The journey of Ural dynamic programming

The journey of Ural dynamic programming

 

一句话概括Ural的dp，输出路径+滚动数组。下文中，#是注意点，$是小优化。3Q for

YY’s Code.

 

 

一、经典题：

l  1146联系大白书P55

l  1017 Sol1:dp[i][j]=sum{dp[i-j][k]} ;(0<=k<j)   

            Sol2:dp[i+j]+=dp[j]; (0<=j<n) 视为背包问题来理解

l  1303 代码贪心，甚至不需排序。

l  1223朱晨光：《优化，再优化！——从《鹰蛋》一题浅析对动态规划算法的优化》

l  1513 f[i]=sum{f[i-1-j]}(+B+j个L)(0<=j<=m)

l  1238 区间dp

l  1276 类似noip2009乌龟棋。#1：火车第一节车厢的头也要和最后一节车厢的尾相匹配。

二、难题：

l  1260 dp[n]=dp[n-1](12……)+ dp[n-3](132……)+1(1357……,根据n奇偶性略有不同)

l  1627 周冬：《生成树的计数及其应用》

l  1171 http://blog.csdn.net/chm517/article/details/18889199

l  1459 代码插头DP+矩阵快速幂

三、好题：

l  1117 代码一般读入[a,b]就可以考虑[1,b]-[1,a-1]

l  1310 代码（类似的题有Spoj 2319）

l  1427 贪心略有坑，写着渣的代码会在n=1时跪了。

l  1900 dp[i][j] = max(dp[i][j],dp[g][j-1]+o[i][i+1]-o[g][i+1])

l  1577 代码If in your current state s1[i]==s2[j], you should not assume states i+1,j and i,j+1. Only i+1,j+1.test：aa/ac

l  1696 代码dp[N][最大值][出现在最大值后的严格小于最大值的尽可能大的值]

l  1552 代码通过27-10进制转化成功优化了一维，代码还很优雅

l  1745 http://blog.csdn.net/chm517/article/details/21652557

l  1526 代码关键在于状态的设计，有点区间的味道，但只需考虑区间长度，还有一维是状压

l  1476预处理的优化http://blog.csdn.net/chm517/article/details/21751089

l  1655代码#1：初始位置那个点的限制时间为inf

l  1739代码

l  1895代码$1:第一维的1000可以降为50*2;  $2:代码中两个break。

四、概率题

l  1776代码

l  1716 http://blog.csdn.net/chm517/article/details/21655187 (类似的有Codeforces  148D Bag of mice)

l  1887 基本同hdu 4336

//ural 1303#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>#include <queue>#include <vector>#include <map>#define pb push_back#define mp make_pair#define eps 1e-9#define zero(x) (fabs(x)<eps)#define pi acos(-1.0)#define f1 first#define f2 secondconst int inf=0x3f3f3f3f;using namespace std;#define N 100005int n,m,o;int ans[N],r[N];void doit(){   memset(r,0,sizeof(r));    int x,y,ori,t;    for (int i=1;;i++)         {scanf("%d%d",&x,&y);          if (x<0) t=0;else t=x;          if (y>r[t]) {r[t]=y; if (t==0) ori=x;}          if (x==0&&y==0) {n=i-1; break;}         }    o=0;    int L=0,R=0,i=0,id;    while (L<m)        {   while (i<=L)                 {   if (R<r[i]){R=r[i];id=i;}                     i++;                 }            if (L==R) {printf("No solution\n"); return;}            ans[++o]=id;            L=R;        }    printf("%d\n",o);    for (int i=1;i<=o;i++)        if (ans[i]==0)printf("%d %d\n",ori,r[0]);                else printf("%d %d\n",ans[i],r[ans[i]]);}int main(){   while (scanf("%d",&m)!=EOF) doit();}

