int j=h[i-1]+1;j<=h[i];j++)
if(j>1) f[i][j]=f[i-1][0]*(fp(2,b[j]-b[j-1]+1)-2)%mod*fp(2,b[h[i]]-b[j])%mod;
else f[i][j]=f[i-1][0]*(fp(2,b[j])-2)%mod*fp(2,b[h[i]]-b[j])%mod;
}
ll ans=0;
for(int i=0;i<=h[n];i++)
ans=(ans+f[n][i])%mod;
cout<<(ans+mod)%mod<<'\n';
return 0;
}
|
#include<bits/stdc++.h>
using namespace std;
const int P=1e9+7;
const int N=205;
const int Gi=(P+1)/2;
#define ll long long
ll fsp(ll x,int y){
ll ans=1;
while(y){
if(y&1) ans=ans*x%P;
x=x*x%P,y>>=1;
}
return ans;
}
ll f[N][2];
vector<int>ch[N];
int n,top,a[N],st[N],len[N];
void dp(int x,int fl){
int si=ch[x].size();
for(int i=0;i<si;i++) dp(ch[x][i],a[x]);
if(!si){
f[x][0]=fsp(2,len[x])-2;
f[x][1]=fsp(2,a[x]-fl);
}
else{
ll r1=1,r2=1;
for(int i=0;i<si;i++){
r1=r1*(f[ch[x][i]][0]+f[ch[x][i]][1]*2)%P;
r2=r2*f[ch[x][i]][1]%P;
}
f[x][0]=((r1-r2+P)*fsp(2,len[x])+r2*(fsp(2,len[x])-2))%P;
f[x][1]=r2*fsp(2,a[x]-fl)%P;
}
}
int main(){
scanf("%d",&n);
for(int i=1;i<=n;i++) scanf("%d",&a[i]),len[i]=1;
for(int i=1;i<=n;i++){
while(top&&a[st[top]]>=a[i]){
if(a[st[top]]==a[i]) len[i]+=len[st[top]],swap(ch[st[top]],ch[i]);
else{
if(a[st[top-1]]>=a[i]) ch[st[top-1]].push_back(st[top]);
else ch[i].push_back(st[top]);
}
top--;
}
st[++top]=i;
}
while(top>1) ch[st[top-1]].push_back(st[top]),top--;
dp(st[top],0);
printf("%lld\n",(f[st[1]][0]+f[st[1]][1])%P);
return 0;
}
|
#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
#define fr first
#define sc second
const ll M = 1000000007;
ll modpow(ll x,ll k){
if(k == 0)return 1;
ll ret = modpow(x,k/2);
ret *= ret; ret %= M;
if(k%2 == 1){
ret *= x; ret %= M;
}
return ret;
}
int N;
ll h[102];
ll dp1[102][102];
ll dp2[102][102];
void solve(int l,int r,int d){
if(l == r){
dp1[l][r] = 0;
dp2[l][r] = modpow(2,h[l]-d);
return;
}
int d_ = M;
for(int i = l ; i <= r ; i ++)d_ = min( (ll)d_ , h[i] );
vector<P> vec;
int l_=l,r_=l-1;
int cnt = 0;
for(int i = l ; i <= r ; i ++){
if(h[i] <= d_){
cnt ++;
if(l_ <= r_){
vec.push_back(P(l_,r_));
solve(l_,r_,d_);
}
l_ = i+1;
r_ = i;
}
else {
r_ = i;
}
}
if(l_ <= r_){
vec.push_back(P(l_,r_));
solve(l_,r_,d_);
}
dp1[l][r] = 1;
dp2[l][r] = 1;
for(int i = 0 ; i < vec.size() ; i ++){
P p = vec[i];
dp1[l][r] *= (dp1[p.fr][p.sc]+dp2[p.fr][p.sc]*2);
dp1[l][r] %= M;
dp2[l][r] *= dp2[p.fr][p.sc];
dp2[l][r] %= M;
}
dp1[l][r] *= modpow(2,cnt);
dp1[l][r] %= M;
dp2[l][r] *= 2;
dp2[l][r] %= M;
dp1[l][r] += M-dp2[l][r];
dp1[l][r] %= M;
dp2[l][r] *= modpow(2,d_-d-1);
dp2[l][r] %= M;
}
int main(){
scanf("%d",&N);
for(int i = 1 ; i <= N ; i ++){
scanf("%lld",&h[i]);
}
solve(1,N,0);
//cout << dp1[1][N] << " " << dp2[1][N] << endl;
cout << (dp1[1][N]+dp2[1][N])%M << endl;
}
|
#include <vector>
#include <iostream>
#define mkpr make_pair
using namespace std;
typedef pair<int, int> pii;
const int MAXN = 100, MOD = 1e9 + 7;
int n, h[MAXN + 5];
inline int qkpow ( int a, int b, const int p = MOD ) {
int ret = 1;
for ( ; b; a = 1ll * a * a % p, b >>= 1 ) ret = 1ll * ret * ( b & 1 ? a : 1 ) % p;
return ret;
}
inline pii solve ( const int l, const int r, const int cut ) {
if ( l > r ) return mkpr ( 1, 0 );
int height = 0x3f3f3f3f;
for ( int i = l; i <= r; ++ i ) height = height < h[i] ? height : h[i];
vector<int> lowpos; lowpos.push_back ( l - 1 );
for ( int i = l; i <= r; ++ i ) if ( height == h[i] ) lowpos.push_back ( i );
lowpos.push_back ( r + 1 );
int lowcnt = ( int ) lowpos.size () - 2, prdfirst = 1, prdboth = 1;
for ( int i = 0; i < ( int ) lowpos.size () - 1; ++ i ) {
pii tmp ( solve ( lowpos[i] + 1, lowpos[i + 1] - 1, height ) );
prdfirst = 1ll * prdfirst * tmp.first % MOD;
prdboth = 1ll * prdboth * ( tmp.first + tmp.second ) % MOD;
}
int pwr = qkpow ( 2, height -= cut );
return lowpos.clear (),
mkpr ( 1ll * pwr * prdfirst % MOD, ( 1ll * qkpow ( 2, lowcnt ) * prdboth % MOD + ( pwr - 2ll ) * prdfirst % MOD ) % MOD );
}
int main () {
ios :: sync_with_stdio ( false );
cin >> n;
for ( int i = 1; i <= n; ++ i ) cin >> h[i];
cout << ( solve ( 1, n, 0 ).second + MOD ) % MOD << endl;
return 0;
} |
#include<bits/stdc++.h>
using namespace std;
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
typedef long long LL;
typedef unsigned long long uLL;
typedef pair<int,int> pii;
const int maxn=111;
const int mod=1e9+7;
int qpow(int x,int y)
{
int ret=1;
while(y)
{
if(y&1)ret=(LL)ret*x%mod;
x=(LL)x*x%mod;
y>>=1;
}
return ret;
}
int n,h[maxn];
pii solve(int l,int r,int v)
{
if(l==r)return mp(qpow(2,h[l]-v),0);
int mn=*min_element(h+l,h+r+1);
vector<int> pos;pos.pb(l-1);for(int i=l;i<=r;i++)if(h[i]==mn)pos.pb(i);pos.pb(r+1);
vector<pii> ansv;
for(int i=1;i<(int)pos.size();i++)if(pos[i]>pos[i-1]+1)ansv.pb(solve(pos[i-1]+1,pos[i]-1,mn));
int v1=2,v2=qpow(2,(int)pos.size()-2);
for(int i=0;i<(int)ansv.size();i++)
{
v1=(LL)v1*ansv[i].ff%mod;
v2=(LL)v2*(ansv[i].ff*2ll+ansv[i].ss)%mod;
}
v2-=v1;if(v2<0)v2+=mod;
v1=(LL)v1*qpow(2,mn-v-1)%mod;
return mp(v1,v2);
}
int main()
{
scanf("%d",&n);
for(int i=1;i<=n;i++)scanf("%d",h+i);
pii ans=solve(1,n,0);
printf("%d\n",(ans.ff+ans.ss)%mod);
return 0;
} |
#ifndef BZ
#pragma GCC optimize "-O3"
#endif
#include <bits/stdc++.h>
#define FASTIO
#ifdef FASTIO
#define scanf abacaba
#define printf abacaba
#endif
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
using namespace std;
const ll MOD = 1e9 + 7;
ll pw(ll a, ll b) {
ll ans = 1; while (b) {
while (!(b & 1)) b >>= 1, a = (a * a) % MOD;
ans = (ans * a) % MOD, --b;
} return ans;
}
int n;
ll h[1200];
vector<ll> vv;
pair<ll, ll> ans[1200];
int en[1200];
int main() {
#ifdef FASTIO
ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
#endif
cin >> n;
for (int i = 0; i < n; ++i)
cin >> h[i], vv.push_back(h[i]);
sort(vv.begin(), vv.end());
vv.resize(unique(vv.begin(), vv.end()) - vv.begin());
reverse(vv.begin(), vv.end());
vv.push_back(0);
for (int i = 0; i < n; ++i)
en[i] = 0;
h[n] = 0;
for (int it = 0; it < vv.size() - 1; ++it) {
ll hh = vv[it];
int st = -1;
int cnt = 0;
vector<pair<ll, ll>> cur;
ll len = vv[it] - vv[it + 1];
ll gd = 1;
ll all = 1;
for (int i = 0; i <= n; ++i) {
if (en[i] == 1) {
if (st == -1)
st = i;
gd = (gd * ans[i].first) % MOD;
all = (all * (ans[i].first * 2 + ans[i].second)) % MOD;
}
else if (h[i] == hh) {
if (st == -1)
st = i;
++cnt;
}
else if (en[i] == 0) {
if (st != -1) {
for (int j = st; j < i; ++j)
en[j] = 2;
en[st] = 1;
ans[st].first = gd * pw(2, len) % MOD;
ans[st].second = (all * pw(2, cnt) % MOD - gd * 2 % MOD + MOD) % MOD;
}
gd = all = 1;
st = -1;
cnt = 0;
}
}
}
cout << (ans[0].first + ans[0].second) % MOD;
return 0;
}
|
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
typedef long long LL;
const int N = 105;
const int MOD = 1000000007;
int n,m,h[N],w[N];
LL dp[N][N];
int pow_(int x,int y) {///快速幂求 x的y次方
int ans = 1;
if(y > 0) {
while(y) {
if(y % 2)ans = (LL)ans * x % MOD;
x = (LL)x * x % MOD;
y /= 2;
}
}
return ans;
}
int main() {
scanf("%d",&n);
for(int i = 1;i <= n;i ++) {
scanf("%d",&h[i]);
w[++ m] = h[i];
}
sort(w + 1,w + m + 1);///高度排序
m = unique(w + 1,w + m + 1) - w - 1;///离散化 m是离散化后的长度
for(int i = 1;i <= n;i ++) {
h[i] = lower_bound(w + 1,w + m + 1,h[i]) - w;
}
dp[0][0]=1;
for(int i = 1;i <= n;i ++) {
for(int j = h[i] + 1;j <= h[i - 1];j ++)