//ural 1459#include<cstdio>#include<iostream>#include<cstring>#include<algorithm>#define MAX 22typedef long long LL;using namespace std;const int HASH=4096;const int INF=0x3f3f3f3f;const LL mod=1000000000;int n,m;int id[HASH];int jz[6];int ex,ey,o;int HA;class Mat{public:    LL s[MAX][MAX];    int sizei,sizej;public:    Mat(int a=MAX,int b=MAX,int type=0);    void clear(int type = 0);    void ReSize(int a = MAX,int b=MAX,int type=0);    void Add(const Mat& B);    void Sub(const Mat& B);    void CopyMat(const Mat& B);    void Multiply(const Mat &B);    void Er_work(int n);    void solve(int p) ;};Mat::Mat(int a,int b,int type):sizei(a),sizej(b){   memset(s,0,sizeof(s));         if(type==1)            for(int i=0;i<min(a,b);i++)            s[i][i]=1;    else if(type == 2)            for(int i=0;i<a;i++)            for(int j=0;j<b;j++)            s[i][j]=1;}void Mat::clear(int type){   memset(s,0,sizeof(s));         if(type==1)            for(int i=0;i<min(sizei,sizej);i++)            s[i][i]=1;    else if(type == 2)            for(int i=0;i<sizei;i++)            for(int j=0;j<sizej;j++)            s[i][j]=1;}void Mat::ReSize(int a,int b,int type){   sizei=a; sizej=b;    memset(s,0,sizeof(s));         if(type==1)            for(int i=0;i<min(sizei,sizej);i++)            s[i][i]=1;    else if(type == 2)            for(int i=0;i<sizei;i++)            for(int j=0;j<sizej;j++)            s[i][j]=1;}void Mat::Add(const Mat& B){   for(int i=0;i<sizei;i++)        for(int j=0;j<sizej;j++)            {s[i][j]=s[i][j]+B.s[i][j];             s[i][j]%=mod;            }}void Mat::Sub(const Mat& B){   for(int i=0;i<sizei;i++)        for(int j=0;j<sizej;j++)            {s[i][j]=s[i][j]-B.s[i][j];             s[i][j]=(s[i][j]+mod)%mod;            }}void Mat::CopyMat(const Mat& B){   sizei=B.sizei; sizej=B.sizej;    for(int i=0;i<sizei;i++)        for(int j=0;j<sizej;j++)            s[i][j]=B.s[i][j];}void Mat::Multiply(const Mat &B){   Mat c(sizei,B.sizej,0) ;    for(int i=0;i<sizei;i++)        for(int k=0;k<sizej;k++)        if (s[i][k]>0)            for(int j=0;j<B.sizej;j++)                {c.s[i][j]+=s[i][k]*B.s[k][j];                 c.s[i][j]%=mod ;                }    *this = c;}void Mat::Er_work(int n){    Mat e(sizei,sizej,1);    while (n)    {   if(n&1)            e.Multiply(*this);        n>>=1;        Multiply(*this);    }    *this = e;}void Mat::solve(int p){    Mat temp1 = *this, temp2 = *this;    Mat e(sizei, sizej, 1);    if(p == 1)        return;    else if(p&1)    {        temp1.Er_work(p);        temp2.solve(p-1);        temp1.Add(temp2);    }    else    {        temp1.Er_work(p>>1);        temp1.Add(e);        temp2.solve(p>>1);        temp1.Multiply(temp2);    }    *this = temp1;};Mat ee,ans;struct HASHMAP{    int head[HASH],next[HASH],size;    int state[HASH];    LL f[HASH];    void init()    {        size=0;        memset(head,-1,sizeof(head));    }    void push(int st,LL ans)    {        int h=st%HA;        if(head[h]!=-1)          {              f[head[h]]+=ans;              f[head[h]]%=mod;              return;          }        state[size]=h;        f[size]=ans;        next[size]=head[h];        head[h]=size++;    }}hm[2];void shift(int cur){    for(int i=0;i<hm[cur].size;i++)         {hm[cur].state[i]<<=2;          hm[cur].state[i]%=HA;         }}inline int cp(int p,int i){    return p&(~(3<<jz[i]));}inline int cp(int p,int i,int j){    return p&(~(3<<jz[i]))&(~(3<<jz[j]));}inline int cp(int p,int i,int j,int k){    return p&(~(3<<jz[i]))&(~(3<<jz[j]))&(~(3<<jz[k]));}inline int getp(int p,int i){    return 3&(p>>jz[i]);}inline int pp(int i,int k){   return k<<jz[i];}inline int lp(int p,int j){   for (int it=j-2,cnt=1;;it--)        {   int pi=getp(p,it);            if (pi==1) cnt--;            else if (pi==2) cnt++;            if (cnt==0) return it;        }}inline int rp(int p,int j){   for (int it=j+1,cnt=1;;it++)        {   int pi=getp(p,it);            if (pi==2) cnt--;            else if (pi==1) cnt++;            if (cnt==0) return it;        }}void dp(int i,int j,int cur){    for(int k=0;k<hm[cur].size;k++)        {int s=hm[cur].state[k];         LL data=hm[cur].f[k];         int left=getp(s,j);         int up=getp(s,j+1);         if (left==0&&up==0)            {if (j+1<m)                {                    hm[cur^1].push(s|pp(j,1)|pp(j+1,2),data);                }             continue;            }         if (left==0||up==0)            {   int w=left+up;                int tmp=cp(s,j,j+1);                if (j+1<m) hm[cur^1].push(tmp|pp(j+1,w),data);                hm[cur^1].push(tmp|pp(j,w),data);                continue;            }         if (left==up)            {   int it=(left==1)?rp(s,j+1):lp(s,j+1);                hm[cur^1].push(cp(s,j,j+1,it)|pp(it,left),data);                continue;            }//         if (left==1&&up==2)//            {   if (i==ex&&j==ey) ans+=data;//                continue;//            }        if (left==2&&up==1)            {   hm[cur^1].push(cp(s,j,j+1),data);                continue;            }        }}void init(){    ex=n-1; ey=m-1;}void solve(){    ee.ReSize(o,o,0);    int cur;    for(int i=0;i<HA;i++)        if (id[i]!=-1)        {cur=0;         hm[cur].init();         hm[cur].push(i,1);            for(int j=0;j<m;j++)            {             hm[cur^1].init();             dp(i,j,cur);             cur^=1;            }         shift(cur);         for(int ii=0;ii<hm[cur].size;ii++)            ee.s[id[i]][id[hm[cur].state[ii]]]=hm[cur].f[ii];        }    ee.Er_work(n);    ans.ReSize(1,o,0);    ans.s[0][0]=1;    ans.Multiply(ee);    LL anss=0;    for (int i=0;i<HA;i++)     if (id[i]!=-1)       {    if ((1<<jz[m])*2+(1<<jz[m-1])==i)            {anss+=ans.s[0][id[i]];             anss%=mod;             //printf("~\n");            }       }    printf("%I64d\n",anss*2%mod);}int tmp[6];void prepared_jinzhi(){   for (int i=0;i<=m;i++)        jz[i]=i*2;    memset(id,255,sizeof(id)); o=0;    for (int i=0;i<HA;i++)    {   int f=1;        for (int j=0;j<=m;j++)            {   tmp[j]=3&(i>>jz[j]);                if (tmp[j]==3) {f=0; break;}            }        if (!f) continue;        if (tmp[0]) continue;        int s=0;        for (int j=1;j<=m;j++)            {                if (tmp[j]==1) s++;                if (tmp[j]==2) s--;                if (s<0) f=0;            }        if (s) f=0;        if (f) id[i]=o++;    }}int main(){    while(scanf("%d%d",&m,&n)!=EOF)    {        init();        HA=1<<(m*2+2);        prepared_jinzhi();        if (m*n%2==1) {printf("%d\n",0);continue;}        solve();    }    return 0;}

//ural 1117#include <cstdio>#include <cstring>#include <algorithm>#include <cstdio>#include <cmath>#include <queue>#include <vector>#include <map>#define pb push_back#define mp make_pair#define eps 1e-9#define zero(x) (fabs(x)<eps)#define pi acos(-1.0)#define f1 first#define f2 secondconst int inf=0x3f3f3f3f;typedef long long LL;using namespace std;LL s[41],l[41],a,b;void pre(){   l[0]=0; s[0]=0;    for (int i=1;i<=40;i++)        {   l[i]=(l[i-1]+s[i-1])*2;            s[i]=s[i-1]+1;        }}LL solve(LL x){   LL ans=0;    while (x>1)        {            LL p=1,t=-1;            while (p<=x) {p<<=1; t++;}            p>>=1; t--;            x-=p;            if (x)ans+=(l[t]+s[t]*2);else ans+=(l[t]+s[t]);        }    return ans;}int main(){    pre();    while (scanf("%I64d%I64d",&a,&b)!=EOF)        printf("%I64d\n",abs(solve(b)-solve(a)));}

//ural 1310#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>#include <queue>#include <vector>#include <iostream>#include <string>#include <cstdlib>#include <map>#define pb push_back#define eps 1e-9#define zero(x) (fabs(x)<eps)#define pi acos(-1.0)#define MS(x, y) memset(x, y, sizeof(x))#define FOR(i, x, y) for(int i=x; i<=y; i++)#define rFOR(i, x, y) for(int i=x; i>=y; i--)using namespace std;const int maxn = 175;struct bigint{    int s[maxn];    bigint() {MS(s, 0);}    bigint(int num) {*this = num;}    bigint(const char* num){*this = num;}    bigint operator = (const char* num)    {        MS(s, 0);        if(num[0] == '-')        {            num = num + 1;            s[0] = -1;        }        else s[0] = 1;        while(num[0] == '0') num = num + 1;        s[0] = s[0] * strlen(num);        int len = abs(s[0]);        FOR(i, 1, len) s[i] = num[len - i] - 48;        return *this;    }    bigint operator = (int num)    {        char s[maxn];        sprintf(s, "%d", num);        *this = s;        return *this;    }    string str() const    {        string res = "";        FOR(i, 1, abs(s[0])) res = (char)(s[i] + 48) + res;        if(res == "") return res = "0";        if(s[0] < 0) res = '-' + res;        return res;    }    bool operator < (const bigint& b) const    {        if(s[0] != b.s[0]) return s[0] < b.s[0];        int len = abs(s[0]);        rFOR(i, len, 1)        if(s[i] != b.s[i])            return (s[i] < b.s[i]) ^ (s[0] < 0);        return false;    }    bool operator > (const bigint& b) const{return b < *this;}    bool operator <= (const bigint& b) const{return !(b < *this);}    bool operator >= (const bigint& b) const{return !(*this < b);}    bool operator != (const bigint& b) const{return b < *this || *this < b;}    bool operator == (const bigint& b) const{return !(b < *this) && !(*this < b);}    friend bigint abs(bigint b)    {        b.s[0] = abs(b.s[0]);        return b;    }    friend bigint _add(const bigint& a, const bigint& b)    {        bigint c;        c.s[0] = max(a.s[0], b.s[0]);        FOR(i, 1, c.s[0]) c.s[i] = a.s[i] + b.s[i];        FOR(i, 1, c.s[0])        if(c.s[i] >= 10)        {            c.s[i+1]++;            c.s[i]-=10;        }        if(c.s[c.s[0]+1]) ++c.s[0];        return c;    }    friend bigint _sub(const bigint& a, const bigint& b)    {        bigint c;        c.s[0] = a.s[0];        FOR(i, 1, c.s[0]) c.s[i] = a.s[i] - b.s[i];        FOR(i, 1, c.s[0])        if(c.s[i] < 0)        {            c.s[i+1]--;            c.s[i] += 10;        }        while(!c.s[c.s[0]] && c.s[0]) --c.s[0];        return c;    }    bigint operator + (const bigint& b) const    {        if(s[0] >= 0 && b.s[0] >= 0) return _add(*this, b);        if(b.s[0] < 0) return *this - abs(b);        if(s[0] < 0) return b - abs(*this);    }    bigint operator - (const bigint& b) const    {        if(s[0] >= 0 && b.s[0] >= 0)        {            bigint c;            if(*this >= b) return _sub(*this, b);            c = _sub(b, *this);            c.s[0] = -c.s[0];            return c;        }        if(b.s[0] < 0) return *this + abs(b);        if(s[0] < 0)        {            bigint c;            c = abs(*this) + b;            c.s[0] = -c.s[0];            return c;        }    }    bigint operator * (const bigint& b) const    {        bigint c;        c.s[0] = abs(s[0]) + abs(b.s[0]);        FOR(i, 1, abs(s[0]))        FOR(j, 1, abs(b.s[0]))            c.s[i + j - 1] += s[i] * b.s[j];        FOR(i, 1, c.s[0])        {            c.s[i+1] += c.s[i] / 10;            c.s[i] %= 10;        }        while(!c.s[c.s[0]] && c.s[0]) --c.s[0];        if((s[0] > 0) != (b.s[0] > 0)) c.s[0] = -c.s[0];        return c;    }    bigint operator / (const