(dp[i][0] += dp[i - 1][j] * 2 % MOD) %= MOD;
(dp[i][0] += dp[i - 1][0] * 2 % MOD) %= MOD;///交叉或者不交叉
for(int j = 1;j <= h[i];j ++) {
dp[i][j]=(LL)dp[i - 1][j] * pow_(2,w[h[i]] - w[h[i-1]]) % MOD;
if(h[i - 1] >= j)continue;///如果是高度不超过前一列的位置 量已经确定了
if(j > 1)(dp[i][j] += dp[i - 1][0] * (pow_(2,w[j] - w[j - 1]) - 1) % MOD * 2 % MOD * pow_(2,w[h[i]] - w[j]) % MOD) %= MOD;
else (dp[i][1] += dp[i - 1][0] * (pow_(2,w[1]) - 2) % MOD * pow_(2,w[h[i]] - w[1]) % MOD) %= MOD;///上一列中无重复的乘上化不超过上一列高度中有重复的
}
}
LL ans = 0;
for(int i = 0;i <= m;i++)
(ans += dp[n][i]) %= MOD;
printf("%lld",ans);
return 0;
}
|
#include<bits/stdc++.h>
using namespace std;
#define INF int(1e9+5)
#define rep(i,n) for(int i=0;i<(n);i++)
#define REP(i,n) for(int i=1;i<=(n);i++)
#define mp make_pair
#define pb push_back
#define fst first
#define snd second
typedef long long ll;
typedef pair<int,int> pii;
const int maxn=105;
const int mod=1e9+7;
int n;
int h[maxn],dp[maxn][maxn][3];
int quickpow(int x,int pow){
int res=1;
for(;pow;pow>>=1){
if(pow&1)res=1LL*res*x%mod;
x=1LL*x*x%mod;
}
return res;
}
void solve(int l,int r,int last){
dp[l][r][0]=dp[l][r][1]=dp[l][r][2]=1;
int mn=INF;
for(int i=l;i<=r;i++)mn=min(mn,h[i]);
int cnt=0;
for(int i=l;i<=r;i++){
if(h[i]==mn)cnt++;
else{
int j=i;
while(j<=r&&h[j]>mn)j++;
solve(i,j-1,mn-1);
dp[l][r][0]=1LL*dp[l][r][0]*dp[i][j-1][(i-l)&1]%mod;
dp[l][r][1]=1LL*dp[l][r][1]*dp[i][j-1][1^((i-l)&1)]%mod;
dp[l][r][2]=1LL*dp[l][r][2]*dp[i][j-1][2]%mod;
i=j-1;
}
}
int cur=dp[l][r][0]+dp[l][r][1];
if(cur>=mod)cur-=mod;
dp[l][r][2]=1LL*dp[l][r][2]*quickpow(2,cnt)%mod;
dp[l][r][2]-=cur;
if(dp[l][r][2]<0)dp[l][r][2]+=mod;
if(mn-last>1)dp[l][r][0]=dp[l][r][1]=1LL*cur*quickpow(2,mn-last-2)%mod;
rep(i,2){
dp[l][r][2]+=dp[l][r][i];
if(dp[l][r][2]>=mod)dp[l][r][2]-=mod;
}
}
int main(){
scanf("%d",&n);
REP(i,n)scanf("%d",&h[i]);
solve(1,n,0);
printf("%d\n",dp[1][n][2]);
return 0;
} |
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<algorithm>
#define ll long long
using namespace std;
const int maxn=1010, inf=1e9, mod=1e9+7;
int n, N;
int h[maxn], b[maxn], f[maxn][maxn];
template<typename T>
inline void read(T &k)
{
int f=1; k=0; char c=getchar();
while(c<'0' || c>'9') c=='-'&&(f=-1), c=getchar();
while(c<='9' && c>='0') k=k*10+c-'0', c=getchar();
k*=f;
}
inline int power(int a, int b)
{
if(b<0) return 1;
int ans=1;
for(;b;b>>=1, a=1ll*a*a%mod)
if(b&1) ans=1ll*a*ans%mod;
return ans;
}
int main()
{
read(n);
for(int i=1;i<=n;i++) read(h[i]), b[++N]=h[i];
sort(b+1, b+1+N); N=unique(b+1, b+1+N)-b-1;
for(int i=1;i<=n;i++) h[i]=lower_bound(b+1, b+1+N, h[i])-b;
f[0][0]=1;
for(int i=1;i<=n;i++)
{
f[i][0]=2ll*f[i-1][0]%mod;
for(int j=h[i]+1;j<=h[i-1];j++) f[i][0]=(f[i][0]+2ll*f[i-1][j])%mod;
for(int j=1;j<=h[i];j++)
{
f[i][j]=1ll*f[i-1][j]*power(2, b[h[i]]-b[h[i-1]])%mod;
if(j>h[i-1])
{
if(j>1) f[i][j]=(f[i][j]+1ll*f[i-1][0]*(power(2, b[j]-b[j-1])-1+mod)*2%mod*power(2, b[h[i]]-b[j]))%mod;
else f[i][j]=(f[i][j]+1ll*f[i-1][0]*(power(2, b[j]-1)-1)*2%mod*power(2, b[h[i]]-b[j]))%mod;
}
}
}
int ans=0;
for(int i=0;i<=N;i++) ans=(ans+f[n][i])%mod;
printf("%d\n", ans);
} |
#include<cstdio>
#include<algorithm>
using namespace std;
#define N 106
#define mod 1000000007
int dp[N][N],n,s[N],st[N],v[N],v2[N],ct,as=1;
int pw(int a,int p){int as=1;while(p){if(p&1)as=1ll*as*a%mod;a=1ll*a*a%mod;p>>=1;}return as;}
int main()
{
scanf("%d",&n);
for(int i=1;i<=n;i++)scanf("%d",&s[i]),v[i]=s[i];
sort(v+1,v+n+1);
v[0]=1;for(int i=1;i<=n;i++)if(v[i]!=v[i-1])v2[++ct]=v[i];
for(int i=1;i<=n;i++)for(int j=1;j<=ct;j++)if(s[i]==v2[j])st[i]=j;
dp[0][0]=1;
for(int i=1;i<=n;i++)
if(s[i]==1)
{
int su=0;
for(int j=0;j<=ct+1;j++)su=(su+dp[i-1][j])%mod;
as=2ll*as*su%mod;
dp[i][0]=1;
}
else if(s[i-1]<=1)
{
for(int j=1;j<=st[i];j++)
dp[i][j]=pw(2,s[i]-v2[j-1]+(j>1));
dp[i][st[i]+1]=2;
for(int j=1;j<=st[i];j++)dp[i][j]=(dp[i][j]-dp[i][j+1]+mod)%mod;
}
else if(s[i]<=s[i-1])
{
for(int j=1;j<=st[i-1]+1;j++)
if(j>st[i])dp[i][st[i]+1]=(dp[i][st[i]+1]+2ll*dp[i-1][j])%mod;
else dp[i][j]=dp[i-1][j];
}
else
{
for(int j=1;j<=st[i-1];j++)dp[i][j]=1ll*dp[i-1][j]*pw(2,s[i]-s[i-1])%mod;
for(int j=st[i-1]+1;j<=st[i];j++)dp[i][j]=2ll*dp[i-1][st[i-1]+1]*pw(2,s[i]-v2[j-1])%mod;
dp[i][st[i]+1]=2ll*dp[i-1][st[i-1]+1]%mod;
for(int j=st[i-1]+1;j<=st[i];j++)dp[i][j]=(dp[i][j]-dp[i][j+1]+mod)%mod;
}
int su=0;
for(int j=0;j<=ct+1;j++)su=(su+dp[n][j])%mod;
as=1ll*as*su%mod;
printf("%d\n",as);
}// |
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int mod=1000000007;
inline void add(int &x,int y){(x+=y)>=mod?x-=mod:0;}
inline int pl(int x,int y){return (x+=y)>=mod?x-mod:x;}
inline int kpow(int a,int b)
{
int s=1;
for(;b;b>>=1,a=1ll*a*a%mod)
if(b&1)s=1ll*s*a%mod;
return s;
}
int n,h[110],dp[110][110],d[110],m,ans;
int main()
{
scanf("%d",&n);
for(int i=1;i<=n;++i)scanf("%d",&h[i]),d[i]=h[i];
sort(d+1,d+1+n);
m=unique(d+1,d+1+n)-d-1;
for(int i=1;i<=n;++i)h[i]=lower_bound(d+1,d+1+m,h[i])-d;
for(int i=0;i<=h[1];++i)dp[1][i]=kpow(2,d[h[1]]-d[i])*(1+(i>0))%mod;
for(int i=0;i<=h[1];++i)add(dp[1][i],mod-dp[1][i+1]);
for(int i=2;i<=n;++i)
{
for(int j=0;j<=h[i-1]&&j<=h[i];++j)dp[i][j]=dp[i-1][j];
if(h[i-1]>=h[i])
{
for(int j=h[i]+1;j<=h[i-1];++j)add(dp[i][h[i]],dp[i-1][j]);
for(int j=h[i];j<=h[i-1];++j)add(dp[i][h[i]],dp[i-1][j]);
}
else
{
int res=pl(dp[i][h[i-1]],dp[i-1][h[i-1]]);
for(int j=h[i-1];j<=h[i];++j)dp[i][j]=1ll*res*kpow(2,d[h[i]]-d[j])%mod;
for(int j=h[i-1];j<=h[i];++j)add(dp[i][j],mod-dp[i][j+1]);
res=kpow(2,d[h[i]]-d[h[i-1]]);
for(int j=0;j<h[i-1];++j)dp[i][j]=1ll*dp[i][j]*res%mod;
}
}
// for(int i=1;i<=n;++i)
// {
// for(int j=0;j<=h[i];++j)printf("%d ",dp[i][j]);
// printf("\n");
// }
for(int j=0;j<=h[n];++j)add(ans,dp[n][j]);
printf("%d",ans);
return 0;
}
|
#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int mod = 1e9 + 7;
int n, m, l[105], r[105];
ll h[105], a[105], dp[105][2];
ll Pow(ll a, int x) {
ll res = 1;
while (x) {
if (x & 1) (res *= a) %= mod;
(a *= a) %= mod;
x >>= 1;
}
return res;
}
int main() {
cin >> n;
for (int i = 1; i <= n; i++) {
cin >> h[i];
a[i] = h[i];
}
sort(a + 1, a + 1 + n);
m = unique(a + 1, a + 1 + n) - a - 1;
for (int i = m; i >= 1; i--) {
for (int j = 1; j <= n; j++) {
if (h[j] > a[i]) {
if (h[j - 1] > a[i]) {
dp[j][0] = dp[j - 1][0];
dp[j][1] = dp[j - 1][1];
}
if (h[j - 1] == a[i]) {
dp[j][0] = (dp[j][0] + dp[j][1]) % mod;
dp[j][1] = (2 * dp[j][1]) % mod;
dp[j][0] = dp[j - 1][0] * dp[j][0] % mod;
dp[j][1] = dp[j - 1][1] * dp[j][1] % mod * Pow(2, mod - 2) % mod;
}
if (h[j - 1] < a[i]) {
dp[j][0] = (dp[j][0] + dp[j][1]) % mod;
dp[j][1] = (2 * dp[j][1]) % mod;
}
}
if (h[j] == a[i]) {
if (h[j - 1] >= h[j]) {
dp[j][0] = dp[j - 1][0] * 2 % mod;
dp[j][1] = dp[j - 1][1];
}
else {
dp[j][0] = 2;
dp[j][1] = 2;
}
}
}
for (int j = n; j >= 1; j--) {
if (h[j] >= a[i] && h[j + 1] >= a[i]) {
dp[j][0] = dp[j + 1][0];
dp[j][1] = dp[j + 1][1];
}
}
for (int j = n; j >= 1; j--) {
int k = a[i] - a[i - 1] - 1;
dp[j][0] = (dp[j][0] + dp[j][1] * (Pow(2, k) - 1) % mod) % mod,
dp[j][1] = dp[j][1] * Pow(2, k) % mod;
}
}
cout << dp[1][0];
}
|
#include<bits/stdc++.h>
using namespace std;
using int64 = long long;
const int64 INF = 1LL << 60;
const int mod = 1e9 + 7;