bigint& _b) const    {        bigint c, t;        bigint b = abs(_b);        c.s[0] = abs(s[0]);        rFOR(i, c.s[0], 1)        {            rFOR(j, t.s[0], 1) t.s[j + 1] = t.s[j];            t.s[1] = s[i];            if (t.s[t.s[0]+1])t.s[0]++;            while(t >= b)            {                ++c.s[i];                t -= b;            }        }        while(!c.s[c.s[0]] && c.s[0]) --c.s[0];        if((s[0] > 0) != (b.s[0] > 0)) c.s[0] = -c.s[0];        return c;    }    bigint operator % (const bigint& _b) const    {        bigint c, t;        bigint b = abs(_b);        rFOR(i, abs(s[0]), 1)        {            rFOR(j, t.s[0], 1) t.s[j + 1] = t.s[j];            t.s[1] = s[i];            if (t.s[t.s[0]+1])t.s[0]++;            while(t >= b) t -= b;        }        if((s[0] < 0)) t.s[0] = -t.s[0];        return t;    }    bigint operator += (const bigint& b) {*this = *this + b;return *this;}    bigint operator -= (const bigint& b) {*this = *this - b;return *this;}    bigint operator *= (const bigint& b) {*this = *this * b;return *this;}    bigint operator /= (const bigint& b) {*this = *this / b;return *this;}    bigint operator %= (const bigint& b) {*this = *this % b;return *this;}    friend bigint operator + (int& a, const bigint& b){return (bigint)a + b;}    friend bigint operator - (int& a, const bigint& b){return (bigint)a - b;}    friend bigint operator * (int& a, const bigint& b){return (bigint)a * b;}    friend bigint operator / (int& a, const bigint& b){return (bigint)a / b;}    friend bigint operator % (int& a, const bigint& b){return (bigint)a % b;}    friend bigint operator <  (int& a, const bigint& b){return (bigint)a < b;}    friend bigint operator <= (int& a, const bigint& b){return (bigint)a <=b;}    friend bigint operator >  (int& a, const bigint& b){return (bigint)a > b;}    friend bigint operator >= (int& a, const bigint& b){return (bigint)a >=b;}    friend bigint operator == (int& a, const bigint& b){return (bigint)a ==b;}    friend bigint operator != (int& a, const bigint& b){return (bigint)a !=b;}};istream& operator >> (istream &in, bigint& x){    string s;    in >> s;    x = s.c_str();    return in;}ostream& operator << (ostream &out, const bigint& x){    out << x.str();    return out;}using namespace std;int l,m,k;bigint x;bigint dp[101][50];void doit(){    cin>>x;x+=1;    for (int z=0;z<k;z++)        dp[0][z]=0;    dp[0][0]=1;    for (int i=1;i<=l;i++)        {   for (int z=0;z<k;z++)                dp[i][z]=0;            for (int j=1;j<=m;j++)            for (int z=0;z<k;z++)                dp[i][(z+j)%k]+=dp[i-1][z];        }    int w=l,i,p=0;    bool have=0;    bigint tmp;    while (w)        {   for (i=1;i<=m;i++)                {  tmp=dp[w-1][((p-i)%k+k)%k];                   if (x<=tmp) break;else x-=tmp;                }            if (have) printf(" "); have=1;            printf("%d",i);            w--;            p=((p-i)%k+k)%k;        }    printf("\n");}int main(){   while (scanf("%d%d%d",&l,&m,&k)!=EOF) doit();}/*3 10 4213*/

//ural 1577//CONTINUE!#include <cstdio>#include <cstring>#include <algorithm>#include <iostream>#include <cstdlib>#include <cmath>#include <queue>#include <vector>#include <map>#define pb push_back#define mp make_pair#define eps 1e-9#define zero(x) (fabs(x)<eps)#define pi acos(-1.0)#define f1 first#define f2 secondconst int inf=0x3f3f3f3f;const long long INF=1LL<<50;using namespace std;typedef long long LL;typedef pair <int,double> PII;int mod,n,m,t,tot;#define N 2005#define e 1000000007int s[N][N],f[N][N];char s1[N],s2[N];void doit(){   int la=strlen(s1),lb=strlen(s2);    memset(f,0x3f,sizeof(f));    f[0][0]=0;    s[0][0]=1;    for (int i=0;i<=la;i++)    for (int j=0;j<=lb;j++)        {   int tmp;            if (i&&j&&s1[i-1]==s2[j-1])                {                    if (f[i][j]>f[i-1][j-1]+1)  {f[i][j]=f[i-1][j-1]+1; s[i][j]=s[i-1][j-1];}else                    if (f[i][j]==f[i-1][j-1]+1) {s[i][j]=(s[i][j]+s[i-1][j-1])%e;}                    continue; //!                }            if (i)                 {if (f[i][j]>f[i-1][j]+1)  {f[i][j]=f[i-1][j]+1; s[i][j]=s[i-1][j];}else                  if (f[i][j]==f[i-1][j]+1) {s[i][j]=(s[i][j]+s[i-1][j])%e;}                 }            if (j)                 {if (f[i][j]>f[i][j-1]+1)  {f[i][j]=f[i][j-1]+1; s[i][j]=s[i][j-1];}else                  if (f[i][j]==f[i][j-1]+1) {s[i][j]=(s[i][j]+s[i][j-1])%e;}                 }            //printf("%d %d %d %d\n\n\n",i,j,f[i][j],s[i][j]);        }    printf("%d\n",s[la][lb]);}int main(){    while (scanf("%s%s",s1,s2)!=EOF) doit();}/*aabaaaab*/

//ural 1696#include <cstdio>#include <cstring>#include <algorithm>#include <iostream>#include <cstdlib>#include <cmath>#include <queue>#include <vector>#include <map>#define pb push_back#define mp make_pair#define eps 1e-9#define zero(x) (fabs(x)<eps)#define pi acos(-1.0)#define f1 first#define f2 secondconst int inf=0x3f3f3f3f;const long long INF=1LL<<50;using namespace std;typedef long long LL;typedef pair <int,double> PII;#define N 202int dp[2][N][N],a[N][N],b[N][N];int n,m,mod;void doit(){   memset(dp,0,sizeof(dp));    memset(a,0,sizeof(a));    memset(b,0,sizeof(b));    for (int i=1;i<=m;i++)         dp[1][i][0]=1;    for (int i=1;i<n;i++)    {memset(dp[(i&1)^1],0,sizeof(dp[(i&1)^1]));     int o=i&1;     for (int j=1;j<=m;j++)  a[j][0]=dp[o][j][0];     for (int j=1;j<=m;j++)     for (int k=1;k<=j-1;k++)a[j][k]=(dp[o][j][k]+a[j][k-1])%mod;     for (int k=0;k<=m-1;k++)  b[k][k]=0;     for (int k=0;k<=m-1;k++)     for (int j=k+1;j<=m;j++)  b[j][k]=(dp[o][j][k]+b[j-1][k])%mod;     for (int j=1;j<=m;j++)     for (int k=0;k<=j-1;k++)        {                        dp[o^1][j][k]=(dp[o^1][j][k]+b[j][k])%mod;            if (j-k!=1) dp[o^1][j][k]=(dp[o^1][j][k]+a[j][k])%mod;        }    }    int ans=0;    for (int j=1;j<=m;j++)    for (int k=0;k<=j-1;k++)        ans=(ans+dp[n&1][j][k])%mod;    printf("%d\n",ans+1);}int main(){    while (scanf("%d%d%d",&n,&m,&mod)!=EOF) doit();}

//ural 1552#include<algorithm>#include<cstring>#include<cstdio>#include<cstdlib>const int inf=0x3f3f3f3f;using namespace std;const int N=27*27*27;#define M 51int f[M][4][N];int dp[M][4][N];char s[M];int num[M+1],n;int a[4];inline int get(int a,int b){   if (a==0) a-=96;    if (b==0) b-=96;    return abs(a-b);}bool miniz(int &a,int b){    if (b>a) return 0;    a=b;    return 1;}void print(int i,int j,int k){   if (!i) {for (int i=1;i<=num[0]+96;i++) printf("+"); printf("."); return;}    int t1=f[i][j][k]/N,t2=f[i][j][k]%N;        print(i-1,t1,t2);    int x=t2;    for (int p=3;p>=0;p--)        if (p==t1) a[p]=num[i-1];        else {a[p]=x%27; x/=27;}    if (t1<j) for (int jj=1;jj<=j-t1;jj++) printf(">");    if (t1>j) for (int jj=1;jj<=t1-j;jj++) printf("<");    if (a[j]<num[i])  for (int jj=1;jj<=get(a[j],num[i]);jj++) printf("+");    if (a[j]>num[i])  for (int jj=1;jj<=get(a[j],num[i]);jj++) printf("-");    printf(".");}void doit(){   for (int i=0;i<n;i++)        num[i]=s[i]-'a'+1;    memset(dp,0x3f,sizeof(dp));    for (int i=0;i<4;i++)        dp[0][i][0]=num[0]+96;    for (int i=1;i<n;i++)    for (int j=0;j<4;j++)    for (int k=0;k<N;k++)        if (dp[i-1][j][k]!=inf)        {   int x=k;            for (int p=3;p>=0;p--)                if (p==j) a[p]=num[i-1];                else {a[p]=x%27; x/=27;}            for (int nj=0;nj<4;nj++)                {   x=0;                    for (int p=0;p<4;p++)                        if (p!=nj) x=x*27+a[p];                    if (miniz(dp[i][nj][x],dp[i-1][j][k]+abs(j-nj)+get(a[nj],num[i])))                        {   //printf("%d %d %d ->%d %d %d\n",i-1,j,k,i,nj,x);                            f[i][nj][x]=j*N+k;                        }                }        }    int ans=inf;    for (int j=0;j<4;j++)    for (int k=0;k<N;k++)        ans=min(ans,dp[n-1][j][k]);    for (int j=0;j<4;j++)    for (int k=0;k<N;k++)        if (ans==dp[n-1][j][k]) {print(n-1,j,k);        return;}}int main(){    while (scanf("%s",s)!=EOF) {n=strlen(s);doit();}}//azazazazazazazazazazazazazazazazazazazaz