int64_t mod_pow(int64_t x, int64_t n, int64_t mod) {
int64_t ret = 1;
while(n > 0) {
if(n & 1) (ret *= x) %= mod;
(x *= x) %= mod;
n >>= 1;
}
return ret;
}
int64 N, A[100];
int64 dp1[100][101], dp2[100][101];
void dfs(int l, int r) {
int64 ret = INF;
int w = r - l;
for(int i = l; i < r; i++) ret = min(ret, A[i]);
for(int i = l; i < r; i++) A[i] -= ret;
vector< pair< int, int > > child;
for(int i = l; i < r; i++) {
if(A[i] == 0) continue;
int left = i;
while(left < r && A[left] > 0) ++left;
child.emplace_back(i, left);
w -= left - i;
i = left - 1;
}
dp1[l][r] = dp2[l][r] = 1;
for(auto &p : child) {
dfs(p.first, p.second);
(dp1[l][r] *= dp1[p.first][p.second]) %= mod;
(dp2[l][r] *= dp1[p.first][p.second] + dp2[p.first][p.second]) %= mod;
}
(dp2[l][r] = dp2[l][r] * mod_pow(2, w, mod) % mod + ((mod_pow(2, ret, mod) + mod - 2) % mod) * dp1[l][r] % mod) %= mod;
(dp1[l][r] *= mod_pow(2, ret, mod)) %= mod;
for(int i = l; i < r; i++) A[i] += ret;
}
int main() {
cin >> N;
for(int i = 0; i < N; i++) {
cin >> A[i];
}
dfs(0, N);
cout << dp2[0][N] << endl;
} |
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
typedef long long LL;
const int N = 105;
const int MOD = 1000000007;
int n,dp[N][N],h[N],w[N],m;
int pow_(int x,int y) {///快速幂求 x的y次方
int ans = 1;
if(y > 0) {
while(y) {
if(y % 2)ans = (LL)ans * x % MOD;
x = (LL)x * x % MOD;
y /= 2;
}
}
return ans;
}
int main() {
scanf("%d",&n);
for(int i = 1;i <= n;i ++) {
scanf("%d",&h[i]);
w[++ m] = h[i];
}
sort(w + 1,w + m + 1);///高度排序
m = unique(w + 1,w + m + 1) - w - 1;///离散化 m是离散化后的长度
for(int i = 1;i <= n;i ++) {
h[i] = lower_bound(w + 1,w + m + 1,h[i]) - w;
}
dp[0][0]=1;
for(int i = 1;i <= n;i ++) {
for(int j = h[i] + 1;j <= h[i - 1];j ++)
(dp[i][0] += dp[i - 1][j] * 2 % MOD) %= MOD;
(dp[i][0] += dp[i - 1][0] * 2 % MOD) %= MOD;///交叉或者不交叉
for(int j = 1;j <= h[i];j ++) {
dp[i][j]=(LL)dp[i - 1][j] * pow_(2,w[h[i]] - w[h[i-1]]) % MOD;
if(h[i - 1] >= j)continue;///如果是高度不超过前一列的位置 量已经确定了
if(j > 1)(dp[i][j] += (LL)dp[i - 1][0] * (pow_(2,w[j] - w[j - 1]) - 1) % MOD * 2 % MOD * pow_(2,w[h[i]] - w[j]) % MOD) %= MOD;
else (dp[i][1] += (LL)dp[i - 1][0] * (pow_(2,w[1]) - 2) % MOD * pow_(2,w[h[i]] - w[1]) % MOD) %= MOD;///上一列中无重复的乘上化不超过上一列高度中有重复的
}
}
int ans = 0;
for(int i = 0;i <= m;i++)
(ans += dp[n][i]) %= MOD;
printf("%d",ans);
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
#define mod 998244353
#define MOD 1000000007
#define inf 0x3f3f3f3f
#define linf 0x3f3f3f3f3f3f3f3fll
typedef long long ll;
typedef pair<int,int> pii;
typedef unsigned long long ull;
int h[110];
int n;
inline ll quickpow(ll base,int ind)
{
ll ans=1;
while(ind>0)
{
if(ind&1)ans=ans*base%MOD;
ind>>=1;
base=base*base%MOD;
}
return ans;
}
pair<ll,ll> solve(int l,int r)
{
int minval=inf;
for(int i=l;i<=r;i++)
minval=min(minval,h[i]);
// cout<<l<<" "<<r<<" "<<minval<<endl;
int st=l;
ll cross=2,all=1;
for(int i=l;i<=r+1;i++)
if(i>r||h[i]==minval)
{
if(i>st)
{
for(int j=st;j<i;j++)
h[j]-=minval;
pair<ll,ll> tmp=solve(st,i-1);
cross=cross*tmp.first%MOD;
all=all*(tmp.first+tmp.second)%MOD;
}
st=i+1;
if(i<=r)all=all*2%MOD;
}
all=(all-cross+MOD)%MOD;
cross=cross*quickpow(2,minval-1)%MOD;
all=(all+cross)%MOD;
// cout<<cross<<" "<<all<<endl;
return make_pair(cross,all);
}
int main()
{
scanf("%d",&n);
for(int i=0;i<n;i++)
{
scanf("%d",&h[i]);
}
printf("%lld\n",solve(0,n-1).second);
return 0;
} |
#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
const int MOD=1e9+7;
inline int mul(int a,int b)
{return 1LL*a*b%MOD;}
inline int add(int a,int b)
{a+=b;return a>=MOD?a-MOD:a;}
inline int sub(int a,int b)
{a-=b;return a<0?a+MOD:a;}
int p2(int b)
{
int a=2,ans=1;
for(;b;b>>=1,a=mul(a,a))
if(b&1)ans=mul(ans,a);
return ans;
}
const int Q=1<<8;
int cmp[Q],a[Q];
struct dt{
int f,g;
dt(){}
dt(int mus,int no)
{f=mus,g=no;}
};
dt Gans(int l,int r,int lim)
{
int mn=MOD,ct=0;
for(int i=l;i<=r;i++)
if(a[i]==mn)++ct;
else if(a[i]<mn)ct=1,mn=a[i];
if(ct==r-l+1)return dt(sub(p2(ct),2),p2(mn-lim));
int p0=1,p1=1;
for(int lst=0,i=l;i<=r+1;i++)
if(lst&&(a[i]==mn||i>r)){
dt now=Gans(lst,i-1,mn);
lst=0;
p0=mul(p0,add(now.f,mul(now.g,2)));
p1=mul(p1,now.g);
}
else if((!lst)&&a[i]>mn)lst=i;
p0=sub(p0,p1);
return dt(add(mul(p0,p2(ct)),mul(p1,sub(p2(ct),2))),mul(p1,p2(mn-lim)));
}
int main()
{
int n;
scanf("%d",&n);
for(int i=1;i<=n;i++)
scanf("%d",&a[i]);
dt als=Gans(1,n,0);
printf("%d",add(als.f,als.g));
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int mod=1e9+7;
const int inf=1e9+9;
int powmod(int x, int k){ int ret=1;for(;k;k>>=1,x=(ll)x*x%mod) if(k&1) ret=(ll)ret*x%mod;return ret;}
pair<int,int> Solve(vector<int> a)
{
int mn=inf;
for(int i:a) mn=min(mn,i);
int cnt=0;
for(int i:a) cnt+=i==mn;
int all=powmod(2,cnt);
int only=2;
vector<int> tmp;
for(int i:a)
{
if(i==mn && tmp.size())
{
pair<int,int> ans=Solve(tmp);
tmp.clear();
all=(ll)all*((ans.first+ans.second)%mod)%mod;
only=(ll)only*ans.second%mod;
}
if(i!=mn) tmp.push_back(i-mn);
}
if(tmp.size())
{
pair<int,int> ans=Solve(tmp);
tmp.clear();
all=(ll)all*((ans.first+ans.second)%mod)%mod;
only=(ll)only*ans.second%mod;
}
all-=only;
if(all<0) all+=mod;
only=(ll)only*powmod(2,mn-1)%mod;
all+=only;
if(all>=mod) all-=mod;
return make_pair(all,only);
}
int main()
{
int n,i;
scanf("%i",&n);
vector<int> a(n);
for(i=0;i<n;i++) scanf("%i",&a[i]);
printf("%i\n",Solve(a).first);
return 0;
} |
#include <bits/stdc++.h>
#define EB emplace_back
typedef long long ll;
typedef std::pair <int, int> pr;
typedef std::vector <int> vector;
const int mod = 1000000007, pmod = mod - 1;
inline void add(int &x, const int y) {x += y - mod, x += x >> 31 & mod;}
inline void sub(int &x, const int y) {x -= y, x += x >> 31 & mod;}
ll PowerMod(ll a, int n, ll c = 1) {for (n += n >> 31 & pmod; n; n >>= 1, a = a * a % mod) if (n & 1) c = c * a % mod; return c;}
pr solve(const vector &h) {
int i, j = -1, n = h.size(), x, y = 0, P1 = 1, P2 = 1, C1, C2, W = n;
vector S; x = *std::min_element(h.begin(), h.end());
for (i = 0; i <= n; ++i)
if (i == n || h[i] == x) {
if (j + 1 == i) ++j;
else if (j + 2 == i) ++j, P1 = PowerMod(2, h[j] - x, P1), P2 = PowerMod(2, h[j] - x, P2), ++j;
else {
W -= i - j - 1, S.clear(), S.reserve(i - j - 1);
for (++y; ++j < i; S.EB(h[j] - x));
std::tie(C1, C2) = solve(S), P1 = (ll)P1 * (C1 + C2) % mod, P2 = (ll)P2 * C2 % mod;
}
}
C2 = PowerMod(2, x, P2), C1 = PowerMod(2, W, P1), sub(C1, P2), sub(C1, P2);
return add(C1, C2), pr(C1, C2);
}
int main() {
int i, n, x; vector h;
scanf("%d", &n), h.reserve(n);
for (i = 0; i < n; ++i) scanf("%d", &x), h.EB(x);
printf("%d\n", solve(h).first);
return 0;
} |
#include<bits/stdc++.h>
using namespace std;
long long n,h[105],dp[105],tmp,mod=1000*1000*1000+7,pre[105],l,r,omega,dest,prog;
deque<pair<long long,int> > v;
long long fastp(long long base,int exp){
if(exp==0)return 1;
long long val=fastp(base,exp/2);
val=(val*val)%mod;
if(exp%2)val*=base;
return val%mod;
}
int main(){
cin>>n;
for(int i=1;i<=n;i++)cin>>h[i];
dp[n+1]=1;
pre[0]=1;
for(int i=1;i<=n;i++){
pre[i]=pre[i-1]*fastp(2,max(0ll,h[i]-h[i-1]));
pre[i]%=mod;
}
for(int i=n;i>0;i--){
tmp=2*dp[i+1];
v.clear();
v.push_back({2,n+1});
for(int j=n;j>=i;j--){