//ural 1655#include<cstdio>#include<iostream>#include<cstring>#include<algorithm>#include<cmath>#define N 505#define eps 1e-6#define MAX 1e7typedef long long LL;using namespace std;const double tt=21600.0;int n,nn,res;double w,aa,tot;double dp[N][N][2];bool vis[N][N][2];int from[N][N][2];//dp[x][y][op];//x,(x+1)%nn,(x+2)%nn,...,y//op==0 end in x;//op==1 end in y;struct node{    double qt,dt;    int id;    bool operator<(const node& oth)const        {            return qt<oth.qt;        }}a[N];double get(int from,int to){    if (from>to) return tot-a[from].qt+a[to].qt;             else return a[to].qt-a[from].qt;}void print(int x,int y,int op){   if (x==res&&y==res) return;    int rr=from[x][y][op]/2,ii=from[x][y][op]%2;    if (rr==0)        {   print((x+1)%nn,y,ii);            printf("%d\n",a[x].id);        }    if (rr==1)        {   print(x,(y-1+nn)%nn,ii);            printf("%d\n",a[y].id);        }}double f(int x,int y,int op){    if (vis[x][y][op]) return dp[x][y][op];    double &ans=dp[x][y][op];       int &fr=from[x][y][op];    vis[x][y][op]=1;    ans=MAX;    int next;    double ad1,ad2,ad3;    next=(y-1+nn)%nn;    ad3=get(next,y);    if (op==0) ad1=get(x,y); else ad1=0;    for (int i=0;i<2;i++)                {if (i==0) ad2=get(x,next); else ad2=0;                 double tmp=f(x,next,i);                 if (tmp+ad2+ad3<=a[y].dt&&ans>tmp+ad1+ad2+ad3)                    {ans=tmp+ad1+ad2+ad3;                     fr=i+2;                    }                }    next=(x+1)%nn;    ad3=get(x,next);    if (op==1) ad1=get(x,y); else ad1=0;    for (int i=0;i<2;i++)                {if (i==1) ad2=get(next,y); else ad2=0;                 double tmp=f(next,y,i);                 if (tmp+ad2+ad3<=a[x].dt&&ans>tmp+ad1+ad2+ad3)                    {ans=tmp+ad1+ad2+ad3;                     fr=i;                    }                }    return ans;}void doit(){   double x,y,z;    w*=tt;    for (int i=1;i<=n;i++)        {            scanf("%lf%lf%lf",&x,&y,&z);            a[i].qt=x/w;            a[i].dt=(y-1)/z+eps;            a[i].id=i;        }    tot=360.0/w;    a[0].qt=aa/w;    a[0].dt=MAX; //imp锛�    a[0].id=0;    nn=n+1;    sort(a,a+n+1);    for (int i=0;i<=n;i++)        if (a[i].id==0) {res=i;break;}    memset(vis,0,sizeof(vis));    for (int i=0;i<nn;i++)    for (int j=0;j<2;j++)        {            vis[i][i][j]=1;            dp[i][i][j]=(i==res)?0:MAX;        }    double ans=MAX,tmp;    int an1,an2,an3;    for (int i=0;i<=n;i++)        {tmp=f(i,(i-1+nn)%nn,0);         if (tmp<ans) {ans=tmp;an1=i;an2=(i-1+nn)%nn;an3=0;}         tmp=f(i,(i-1+nn)%nn,1);         if (tmp<ans) {ans=tmp;an1=i;an2=(i-1+nn)%nn;an3=1;}        }    if (ans+eps>=MAX) {printf("Impossible\n"); return;}    printf("%.6lf\n",ans*60);    print(an1,an2,an3);}int main(){    while (scanf("%lf%lf%d",&aa,&w,&n)!=EOF) doit();}/*0 0.0278 3280 46 10090 16 100180 61 100*/