while(v.size()>0 && v.back().first>=h[j]+1)v.pop_back();
v.push_back({h[j]+1,j});
}
while(v.size()>1 && v[1].first<=h[i-1])v.pop_front();
v[0].first=max(v[0].first,h[i-1]+1);
for(int j=0;j<v.size()-1;j++){
l=v[j].first;
r=v[j+1].first-1;
if(l>r)continue;
dest=v[j].second;
omega=(pre[dest-1]*fastp(pre[i],mod-2))%mod;
prog=(fastp(2,h[i]-l)*(2-fastp(fastp(2,r-l),mod-2)))%mod;
prog+=mod;
prog%=mod;
tmp+=((2ll*omega*prog)%mod*dp[dest])%mod;
tmp%=mod;
}
dp[i]=tmp%mod;
}
cout<<(dp[1]%mod+mod)%mod<<endl;
return 0;
}
|
#include<bits/stdc++.h>
#define maxn 123456
#define F first
#define S second
#define M 1000000007
using namespace std;
typedef long long ll;
ll a[maxn],s[maxn],dp[105][105],n,b[maxn],ans,m;
set <ll> f;
ll pow_(ll x,ll y){
ll rt=1;
while (y){
if (y&1) rt=rt*x%M;
x=x*x%M; y>>=1;
}
return rt;
}
int main(){
cin >> n;
for (int i=1;i<=n;i++) cin >> a[i];
for (int i=1;i<=n;i++) {
if (f.find(a[i])==f.end()) f.insert(a[i]),b[++m]=a[i];
}
sort(b+1,b+m+1);
for (int i=1;i<=n;i++) for (int j=1;j<=m;j++) if (a[i]==b[j]) s[i]=j;
dp[0][0]=1;
for (int i=0;i<n;i++){
for (int j=1;j<=s[i];j++){
if (j<=s[i+1]) (dp[i+1][j]+=dp[i][j]*pow_(2ll,max(b[s[i+1]]-b[s[i]],0ll)))%=M;
else (dp[i+1][0]+=dp[i][j]*2)%=M;
}
(dp[i+1][0]+=dp[i][0]*2)%=M;
if (s[i+1]>s[i]){
for (int j=s[i]+1;j<=s[i+1];j++) (dp[i+1][j]+=dp[i][0]*(pow_(2ll,b[j]-b[j-1]-(j==1))-1)*2%M*pow_(2ll,b[s[i+1]]-b[j]))%=M;
}
}
for (int i=0;i<=s[n];i++) (ans+=dp[n][i])%=M;
cout << (ans+M)%M << endl;
}
|
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i,n) for(int i=0;i<(n);i++)
#define pb push_back
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second
typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;
template<typename A,typename B>inline void chmin(A &a,B b){if(a>b)a=b;}
template<typename A,typename B>inline void chmax(A &a,B b){if(a<b)a=b;}
const int mod=1000000007;
inline void add(int &a,int b){
a+=b;
if(a>=mod)a-=mod;
}
int mpow(int a,int b){
int ret=1;
while(b){
if(b&1)ret=ret*a%mod;
a=a*a%mod;
b>>=1;
}
return ret;
}
int N;
int H[111];
int dp[111][111],dp2[111][111];
void solve(int l,int r,int b){
int &ret=dp[l][r];
int &ret2=dp2[l][r];
if(ret!=-1)return;
int bb=*min_element(H+l,H+r);
if(*max_element(H+l,H+r)==bb){
ret=(mpow(2,r-l)-2+mod)%mod;
ret2=mpow(2,bb-b);
return;
}
vpint lis;
int cur=l;
while(cur<r){
if(H[cur]==bb){
cur++;
continue;
}
int nex=cur;
while(nex<r&&H[nex]>bb)nex++;
lis.pb({cur,nex});
solve(cur,nex,bb);
cur=nex;
}
int num=count(H+l,H+r,bb);
int x=mpow(2,num);
ret2=2;
for(auto &p:lis){
x=x*(dp[p.fi][p.se]+dp2[p.fi][p.se]*2)%mod;
ret2=ret2*dp2[p.fi][p.se]%mod;
}
ret=(x-ret2+mod)%mod;
ret2=ret2*mpow(2,bb-b-1)%mod;
}
signed main(){
cin>>N;
rep(i,N)cin>>H[i];
memset(dp,-1,sizeof(dp));
solve(0,N,0);
cout<<(dp[0][N]+dp2[0][N])%mod<<endl;
return 0;
}
|
#include<bits/stdc++.h>
#define to edge[i].v
#define mp make_pair
#define rint register int
#define debug(x) cerr<<#x<<"="<<x<<endl
#define fgx cerr<<"-------------"<<endl
#define N 1000
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const int mod=1e9+7;
int a[N],b[N],h[N],f[N][N];
inline int qpow(int y,int x=2){int A=1;for(;y;y>>=1,x=(ll)x*x%mod)if(y&1)A=(ll)A*x%mod;return A;}
int main()
{ int n,ans=0; cin>>n;
for(rint i=1;i<=n;i++) scanf("%d",&h[i]),b[i]=h[i];
sort(b+1,b+n+1); int l=unique(b+1,b+n+1)-b-1;
for(rint i=1;i<=n;i++) a[i]=lower_bound(b+1,b+l+1,h[i])-b;
f[0][0]=1;
for(rint i=1;i<=n;i++)
{ f[i][0]=f[i-1][0]*2%mod;
for(rint j=a[i]+1;j<=a[i-1];j++) (f[i][0]+=2*f[i-1][j]%mod)%=mod;
for(rint j=1;j<=a[i];j++)
{ f[i][j]=(ll)f[i-1][j]*qpow(max(0,b[a[i]]-b[a[i-1]]))%mod;
if(j>a[i-1])
(f[i][j]+=((j!=1)+1LL)*f[i-1][0]%mod*qpow(b[a[i]]-b[j])%mod*(qpow(b[j]-b[j-1])-1-(j==1))%mod)%=mod;
}
}
for(rint i=0;i<=a[n];i++) (ans+=f[n][i])%=mod;
cout<<ans;
return 0;
}
|
#include <cstdio>
#include <cstring>
#include <algorithm>
#define P 1000000007
using namespace std;
typedef long long ll;
ll h[111], Mn[111][111], Sm[111][111], SS[111][111], n, F[111];
ll powmod(ll x, ll y = P - 2, ll p = P) {
ll ans = 1;
while(y) {
if(y & 1) ans = ans * x % p;
x = x * x % p;
y >>= 1;
}
return ans;
}
int main() {
scanf("%lld", &n);
for(int i = 1; i <= n; i++) scanf("%lld", &h[i]);
h[0] = (h[n + 1] = 1);
for(int i = 1; i <= n; i++) {
Mn[i][i] = h[i], Sm[i][i] = h[i], SS[i][i] = h[i];
for(int j = i + 1; j <= n; j++) Mn[i][j] = min(Mn[i][j - 1], h[j]), Sm[i][j] = Sm[i][j - 1] + h[j], SS[i][j] = SS[i][j - 1] + max(h[j] - h[j - 1], 0ll);
}
F[0] = 1;
for(int i = 1; i <= n; i++) {
F[i] = F[i - 1] * 2 % P;
for(int j = 1; j <= i; j++) {
int r = Mn[j][i], l = max(h[i + 1], h[j - 1]) + 1;
if(l <= r) F[i] = (F[i] + 2 * F[j - 1] * (powmod(2, SS[j][i] - l + 1) - powmod(2, SS[j][i] - r))) % P;
}
}
printf("%lld\n", (F[n] % P + P) % P);
return 0;
}
|
#include<bits/stdc++.h>
#define ll long long
#define INF 2e9
#define mo 1000000007
using namespace std;
struct Info{ll p1,p2;};
int a[1010],n;
ll po(ll x,ll y){ll z=1;while (y){if (y%2==1)z=(x*z)%mo;x=(x*x)%mo;y/=2;}return z;}
Info work(int l,int r,int x){
int mi=INF;
Info z,y;
ll c1=1,c2=1,c3=0;
for(int i=l;i<=r;i++)mi=min(mi,a[i]);
for(int i=l;i<=r;i++)if(a[i]==mi)c3++;
for(int i=l,j;i<=r;i=j+1){
j=i;
if (a[i]>mi){while (a[j+1]>mi)j++;y=work(i,j,mi);c1=c1*y.p1%mo,c2=c2*(y.p1+y.p2)%mo;}
}
z.p1=c1*po(2,mi-x)%mo;
z.p2=(c2*po(2,c3)+c1*(po(2,mi-x)-2+mo))%mo;
return z;
}
int main(){
scanf("%d",&n);
for (int i=1;i<=n;i++) scanf("%d",&a[i]);
cout<<work(1,n,0).p2<<endl;
return 0;
} |
#include <bits/stdc++.h>
//#include <windows.h>
using namespace std;
typedef long long LL;
const int mod = 1e9 + 7, MAX = 110;
int n, h[MAX], pw[MAX];
inline int add(int a, int b) {
return a + b >= mod ? a + b - mod : a + b;
}
inline int sub(int a, int b) {
return a >= b ? a - b : a - b + mod;
}
inline int mul(int a, int b) {
return LL(a) * b % mod;
}
int pm(int a, LL b) {
if (b == 0) return 1;
if (b & 1) return mul(a, pm(a, b - 1));
return pm(mul(a, a), b / 2);
}
pair<int, int> solve(int a, int b, int s) {
if (b - a == 1) {
int w = pm(2, h[a] - s);
return make_pair(w, w);
}
int m = *min_element(h + a, h + b);
vector <pair<int, int> > v;
int i = a;
while (i < b) {
int j = i;
while (j < b && (h[i] == m) == (h[j] == m))
j ++;
v.push_back(make_pair(i, j));
i = j;
}
int fT = 1, fA = 2;
for (int i = 0; i < v.size(); i ++) {
pair<int, int> p = v[i];
int x = p.first, y = p.second;
if (h[x] != m) {
pair <int,int> g = solve(x, y, m);
fT = mul(fT, add(g.first, g.second));
fA = mul(fA, g.first);
} else {
fT = mul(fT, pw[y - x]);
}
}
fT = sub(fT, fA);
fA = mul(fA, pm(2, m - s - 1));
fT = add(fT, fA);
return make_pair(fA, fT);
}
int main(void) {
cin >> n;
//DWORD start_time = GetTickCount();
for (int i = 0; i < n; i ++)
cin >> h[i];
pw[0] = 1;
for (int i = 0; i < n; i ++)
pw[i + 1] = mul(pw[i], 2);
pair <int, int> g = solve(0, n, 0);
cout << g.second << endl;
//DWORD end_time = GetTickCount();
//cout << "Time costed : " << (end_time - start_time) << ".ms" << endl;
return 0;
} |
#include<bits/stdc++.h>
#define mod 1000000007
using namespace std;
int n,dp[105][105],ans;
int h[105],H[105],hi[105],cnt,r[105];
int ksm(int x,int y){
int res=1;
while(y){
if(y&1) res=1ll*res*x%mod;
x=1ll*x*x%mod,y/=2;