//ural 1739#include <cstdio>#include <cstring>#include <algorithm>#include <iostream>#include <cstdlib>#include <cmath>#include <queue>#include <vector>#include <map>#define pb push_back#define mp make_pair#define eps 1e-9#define zero(x) (fabs(x)<eps)#define pi acos(-1.0)#define f1 first#define f2 secondconst int inf=0x3f3f3f3f;const long long INF=1LL<<50;using namespace std;typedef long long LL;typedef pair <int,double> PII;#define N 12int a[N];int tmp[N+1];int n,tot;int dp[1<<N][2][2],dp2[1<<N][2][2];int from1[1<<N][2][2],from2[1<<N][2][2],from3[1<<N][2][2];int sum[1<<N];#define M 4097int c1[M];int c2[N][M];int c3[N][M];int c4[N][N][M];int c5[N][M];//c1//c2[j] j-25%//c3[j] j+10%//c4[j1][j2] j1-25% j2+10%//c5[j] j-25% +10%bool minize(int &a,int b,int& a1,int b1){    if (b>a) return 0;    if (b==a&&b1>=a1) return 0;    a=b;    a1=b1;    return 1;}void print(int left,int x1,int x2){   if (left==0) return;    int f1=from1[left][x1][x2],f2=from2[left][x1][x2],f3=from3[left][x1][x2];    int v1=f2/13,v2=f2%13;    //printf("~~~~~%d %d %d %d %d %d\n",left,x1,x2,f1,f2,f3);    if (f1>0)        {   tmp[0]=0;            for (int i=0;i<n;i++)                if (f1&(1<<i))                tmp[++tmp[0]]=i;            printf("return %d",tmp[0]);            for (int i=1;i<=tmp[0];i++)                printf(" %d",tmp[i]+1);                printf("\n");        }    if (v1) printf("dearomatize %d\n",v1);    if (v2) printf("aromatize %d\n",v2);    f3=left+f1-f3;    if (f3>0)        {   tmp[0]=0;            for (int i=0;i<n;i++)                if (f3&(1<<i))                tmp[++tmp[0]]=i;            printf("take %d",tmp[0]);            for (int i=1;i<=tmp[0];i++)                printf(" %d",tmp[i]+1);                printf("\n");        }    f3=from3[left][x1][x2];    print(f3,x1||v1,x2||v2);}void f(int left,int x1,int x2){   if (dp[left][x1][x2]!=-1) return;    if (left==0) {dp[left][x1][x2]=0;dp2[left][x1][x2]=0;return;}    int &re=dp[left][x1][x2],&re2=dp2[left][x1][x2];    int &f1=from1[left][x1][x2],&f2=from2[left][x1][x2],&f3=from3[left][x1][x2];    re=inf; re2=inf;    int v,j;    for (int i=1;i<=c1[0];i++)        {j=c1[i];         v=left^(left&j);         f(v,x1,x2);         if (minize(re,1+dp[v][x1][x2],re2,1+dp2[v][x1][x2]+((left&j)!=j)))            {                f1=j-(left&j);                f2=0;                f3=v;            }        }    if (!x1)    for (int k=0;k<n;k++)    for (int i=1;i<=c2[k][0];i++)        {j=c2[k][i];         v=left^(left&j);         f(v,1,x2);         if (minize(re,1+dp[v][1][x2],re2,2+dp2[v][1][x2]+((left&j)!=j)))            {   f1=j-(left&j);                f2=(k+1)*13;                f3=v;            }        }    if (!x2)    for (int k=0;k<n;k++)    for (int i=1;i<=c3[k][0];i++)        {j=c3[k][i];         v=left^(left&j);         f(v,x1,1);         if (minize(re,1+dp[v][x1][1],re2,2+dp2[v][x1][1]+((left&j)!=j)))            {   f1=j-(left&j);                f2=(k+1);                f3=v;            }        }    if (!x1&&!x2)    for (int k1=0;k1<n;k1++)    for (int k2=0;k2<n;k2++)    for (int i=1;i<=c4[k1][k2][0];i++)        {j=c4[k1][k2][i];         v=left^(left&j);         f(v,1,1);         if (minize(re,1+dp[v][1][1],re2,3+dp2[v][1][1]+((left&j)!=j)))            {   f1=j-(left&j);                f2=(k1+1)*13+(k2+1);                f3=v;            }        }    if (!x1&&!x2)    for (int k=0;k<n;k++)    for (int i=1;i<=c5[k][0];i++)        {j=c5[k][i];         v=left^(left&j);         f(v,1,1);         if (minize(re,1+dp[v][1][1],re2,3+dp2[v][1][1]+((left&j)!=j)))            {   f1=j-(left&j);                f2=(k+1)*13+(k+1);                f3=v;            }        }}void doit(){    for (int i=0;i<n;i++) scanf("%d",&a[i]);    tot=1<<n; tot--;    memset(sum,0,sizeof(sum));    for (int i=1;i<=tot;i++)         {  int x=i&(-i);            int t=int(log(double(x))/log(2.0)+eps);            sum[i]=sum[i-x]+a[t];         }    memset(c1,0,sizeof(c1));    memset(c2,0,sizeof(c2));    memset(c3,0,sizeof(c3));    memset(c4,0,sizeof(c4));    memset(c5,0,sizeof(c5));    for (int i=1;i<=tot;i++)        if (sum[i]%256==0) {c1[++c1[0]]=i;}    for (int j=0;j<n;j++)        if (a[j]%4==0)        {   int x;            for (int i=1;i<=tot;i++)                {   if (!(i&(1<<j))) continue;                    x=sum[i]-a[j]+a[j]/4*3;                    if (x%256==0) {c2[j][++c2[j][0]]=i;}                }        }        for (int j=0;j<n;j++)        if (a[j]%10==0)        {   int x;            for (int i=1;i<=tot;i++)                {   if (!(i&(1<<j))) continue;                    x=sum[i]-a[j]+a[j]/10*11;                    if (x%256==0) {c3[j][++c3[j][0]]=i;}                }        }    for (int j1=0;j1<n;j1++)    for (int j2=0;j2<n;j2++)    if (j1!=j2)        if ((a[j1]*15+a[j2]*22)%20==0)        {   int x;            for (int i=1;i<=tot;i++)                {   if (!(i&(1<<j1)))continue;                    if (!(i&(1<<j2)))continue;                    x=sum[i]-a[j1]-a[j2]+(a[j1]*15+a[j2]*22)/20;                    if (x%256==0) {c4[j1][j2][++c4[j1][j2][0]]=i;}                }        }    for (int j=0;j<n;j++)        if (a[j]%40==0)        {   int x;            for (int i=1;i<=tot;i++)                {   if (!(i&(1<<j))) continue;                    x=sum[i]-a[j]+a[j]/40*33;                    if (x%256==0) {c5[j][++c5[j][0]]=i;}                }        }    memset(dp,255,sizeof(dp));    f(tot,0,0);    if (dp[tot][0][0]==inf) {printf("IMPOSSIBLE\n"); return;}    if (dp2[tot][0][0]>20000) {printf("IMPOSSIBLE\n"); return;}    printf("%d\n",dp2[tot][0][0]);    print(tot,0,0);}int main(){    while (scanf("%d",&n)!=EOF) doit();}/*240 223*/