}
return res;
}
int main(){
scanf("%d",&n);
for(int i=1;i<=n;i++) scanf("%d",&h[i]),hi[i]=h[i];
sort(hi+1,hi+n+1);
for(int i=1;i<=n;i++) if(hi[i]!=hi[i-1]) H[++cnt]=hi[i];
for(int i=1;i<=n;i++) r[i]=lower_bound(H+1,H+cnt+1,h[i])-H;
for(int j=0;j<r[1];j++){
int i=1;
if(j) dp[i][j]=2ll*(ksm(2,H[j+1]-H[j])-1)*ksm(2,h[1]-H[j+1])%mod;
else dp[i][j]=1ll*(ksm(2,H[j+1]-H[j])-2)*ksm(2,h[1]-H[j+1])%mod;
}
dp[1][r[1]]=2;
for(int i=2;i<=n;i++){
if(h[i]<=h[i-1]){
for(int j=0;j<r[i];j++) dp[i][j]=dp[i-1][j];
for(int j=r[i];j<=r[i-1];j++) (dp[i][r[i]]+=2ll*dp[i-1][j]%mod)%=mod;
}
else{
for(int j=0;j<r[i-1];j++) dp[i][j]=1ll*dp[i-1][j]*ksm(2,h[i]-h[i-1])%mod;
int S=2ll*dp[i-1][r[i-1]]%mod;
for(int j=r[i-1];j<r[i];j++) dp[i][j]=1ll*S*(ksm(2,H[j+1]-H[j])-1)%mod*ksm(2,h[i]-H[j+1])%mod;
dp[i][r[i]]=S;
}
}
for(int i=0;i<=r[n];i++) (ans+=dp[n][i])%=mod;
printf("%d\n",ans);
return 0;
} |
#include <bits/stdc++.h>
#define rep(i, a, n) for(int i = a; i < n; i++)
#define int long long
using namespace std;
typedef pair<int, int> P;
const int INF = 1e15;
const int mod = 1e9 + 7;
int n;
int h[105];
long long mod_pow(long long x, long long n){
if(n == 0) return 1;
long long res = mod_pow(x*x % mod, n / 2);
if(n & 1) res = res*x % mod;
return res;
}
P calc(int L, int R, int v){
int dp1 = 1, dp2 = 1;
if(L > R) return {-1, -1};
int MIN = INF;
rep(i, L, R + 1) MIN = min(MIN, h[i]);
int w = R - L + 1;
rep(i, L, R + 1) if(MIN != h[i]) w--;
int pre = L - 1;
rep(i, L, R + 1){
if(MIN == h[i]){
P p = calc(pre + 1, i - 1, MIN);
if(p.first >= 0){
(dp1 *= p.first) %= mod;
(dp2 *= p.first + p.second) %= mod;
}
pre = i;
}
}
P p = calc(pre + 1, R, MIN);
if(p.first >= 0){
(dp1 *= p.first) %= mod;
(dp2 *= p.first + p.second) %= mod;
}
(dp2 = dp2 * mod_pow(2, w) + (mod_pow(2, MIN - v) + mod - 2) * dp1) %= mod;
(dp1 *= mod_pow(2, MIN - v)) %= mod;
return {dp1, dp2};
}
signed main(){
cin >> n;
rep(i, 1, n + 1) cin >> h[i];
cout << calc(1, n, 0).second << endl;
} |
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
#define pll pair <ll , ll>
#define pb push_back
#define pf push_front
#define pob pop_back
#define pof pop_front
#define mp make_pair
#define X first
#define Y second
#define LB(x) ((x) & -(x))
#define BIT(a , b) (((a)>>(b)) & 1)
const ll MAXN=1e2+10;
const ll Mod=1e9+7;
const ll INF=1e9+10;
ll a[MAXN];
ll pw(ll x , ll n)
{
if (n==0)
{
return 1;
}
ll w=pw(x , n/2);
w*=w;
w%=Mod;
if (n&1)
{
w*=x;
w%=Mod;
}
return w;
}
pll solve(ll l , ll r)
{
if (l>r)
{
return mp(1 , 1);
}
ll res=0 , t=1 , w=1 , d=0 , e=INF;
for(ll i=l;i<=r;i++)
{
e=min(e , a[i]);
}
ll z=l;
for(ll i=l;i<=r;i++)
{
a[i]-=e;
if (a[i]==0)
{
pll f=solve(z , i-1);
t*=f.Y;
t%=Mod;
w*=f.X;
w%=Mod;
d++;
z=i+1;
}
}
pll f=solve(z , r);
t*=f.Y;
t%=Mod;
w*=f.X;
w%=Mod;
res+=(pw(2 , d)*w)%Mod;
res%=Mod;
res+=(pw(2 , e)*t)%Mod;
res%=Mod;
res+=(t*((pw(2 , e)-2+Mod)%Mod))%Mod;
res%=Mod;
return mp(res , (pw(2 , e)*t)%Mod);
}
int main()
{
ios_base :: sync_with_stdio(false);
cin.tie(0);
ll n;
cin>>n;
for(ll i=1;i<=n;i++)
{
cin>>a[i];
}
pll res=solve(1 , n);
cout<<(res.X-res.Y+Mod)%Mod;
}
|
// Ala be zekrellah tatmaenolgholoob ...
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
#define F first
#define S second
#define MP make_pair
const int maxn = 100+9;
const ll mod = 1e9+7;
set <int> st;
map <int,int> mp;
ll dp[maxn][maxn];
int h[maxn], val[maxn], len[maxn];
ll cal (ll x, ll p) {
if (p == 0)
return 1;
ll res = cal(x, p / 2);
res = (res * res) % mod;
if (p % 2)
res = res * x % mod;
return res;
}
int main () {
ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
int n, num = 1;
cin >> n;
for (int i = 0; i < n; i++) {
cin >> h[i];
st.insert(h[i]);
}
int last = 0;
for (auto x : st) {
val[num] = x;
len[num] = x - last;
mp[x] = num;
num++;
last = x;
}
// base
dp[0][0] = 2;
for (int i = 1; i <= mp[h[0]]; i++) {
if (val[i] == 1)
continue;
ll cur = cal(2, h[0] - val[i] + 1) * (cal(2, len[i]) - 1) % mod;
if (i == 1)
cur = cal(2, h[0] - val[i]) * (cal(2, len[i]) - 2) % mod;
cur = (cur + mod) % mod;
dp[0][i] = cur;
}
for (int i = 1; i < n; i++) {
// dp[i][0]
dp[i][0] = dp[i - 1][0] * 2 % mod;
for (int t = mp[h[i]] + 1; t < maxn; t++)
dp[i][0] = (dp[i][0] + dp[i - 1][t] * 2 % mod) % mod;
// dp[i][a]
for (int t = 1; t <= mp[h[i]]; t++)
dp[i][t] = dp[i - 1][t] * cal(2, max(h[i] - h[i - 1], 0)) % mod;
if (h[i] <= h[i - 1])
continue;
ll f = dp[i - 1][0];
for (int t = mp[h[i - 1]] + 1; t <= mp[h[i]]; t++)
dp[i][t] = f * cal(2, h[i] - val[t] + 1) % mod * (cal(2, len[t]) - 1) % mod;
}
// ans
ll res = 0;
for (int i = 0; i < maxn; i++)
res = (res + dp[n - 1][i]) % mod;
cout << res << "\n";
}
|
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<algorithm>
#define ll long long
using namespace std;
const int maxn=1010, inf=1e9, mod=1e9+7;
int n, N;
int h[maxn], b[maxn], f[maxn][maxn];
template<typename T>
inline void read(T &k)
{
int f=1; k=0; char c=getchar();
while(c<'0' || c>'9') c=='-'&&(f=-1), c=getchar();
while(c<='9' && c>='0') k=k*10+c-'0', c=getchar();
k*=f;
}
inline int power(int a, int b)
{
if(b<0) return 1;
int ans=1;
for(;b;b>>=1, a=1ll*a*a%mod)
if(b&1) ans=1ll*a*ans%mod;
return ans;
}
int main()
{
read(n);
for(int i=1;i<=n;i++) read(h[i]), b[++N]=h[i];
sort(b+1, b+1+N); N=unique(b+1, b+1+N)-b-1;
for(int i=1;i<=n;i++) h[i]=lower_bound(b+1, b+1+N, h[i])-b;
f[0][0]=1;
for(int i=1;i<=n;i++)
{
f[i][0]=2ll*f[i-1][0]%mod;
for(int j=h[i]+1;j<=h[i-1];j++) f[i][0]=(f[i][0]+2ll*f[i-1][j])%mod;
int sj=min(h[i], h[i-1]);
for(int j=1;j<=sj;j++)
f[i][j]=1ll*f[i-1][j]*power(2, b[h[i]]-b[h[i-1]])%mod;
for(int j=h[i-1]+1;j<=h[i];j++)
if(j>1) f[i][j]=(f[i][j]+1ll*f[i-1][0]*(power(2, b[j]-b[j-1])-1+mod)*2%mod*power(2, b[h[i]]-b[j]))%mod;
else f[i][j]=(f[i][j]+1ll*f[i-1][0]*(power(2, b[j]-1)-1)*2%mod*power(2, b[h[i]]-b[j]))%mod;
}
int ans=0;
for(int i=0;i<=N;i++) ans=(ans+f[n][i])%mod;
printf("%d\n", ans);
} |
#include<iostream>
#define int long long
using namespace std;
const int N=102;
const int mod=1e9+7;
int ar[N];
int binpow(int x,int y){
int tich=1;
while(y){
if(y&1){
tich*=x;
tich%=mod;
}
x*=x;
x%=mod;
y>>=1;
}
return tich;
}
pair<int,int> solve(int l,int r){
// cout<<l<<' '<<r<<endl;
int i,dem=0,num1=1,num2=1,min1=mod,lst=l;
pair<int,int> tmp;
for(i=l;i<=r;i++){
min1=min(min1,ar[i]);
}
for(i=l;i<=r;i++){
ar[i]-=min1;
}
for(i=l;i<=r;i++){
if(!ar[i]){
dem++;
if(lst!=i){
tmp=solve(lst,i-1);
num1*=tmp.first;
num1%=mod;
num2*=(tmp.first+tmp.second);
num2%=mod;
}
lst=i+1;
}
// dem++;
}
if(lst!=r+1&&lst!=l){
tmp=solve(lst,r);
num1*=tmp.first;
num1%=mod;
num2*=(tmp.first+tmp.second);
num2%=mod;
}
num2=(binpow(2,dem)*num2+(binpow(2,min1)-2)*num1)%mod;
if(num2<0){
num2+=mod;
}
num1*=binpow(2,min1);
num1%=mod;
return {num1,num2};
}
signed main(){
ios::sync_with_stdio(0);
cin.tie(0);
int n,i,j,k,l;
cin>>n;
for(i=1;i<=n;i++){
cin>>ar[i];
}
cout<<solve(1,n).second;
}
|
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MAX_N = 123;
const ll MOD = 1e9 + 7;
ll sq(ll x) { return x * x % MOD; }
ll qpow(ll a, ll b) { return b ? sq(qpow(a, b / 2)) * (b & 1 ? a : 1) % MOD : 1; }
ll inv(ll x) { return qpow(x, MOD - 2); }
int N, H[MAX_N];
ll F[MAX_N];
int main() {
scanf("%d", &N);
for (int i = 1; i <= N; i++) scanf("%d", &H[i]);
H[0] = H[N + 1] = 1;
F[0] = 2;
for (int i = 1; i <= N; i++) {
ll sum = 0; int prev = H[i + 1];
for (int j = i; j; j--) {
int l = max(H[j - 1], prev), r = H[j];
if (r > l) {
sum += r - l;
}
prev = min(prev, H[j]);
(F[i] += F[j - 1] * qpow(2, sum)) %= MOD;
}
}
printf("%lld\n", F[N]);
}
|
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pll;
#define fi first
#define se second
const int maxn=105;
const int mod=1e9+7;
const int inf=0x3f3f3f3f;
int n,h[maxn];
inline ll fpow(ll a,ll b)
{
ll ret=1;
for(;b;b>>=1,a=a*a%mod)
if(b&1) ret=ret*a%mod;
return ret;
}
inline pll solve(int l,int r,int k)
{
int mn=inf,cnt=0;
for(int i=l;i<=r;i++)
if(h[i]<mn) mn=h[i],cnt=1;
else if(h[i]==mn) cnt++;
if(cnt==r-l+1) return pll(fpow(2,r-l+1)-2,fpow(2,mn-k));
int last=0; ll s0=1,s1=1; pll ret=pll(0,0);
for(int i=l;i<=r+1;i++)
if(!last && h[i]>mn) last=i;
else if((i>r || h[i]==mn) && last)
{
pll tmp=solve(last,i-1,mn);
(s0*=(tmp.fi+2*tmp.se))%=mod;
(s1*=tmp.se)%=mod;
last=0;
}
(s0-=s1)%=mod;
ret.fi=(s0*fpow(2,cnt)+s1*(fpow(2,cnt)-2))%mod;
ret.se=s1*fpow(2,mn-k)%mod;
return ret;
}
int main()
{
scanf("%d",&n);
for(int i=1;i<=n;i++) scanf("%d",&h[i]);
ll ans=1;
for(int i=1;i<=n;i++)
if(h[i]>h[i-1] && h[i]>h[i+1])
(ans*=fpow(2,h[i]-max(h[i-1],h[i+1])))%=mod,h[i]=max(h[i-1],h[i+1]);
pll ret=solve(1,n,0);
printf("%lld\n",(ans*(ret.fi+ret.se)%mod+mod)%mod);
return 0;
} |
#include <bits/stdc++.h>
#define ln '\n'
#define all(dat) dat.begin(), dat.end()
#define loop(i, to) for (int i = 0; i < to; ++i)
#define cont(i, to) for (int i = 1; i <= to; ++i)
#define circ(i, fr, to) for (int i = fr; i <= to; ++i)
#define foreach(i, dat) for (__typeof(dat.begin()) i = dat.begin(); i != dat.end(); ++i)
typedef long long num;
using namespace std;
const int nsz = 1e2, mod = 1e9 + 7;
int n, h[nsz + 5], dp[nsz + 5], f[nsz + 5][nsz + 5];
num inline qpow(num a, int p) {
num res = 1;
for (; p > 0; p >>= 1) {
if (p & 1) {
res *= a;
res %= mod;
}
a *= a;
a %= mod;
}
return res;
}
int main() {
ios_base::sync_with_stdio(0);
cin >> n;
cont (i, n) {
cin >> h[i];
}
dp[1] = qpow(2, h[1]);
cont (i, n) {
f[1][i] = 2 * qpow(2, h[1] - h[i]) % mod;
}
circ (i, 2, n) {
dp[i] = (dp[i - 1] + f[i - 1][i]) * qpow(2, h[i] - h[i - 1]) % mod;
cont (j, n) {
if (h[i] <= h[i - 1]) {
f[i][j] = h[i] > h[j] ? f[i - 1][j] : f[i - 1][i];
} else {
if (h[i] > h[j]) {
f[i][j] = f[i - 1][j] * qpow(2, h[i] - (h[j] > h[i - 1] ? h[j] : h[i - 1])) % mod;
} else {
f[i][j] = f[i - 1][j];
}
}
f[i][j] += f[i - 1][i] * qpow(2, h[i] - max(h[i - 1], h[j])) % mod;
f[i][j] %= mod;
}
}
cout << dp[n] << ln;
}
|
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
#define x first
#define y second
#define mp make_pair
#define pb push_back
template <typename TYPE> inline void chkmax(TYPE &x,TYPE y){x<y?x=y:0;}
template <typename TYPE> inline void chkmin(TYPE &x,TYPE y){y<x?x=y:0;}
template <typename TYPE> void readint(TYPE &x)
{
x=0;int f=1;char c;
for(c=getchar();!isdigit(c);c=getchar())if(c=='-')f=-1;
for(;isdigit(c);c=getchar())x=x*10+c-'0';
x*=f;
}
const int MAXN=105,MOD=1000000007;
int qmi(int x,int y)
{
int ans=1;
for(;y;y>>=1,x=1ll*x*x%MOD)
if(y&1)ans=1ll*ans*x%MOD;
return ans;
}
int n,a[MAXN],f[MAXN][MAXN],g[MAXN][MAXN];
void solve(int l,int r,int x)
{
int y=1<<30,las=l-1,w=0;
for(int i=l;i<=r;++i)chkmin(y,a[i]);
for(int i=l;i<=r;++i)if(a[i]==y)++w;
if(w==r-l+1)
{
f[l][r]=(1ll*qmi(2,y-x)+qmi(2,r-l+1)-2+MOD)%MOD;
g[l][r]=qmi(2,y-x);
return;
}
f[l][r]=qmi(2,w);
g[l][r]=1;
for(int i=l;i<=r+1;++i)
if(i>r || a[i]==y)
{
if(i-las>=2)
{
solve(las+1,i-1,y);
g[l][r]=1ll*g[l][r]*g[las+1][i-1]%MOD;
f[l][r]=1ll*f[l][r]*(g[las+1][i-1]+f[las+1][i-1])%MOD;
}
las=i;
}
f[l][r]=(f[l][r]+1ll*g[l][r]*(qmi(2,y-x)-2+MOD))%MOD;
g[l][r]=1ll*g[l][r]*qmi(2,y-x)%MOD;
//cerr<<l<<" "<<r<<":"<<f[l][r]<<" "<<g[l][r]<<endl;
}
int main()
{
#ifndef ONLINE_JUDGE
// freopen("code.in","r",stdin);
// freopen("code.out","w",stdout);
#endif
readint(n);
for(int i=1;i<=n;++i)readint(a[i]);
solve(1,n,0);
printf("%d\n",f[1][n]);
return 0;
} |
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn=1e2+10,mod=1e9+7;
int n,h[maxn],cnt;
int dp[maxn][2],l[maxn],r[maxn],a[maxn],b[maxn];
vector<int> ch[maxn];
void dfs(int pos){
b[pos]=*min_element(h+l[pos],h+r[pos]+1);
for(int i=l[pos],j;i<=r[pos];++i){
if(h[i]==b[pos])
continue;
j=i;
while(j<r[pos]&&h[j+1]>b[pos])
++j;
++cnt;
l[cnt]=i,r[cnt]=j,a[cnt]=b[pos];
ch[pos].push_back(cnt);
dfs(cnt);
i=j;
}
}
inline ll fpow(ll a,ll n){
ll res=1;
for(;n;n>>=1,a=a*a%mod)
if(n&1ll)
res=res*a%mod;
return res;
}
void solve(int pos){
if(ch[pos].empty()){
dp[pos][1]=fpow(2,b[pos]-a[pos]);
dp[pos][0]=(fpow(2,r[pos]-l[pos]+1)+mod-2)%mod;
return;
}
ll tmp[2],temp[2];
for(int i=l[pos],j=0;i<=r[pos];)
if(j<ch[pos].size()&&i==l[ch[pos][j]]){
solve(ch[pos][j]);
if(i==l[pos]){
tmp[0]=dp[ch[pos][j]][0];
tmp[1]=dp[ch[pos][j]][1]*2%mod;
}
else{
temp[0]=(tmp[0]*dp[ch[pos][j]][0]+tmp[0]*dp[ch[pos][j]][1]*2+tmp[1]*dp[ch[pos][j]][0]+tmp[1]*dp[ch[pos][j]][1])%mod;
temp[1]=tmp[1]*dp[ch[pos][j]][1]%mod;
tmp[0]=temp[0];
tmp[1]=temp[1];
}
i=r[ch[pos][j]]+1;
++j;
}
else{
if(i==l[pos]){
tmp[0]=0;
tmp[1]=2;
}
else{
temp[0]=(tmp[0]*2+tmp[1])%mod;
temp[1]=tmp[1];
tmp[0]=temp[0];
tmp[1]=temp[1];
}
++i;
}
dp[pos][0]=tmp[0];
dp[pos][1]=tmp[1]*fpow(2,b[pos]-a[pos]-1)%mod;
}
int main(){
cin>>n;
for(int i=1;i<=n;++i)
cin>>h[i];
++cnt;
l[1]=1,r[1]=n,a[1]=0;
dfs(1);
solve(1);
cout<<(dp[1][0]+dp[1][1])%mod<<endl;
return 0;
} |
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <math.h>
using namespace std;
typedef long long ll;
const int MAXN = 100 + 10;
const int Mod = 1e9 + 7;
int N;
int A[MAXN];
int f[MAXN];
inline int fastpow_mod(int a, ll b) {
int x = 1;
while(b) {
if(b & 1) x = 1ll * x * a % Mod;
a = 1ll * a * a % Mod; b >>= 1;
}
return x;
}
int main() {
register int i, j, k;
scanf("%d", &N);
for(i = 1; i <= N; ++i)
scanf("%d", A + i);
f[0] = 1;
A[N + 1] = 1;
for(i = 1; i <= N + 1; ++i) {
f[i] = f[i - 1] * 2 % Mod;
for(j = 1; j < i; ++j) {
int l = max(A[i], A[j - 1]), r = A[j] - 1;
ll s = 0;
for(k = j; k < i; ++k)
r = min(r, A[k] - 1), s += max(A[k + 1] - A[k], 0);
if(l <= r) {
int t1 = fastpow_mod(2, A[j] - r - 1);
int t2 = fastpow_mod(2, r - l + 1) - 1;
int t3 = fastpow_mod(2, s);
f[i] = (f[i] + 4ll * f[j - 1] * t1 % Mod * t2 % Mod * t3 % Mod) % Mod;
}
}
}
printf("%lld\n", 1ll * f[N + 1] * (Mod + 1) / 2 % Mod);
return 0;
} |
#include <utility>
#include <cstdio>
#define MOD 1000000007
typedef long long ll;
inline ll quick_pow(ll a, int n)
{
ll res = 1;
while (n)
{
if (n & 1)
res = res * a % MOD;
a = a * a % MOD;
n >>= 1;
}
return res;
}
int arr[105];
std::pair<ll, ll> work(int l, int r, int d)
{
int pos = l;
for (int i = l; i <= r; i++)
{
if (arr[i] < arr[pos])
pos = i;
}
ll val = quick_pow(2, arr[pos] - d);
if (l == r)
return {val, val};
if (pos == l)
{
auto res = work(l + 1, r, arr[pos]);
return {(2 * res.first + (val - 1) * res.second) % MOD, val * res.second % MOD};
}
if (pos == r)
{
auto res = work(l, r - 1, arr[pos]);
return {(2 * res.first + (val - 1) * res.second) % MOD, val * res.second % MOD};
}
auto x = work(l, pos - 1, arr[pos]), y = work(pos + 1, r, arr[pos]);