//ural 1895#include <cstdio>#include <cstring>#include <algorithm>#include <iostream>#include <cstdlib>#include <cmath>#include <queue>#include <vector>#include <map>#define pb push_back#define mp make_pair#define eps 1e-9#define zero(x) (fabs(x)<eps)#define pi acos(-1.0)#define f1 first#define f2 secondconst int inf=0x3f3f3f3f;const long long INF=1LL<<50;using namespace std;typedef long long LL;typedef pair <int,double> PII;#define N 1005#define M 55#define M2 110int n,X,K,o;int f[M2][M][M],from1[M2][M][M],from2[M2][M][M];;int t[M],ans1[M],ans2[M];int num[M2];int vis[N],have[N];void print(int an1,int an2,int an3){   if (an1==0) return;    int t1=from1[an1][an2][an3],t2=from2[an1][an2][an3];    for (int i=t1+1;i<=an2;i++)        ans1[i]=an1;    for (int i=t2+1;i<=an3;i++)        ans2[i]=an1;    print(an1-1,t1,t2);}void doit(){    scanf("%d",&n);    for (int i=1;i<=n;i++)        scanf("%d",&t[i]); t[n+1]=-1;    memset(vis,0,sizeof(vis));//    for (int i=0;i<t[n];i++)//        num[++o]=i;    for (int i=1;i<=n;i++)        {int x=t[i]-1;         while (vis[x]&&x) x--; vis[x]=1;         x--;         if (x<0) continue;         while (vis[x]&&x) x--; vis[x]=1;        }    o=0;    for (int i=0;i<t[n];i++)         if (vis[i]) {num[++o]=i;vis[i]=o;}    int lx=1,x=1;    for (int i=1;i<t[n];i++)        {   while (t[x]==i) x++;            have[i]=have[i-1]+x-lx;            lx=x;        }//    for (int i=1;i<=o;i++)//    printf("%d %d %d\n",i,num[i],have[num[i]]);    memset(f,0x3f,sizeof(f));    f[0][0][0]=0;    for (int i=1;i<=o;i++)    for (int j=0;j<=n;j++)    for (int k=0;k<=j;k++)        {   if (j<have[num[i]]||k<have[num[i]]) continue;            if (f[i][j][k]>f[i-1][j][k])                    {                        f[i][j][k]=f[i-1][j][k];                        from1[i][j][k]=j;                        from2[i][j][k]=k;                    }            for (int nk=k;nk<=j;nk++)            {   if (nk-k>K)break;                int left=K-(nk-k);                for (int use=0;use<=left;use++)                    {    int nj=j+use;                         if (nj>n) nj=n;                         if (num[i]+X<t[nj]) break;                         if (f[i][nj][nk]>f[i-1][j][k]+1)                            {f[i][nj][nk]=f[i-1][j][k]+1;                             from1[i][nj][nk]=j;                             from2[i][nj][nk]=k;                            }                    }             }        }    if (f[o][n][n]==inf) {printf("%d\n",-1); return;}    printf("%d\n",f[o][n][n]);    print(o,n,n);    for (int i=1;i<=n;i++)        printf("%d %d\n",num[ans1[i]],num[ans2[i]]);}int main(){    while (scanf("%d%d",&X,&K)!=EOF) doit();}/*10 232 16 25*/

//ural 1776#include <cstdio>#include <cstring>#include <algorithm>#include <iostream>#include <cstdlib>#include <cmath>#include <queue>#include <vector>#include <map>#define pb push_back#define mp make_pair#define eps 1e-9#define zero(x) (fabs(x)<eps)#define pi acos(-1.0)#define f1 first#define f2 secondconst int inf=0x3f3f3f3f;const long long INF=1LL<<50;using namespace std;typedef long long LL;typedef pair <int,double> PII;#define N 402double dp[N][N],sum[N][N];int n;int main(){   memset(dp,0,sizeof(dp));    memset(sum,0,sizeof(sum));    dp[0][0]=1;    for (int i=0;i<=400;i++)        sum[0][i]=1;    for (int i=1;i<=400;i++)    {      for (int k=1;k<=i;k++)           {   int t=max(k-1,i-k)+1;               for (int j=1;j<=t;j++)                dp[i][j]+= (dp[k-1][j-1] * sum[i-k][j-1]+                            sum[k-1][j-1]*  dp[i-k][j-1]-                            dp[k-1][j-1] *  dp[i-k][j-1])/i;           }           for (int j=1;j<=400;j++)                sum[i][j]=sum[i][j-1]+dp[i][j];    }    while (scanf("%d",&n)!=EOF)        {   n-=2;            double ans=0;            for (int i=1;i<=n;i++)                ans+=dp[n][i]*i;            printf("%.6lf\n",ans*10);        }}