return {4 * x.first % MOD * y.first % MOD + (val - 1) * x.second % MOD * y.second % MOD
, val * x.second % MOD * y.second % MOD};
}
int main()
{
// freopen("AGC026-D.in", "r", stdin);
int n;
scanf("%d", &n);
for (int i = 0; i < n; i++)
{
scanf("%d", arr + i);
arr[i]--;
}
printf("%lld\n", work(0, n - 1, 0).first * 2 % MOD);
return 0;
}
|
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define mod 1000000007LL
ll f[110][2],bin[110];
int h[110],n,tt;
inline int rd()
{
int x=0;char ch=getchar();
for (;ch<'0'||ch>'9';ch=getchar());
for (;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0';
return x;
}
inline ll pls(const ll &x,const ll &y) { return (x+y<mod)?x+y:x+y-mod; }
inline ll mns(const ll &x,const ll &y) { return (x-y<0)?x-y+mod:x-y; }
inline ll ksm(ll x,ll y) { ll res=1;for (;y;y>>=1,x=x*x%mod) if (y&1) res=res*x%mod;return res; }
inline void pre_gao()
{
bin[0]=1;
for (int i=1;i<=n;i++) bin[i]=bin[i-1]*2%mod;
}
inline void solve(int l,int r)
{
int id=++tt,mn=h[l];
for (int i=l;i<=r;i++) mn=min(mn,h[i]);
ll g[110][2];
memset(g,0,sizeof(g));
g[l-1][0]=0;g[l-1][1]=2;
for (int i=l;i<=r;i++)
{
if (h[i]==mn)
{
g[i][0]=pls(g[i-1][0]*2%mod,(i==l)?0:g[i-1][1]);
g[i][1]=g[i-1][1];
}
else
{
int j=i;
for (;j<=r&&h[j]>mn;j++);j--;
for (int k=i;k<=j;k++) h[k]-=mn;
int now=tt+1;solve(i,j);
g[j][0]=pls(g[i-1][0]*pls(f[now][0],f[now][1]*2%mod)%mod,(i==l)?f[now][0]:g[i-1][1]*pls(f[now][0],f[now][1])%mod);
g[j][1]=g[i-1][1]*f[now][1]%mod;
i=j;
}
}
f[id][0]=g[r][0];f[id][1]=g[r][1]*ksm(2,mn-1)%mod;
}
int main()
{
n=rd();pre_gao();
for (int i=1;i<=n;i++) h[i]=rd();
solve(1,n);
printf("%lld\n",pls(f[1][0],f[1][1]));
return 0;
} |
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
typedef long long LL;
const int N=105;
const int MOD=1000000007;
int n,f[N][N],h[N],w[N],m;
int ksm(int x,int y)
{
if (y<0) return 1;
int ans=1;
while (y)
{
if (y&1) ans=(LL)ans*x%MOD;
x=(LL)x*x%MOD;y>>=1;
}
return ans;
}
int main()
{
scanf("%d",&n);
for (int i=1;i<=n;i++) scanf("%d",&h[i]),w[++m]=h[i];
std::sort(w+1,w+m+1);
m=std::unique(w+1,w+m+1)-w-1;
for (int i=1;i<=n;i++) h[i]=std::lower_bound(w+1,w+m+1,h[i])-w;
f[0][0]=1;
for (int i=1;i<=n;i++)
{
for (int j=h[i]+1;j<=h[i-1];j++) (f[i][0]+=f[i-1][j]*2%MOD)%=MOD;
(f[i][0]+=f[i-1][0]*2%MOD)%=MOD;
for (int j=1;j<=h[i];j++)
{
f[i][j]=(LL)f[i-1][j]*ksm(2,w[h[i]]-w[h[i-1]])%MOD;
if (h[i-1]>=j) continue;
if (j>1) (f[i][j]+=(LL)f[i-1][0]*(ksm(2,w[j]-w[j-1])-1)%MOD*2%MOD*ksm(2,w[h[i]]-w[j])%MOD)%=MOD;
else (f[i][j]+=(LL)f[i-1][0]*(ksm(2,w[j])-2)%MOD*ksm(2,w[h[i]]-w[j])%MOD)%=MOD;
}
}
int ans=0;
for (int i=0;i<=m;i++) (ans+=f[n][i])%=MOD;
printf("%d",ans);
return 0;
return 0;
} |
#include <bits/stdc++.h>
#define MOD 1000000007LL
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
ll mod_pow(ll x,ll n){
ll res=1;
while(n>0){
if(n&1LL)res=res*x%MOD;
x=x*x%MOD;
n>>=1;
}
return res;
}
ll h[105];
ll h_min[205];
ll h_dif[205];
int l[205],r[205];
int w[205];
int siz;
vector<int> G[205];
ll dp1[205],dp2[205];
void build(int lx,int rx){
l[siz]=lx;
r[siz]=rx;
h_min[siz]=h[lx];
w[siz]=rx-lx;
for(int i=lx;i<rx;i++){
h_min[siz]=min(h_min[siz],h[i]);
}
h_dif[siz]+=h_min[siz];
int par=siz;
int prv=lx;
for(int i=lx;i<rx;i++){
if(h[i]==h_min[par]){
if(i==prv){
prv++;
}else{
siz++;
G[par].push_back(siz);
h_dif[siz]-=h_min[par];
w[par]-=i-prv;
build(prv,i);
prv=i+1;
}
}
}
if(prv!=rx){
siz++;
G[par].push_back(siz);
h_dif[siz]-=h_min[par];
w[par]-=rx-prv;
build(prv,rx);
}
}
void solve(int v){
if(h_dif[v]==0)w[v]=0;
dp1[v]=1;
dp2[v]=1;
for(int i=0;i<G[v].size();i++){
solve(G[v][i]);
dp1[v]*=dp1[G[v][i]];
dp1[v]%=MOD;
dp2[v]*=(dp1[G[v][i]]+dp2[G[v][i]])%MOD;
dp2[v]%=MOD;
}
dp2[v]=dp2[v]*mod_pow(2,w[v])%MOD;
if(h_dif[v]>0)dp2[v]+=dp1[v]*(mod_pow(2,h_dif[v])-2)%MOD;
dp2[v]%=MOD;
if(dp2[v]<0)dp2[v]+=MOD;
dp1[v]*=mod_pow(2,h_dif[v]);
dp1[v]%=MOD;
}
int main(void){
int n;
scanf("%d",&n);
for(int i=0;i<n;i++){
scanf("%lld",&h[i]);
}
build(0,n);
solve(0);
printf("%lld\n",dp2[0]);
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
const int N=150,mo=1e9+7;
int fap(int a,int b){
if (b<=0) return 1;
int s=1;
for (; b; b>>=1,a=1ll*a*a%mo)
if (b&1) s=1ll*s*a%mo;
return s;
}
void cal(int &x,int y){
(x+=y)%=mo; return;
}
int n,h[N],a[N],f[N][N];
int main(){
cin>>n;
for (int i=1; i<=n; ++i)
cin>>h[i],a[i]=h[i];
int tmp=n;
sort(a+1,a+n+1);
tmp=unique(a+1,a+n+1)-a-1;
for (int i=1; i<=n; ++i)
h[i]=lower_bound(a+1,a+tmp+1,h[i])-a;
f[0][0]=1;
for (int i=1; i<=n; ++i){
f[i][0]=f[i-1][0]*2%mo;
for (int j=h[i]+1; j<=h[i-1]; ++j)
cal(f[i][0],f[i-1][j]*2%mo);
tmp=fap(2,a[h[i]]-a[h[i-1]]);
for (int j=min(h[i],h[i-1]); j; --j)
cal(f[i][j],1ll*tmp*f[i-1][j]%mo);
for (int j=h[i-1]+1; j<=h[i]; ++j){
if (j==1)
cal(f[i][j],1ll*f[i-1][0]*(fap(2,a[1])-2)%mo*fap(2,a[h[i]]-a[j])%mo);
else
cal(f[i][j],2ll*f[i-1][0]*(fap(2,a[j]-a[j-1])-1)%mo*fap(2,a[h[i]]-a[j])%mo);
}
}
int ans=0;
for (int i=0; i<=h[n]; ++i)
cal(ans,f[n][i]);
cout<<ans;
return 0;
}
|
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<cctype>
#include<iostream>
#include<string>
#include<sstream>
#include<set>
#include<map>
#include<vector>
#include<algorithm>
#include<queue>
#include<utility>
using namespace std;
#define i64 long long int
struct mod_arith {
int mod;
mod_arith() {
mod = 1000000007;
}
void set_mod(int _mod) { mod = _mod; }
int add(int x, int y) { return (x + y) % mod; }
int sub(int x, int y) { return (x - y + mod) % mod; }
int mul(int x, int y) { return (int)((long long int)x*y%mod); }
int pw(int x, i64 y) {
int r = 1;
while (1) {
if (y & 1)r = mul(r, x);
if (y >>= 1)x = mul(x, x);else
break;
}
return r;
}
};
mod_arith ma;
int dp[111],h[111];
int h2[111], m, n;
int main() {
scanf("%d", &n);
for (int i = 0; i < n; i++) {
scanf("%d", &h[i]);
h2[i] = h[i];
}
m = n + 1;
h2[n] = 1;
sort(h2, h2 + m);
m = unique(h2, h2 + m) - h2;
for (int i = 0; i < n; i++) {
h[i] = lower_bound(h2, h2 + m, h[i])-h2;
}
dp[0] = 1;
for (int i = 0; i < n; i++) {
for (int j = 1; i + j <= n; j++) {
i64 cur = 0;
for (int H = 0; H < m - 1; H++) {
int S = i, E = i + j;
while (1) {
for (; S < E && h[S] <= H; S++);
if (S == E)break;
int T = S;
for (;T < E && h[T] > H; T++);
bool flag = true;
if (S == i && (i > 0 && h[i - 1] > H))flag = false;
if (T == E && (E < n && h[E] > H))flag = false;
if (flag) {
cur += h2[H + 1] - h2[H];
}
S = T;
}
}
dp[i + j] = ma.add(dp[i + j], ma.mul(dp[i], ma.pw(2, cur)));
}
}
printf("%d\n", ma.mul(dp[n], 2));
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
void add(int &x,int y) {
x += y; if (x >= mod) x -= mod;
}
int mul(int x,int y) {
return (long long) x * y % mod;
}
int pw(int x,int y) {
int ret = 1;
while (y) {
if (y & 1) ret = mul(ret, x);
x = mul(x, x);
y >>= 1;
}
return ret;
}
pair<int,int> solve(vector<int> h) {
int n = h.size();
int mn = mod, cnt = 0;
for (int i = 0; i < n; ++i) {
if (mn > h[i]) {
mn = h[i], cnt = 0;
}
cnt += (h[i] == mn);
}
int l = 0, r = 0;
vector<pair<int,int>> vec;
while (l < n) {
vector<int> new_h;
while (l < n && h[l] == mn) l++;
r = l;
while (r < n && h[r] > mn) r++;
for (int i = l; i < r; ++i) new_h.push_back(h[i] - mn);
if (new_h.size()) vec.push_back(solve(new_h));
l = r;
}
pair<int,int> ret;
ret.first = pw(2, mn);
for (auto p : vec) ret.first = mul(ret.first, p.first);
ret.second = pw(2, cnt);
for (auto p : vec) ret.second = mul(ret.second, p.first + p.second);
int coef = pw(2, mn); add(coef, mod - 2);
for (auto p : vec) coef = mul(coef, p.first);
add(ret.second, coef);
return ret;
}
int main() {
ios_base::sync_with_stdio(false);
int n; cin >> n;
vector<int> h(n);
for (int i = 0; i < n; ++i) cin >> h[i];
cout << solve(h).second << '\n';
}
|
#include <bits/stdc++.h>
#define mod 1000000007
#define fir first
#define sec second
#define mp make_pair
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
inline int add(int x,int y){
x += y;if (x >= mod) x -= mod;
return x;
}
inline int sub(int x,int y){
x -= y;if (x < 0) x += mod;
return x;
}
inline int qpow(int x,int y){
int res = 1;
while (y){
if (y & 1) res = 1ll * res * x % mod;
x = 1ll * x * x % mod;
y >>= 1;
}
return res;
}
const int N = 1e5 + 10;
int n , h[N];
pii solve(int l,int r,int lim){//first not ababab second ababa
int minm = 0x3f3f3f3f , cntminm = 0 , block = 0;
for (int i = l;i <= r;i++){
if (h[i] < minm){
minm = h[i];
cntminm = 0;
}
if (h[i] == minm) cntminm++;
}
if (cntminm == r - l + 1){
// printf("%d %d %d [%d %d]\n",l,r,lim,qpow(2,r-l+1)-2,qpow(2,h[l]-lim));
return mp(qpow(2 , r - l + 1) - 2 , qpow(2 , h[l] - lim));
}
pii res = mp(1 , 1);
for (int i = l;i <= r;i++){
if (h[i] == minm) continue;
int j = i;while (j + 1 <= r && h[j + 1] != minm)j++;
pii tmp = solve(i , j , minm);
res.first = 1ll * res.first * add(tmp.first , 2ll * tmp.second % mod) % mod;
res.second = 1ll * res.second * tmp.second % mod;
block++;
i = j;
}
res.first = 1ll * qpow(2 , cntminm) * res.first % mod;
res.first = sub(res.first , 2ll * res.second % mod);
res.second = 1ll * qpow(2 , minm - lim) * res.second % mod;
// printf("%d %d %d %d %d\n",l,r,lim,res.fir,res.sec);
return res;
}
int main() {
cin >> n;
for (int i = 1;i <= n;i++) cin >> h[i];
pii res = solve(1 , n , 0);
cout<<add(res.first,res.second);
return 0;
} |
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=105,p=1000000007;
int read(){
int f=1,g=0;
char ch=getchar();
for (;!isdigit(ch);ch=getchar()) if (ch=='-') f=-1;
for (;isdigit(ch);ch=getchar()) g=g*10+ch-'0';
return f*g;
}
int qpow(int x,int k){
int t=1;
for (;k;k>>=1){
if (k&1) t=(ll)t*x%p;
x=(ll)x*x%p;
}
return t;
}
int n,m,K,a[N];
void check(int &x,int y){if ((x+=y)>=p) x-=p;}
typedef pair<int,int> pr;
pr work(int dep,int l,int r){
int d=0x3f3f3f3f,las=l;
pr ans=make_pair(2,1);
for (int i=l;i<=r;i++) d=min(d,a[i]);
for (int i=l;i<=r;i++)
if (a[i]==d) {
check(ans.second,ans.second);
if (las<i){
pr t=work(d+1,las,i-1);
ans.first=(ll)ans.first*t.first%p;
ans.second=(ll)ans.second*(t.second+t.first)%p;
}
las=i+1;
}
if (las<=r){
pr t=work(d+1,las,r);
ans.first=(ll)ans.first*t.first%p;
ans.second=(ll)ans.second*(t.second+t.first)%p;
}
check(ans.second,p-ans.first);
ans.first=(ll)ans.first*qpow(2,d-dep)%p;
check(ans.second,ans.first);
return ans;
}
int main(){
n=read();
for (int i=1;i<=n;i++) a[i]=read();
printf("%d\n",work(1,1,n).second);
return 0;
} |
#include <bits/stdc++.h>
#define For(i, j, k) for (int i = j; i <= k; i++)
using namespace std;
const int N = 110;
const int Mod = 1e9 + 7;
int h[N], fa[N], n;
int dp[N][2];
int find(int x) {
return x == fa[x] ? x : fa[x] = find(fa[x]);
}
int Pow(int x, int e) {
int ret = 1;
while (e) {
if (e & 1) ret = 1ll * ret * x % Mod;
x = 1ll * x * x % Mod;
e >>= 1;
}
return ret;
}
int rk[N];
bool cmp(int x, int y) {
return h[x] > h[y];
}
bool vis[N];
int main() {
scanf("%d", &n);
For(i, 1, n) scanf("%d", &h[i]), fa[i] = i, rk[i] = i;
sort(rk + 1, rk + n + 1, cmp);
For(i, 1, n) {
int x = rk[i], u = 0, v = 0;
vis[x] = true;
if (vis[x - 1]) u = find(x - 1), dp[u][0] = 1ll * dp[u][0] * Pow(2, h[u] - h[x]) % Mod, fa[u] = x;
if (vis[x + 1]) v = find(x + 1), dp[v][0] = 1ll * dp[v][0] * Pow(2, h[v] - h[x]) % Mod, fa[v] = x;
if (!u) u = v, v = 0;
if (!u) {
dp[x][0] = 1, dp[x][1] = 0;
} else if (!v) {
dp[x][0] = dp[u][0];
dp[x][1] = (dp[u][1] * 2ll + dp[u][0] * 2ll) % Mod;
} else {
dp[x][0] = 1ll * dp[u][0] * dp[v][0] % Mod;
dp[x][1] = 2ll * dp[u][1] * dp[v][1] % Mod;
dp[x][1] = (dp[x][1] + 4ll * dp[u][0] * dp[v][1] + 4ll * dp[v][0] * dp[u][1]) % Mod;
dp[x][1] = (dp[x][1] + 6ll * dp[u][0] * dp[v][0]) % Mod;
}
}
int x = find(1);
int ans = (dp[x][1] + 1ll * dp[x][0] * Pow(2, h[x])) % Mod;
printf("%d\n", ans);
return 0;
} |
#include<bits/stdc++.h>
using namespace std;
const int N = 111;
const int mod = 1e9 + 7;
int f[N][N];
int h[N], d[N], n, tot;
int ksm(int base, int x){
int ans = 1;
while(x){
if(x & 1)ans = 1LL * ans * base % mod;
x >>= 1;
base = 1LL * base * base % mod;
}
return ans;
}
int main(){
cin>>n;
for(int i = 1;i <= n; i++){
scanf("%d", &h[i]);
d[++tot] = h[i];
}
sort(d + 1, d + 1 + tot);
tot = unique(d + 1, d + 1 + tot) - (d + 1);
f[1][0] = (ksm(2, h[1]) - 2 * ksm(2, h[1] - d[1]) % mod + mod) % mod;
for(int i = 1;i <= tot && d[i] <= h[1]; i++){
if(d[i] < h[1])f[1][i] = 2ll * (ksm(2, h[1] - d[i]) - ksm(2, h[1] - d[i+1]) + mod) % mod;
else f[1][i] = 2;
}
for(int i = 1;i < n; i++){
// printf("i=%d\n", i);
int x = lower_bound(d + 1, d + 1 + tot, h[i+1]) - d;
for(int j = 0;d[j] <= h[i] && j <= tot; j++){
if(h[i] >= h[i+1]){
if(d[j] < h[i+1])f[i+1][j] = f[i][j];
else{
f[i+1][x] = (f[i+1][x] + 2 * f[i][j] % mod) % mod;
}
}
else{
if(d[j] < h[i]){
f[i+1][j] = (f[i+1][j] + 1LL * f[i][j] * ksm(2, h[i+1] - h[i]) % mod) % mod;
}
if(d[j] == h[i]){
for(int k = j;k < x; k++){
f[i+1][k] = (f[i+1][k] + 2LL * f[i][j] * (ksm(2, h[i+1] - d[k]) - ksm(2, h[i+1] - d[k+1]) + mod) % mod);
}
f[i+1][x] = 2 * f[i][j] % mod;
}
}
}
}
int ans = 0;
for(int i = 0;i <= tot; i++){
ans = (ans + f[n][i]) % mod;
}
cout<<ans<<endl;
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
#define modulo 1000000007
#define mod(mod_x) ((((long long)mod_x+modulo))%modulo)
#define Inf 10000000000000000
int beki(long long a,long long b,int M = modulo){
int x = 1;
while(b!=0){
if(b&1){
x=((long long)x*a)%M;
}
a=((long long)a*a)%M;
b>>=1;
}
return x;
}
pair<int,int> dfs(vector<int> h){
int width = h.size();
int m = 1000000004;
for(int i=0;i<h.size();i++){
m = min(m,h[i]);
}
int height = m;
for(int i=0;i<h.size();i++){
h[i] -= m;
}
int check = 1,notcheck = 1;
bool f = false;
int cnt0 = 0;
while(h.size()!=0){
while(h.size()!=0&&h.back()==0){
h.pop_back();
cnt0 ++;
}
if(h.size()==0)break;
vector<int> t;
while(h.size()!=0&&h.back()!=0){
t.push_back(h.back());
h.pop_back();
}
pair<int,int> p = dfs(t);
if(!f){
f=true;
}
check = mod(check * p.first);
notcheck = mod(notcheck * mod(p.first*2 + p.second));
}
if(f){
notcheck = mod(notcheck * beki(2,cnt0));
check = mod(check * 2);
notcheck = mod(notcheck - check);
check = mod(check * beki(2,height-1));
}
else{
check = beki(2,height);
notcheck = mod(beki(2,width)-2);
}
//cout<<height<<','<<width<<','<<check<<','<<notcheck<<endl;
return make_pair(check,notcheck);
}
int main(){
int N;
cin>>N;
vector<int> h(N);
for(int i=0;i<N;i++){
cin>>h[i];
}
pair<int,int> p = dfs(h);
cout<<mod(p.first+p.second)<<endl;
return 0;
}
|
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