ZOJ 3962Seven Segment Display (数位DP)

题意

数字时钟每秒钟会消耗显示的数字所需的能量，给定时间长度m和起点st，求m秒内会消耗的能量

思路

没有什么比看错题目却一直没发现更悲催的了。。。
队友和我说了题意，然后我想都没想就开始写了，一直以为前导零是不需要计算代价的，虽然样例就是有前导零的。。
就这样带着错误的思路打了三个小时。。
好吧，不怪队友，谁让自己连样例都不看呢。。

这题的打法很多，延续昨天想到的思路，用数位dp来做
我们用dp[i][j]表示长度为i，以j开头，形式为jxxxx所需的代价总和。
因为后面的x的范围一定是0000-FFFF，所以代价可以直接推算出来

如果是0000-FFFF，那么一共有16^4个数字，0-F各出现(16^3)*4次，其实和数位dp已经没太大关系了，毕竟是可以直接推出答案而不需要递推的

代码(前导零不计代价，错误思路)

思路错了以后代码实现更复杂一些，但是也是能用数位dp做出来的

#include <bits/stdc++.h>#define mem(a,b) memset(a,b,sizeof(a))#define rep(i,a,b) for(int i=a;i<b;i++)#define sc(a) scanf("%d",&a)const int INF=0x3f3f3f3f;const int maxn=2e5+50;const int mod=1e9+7;const double eps=1e-8;#define pii pair<int,int>typedef long long ll;typedef unsigned int ui;using namespace std;ll val[16]={6,2,5,5,4,5,6,3,7,6,6,5,4,5,5,4};inline ll pow16(ll i){    return (1ll<<(i*4));}inline char toChar(int x){    assert(x>=0 && x<16);    if(x>=0 && x<=9) return x+'0';    return x+'A'-10;}inline int toInt(char x){    if(x>='0' && x<='9') return x-'0';    return x-'A'+10;}ll bruteForce(int x){    ll ret=0;    while(x>=0){        char buf[66]={0};        sprintf(buf,"%08X",x);        if(x==0) ret+=val[0];        int len=strlen(buf);        int pos=0;        while(buf[pos]=='0') pos++;        for(;pos<8;pos++) ret+=val[toInt(buf[pos])];        x--;    }    return ret;}string toHex(ll x){    string ret="";    for(int i=0;i<8;i++){        ret=toChar(x%16)+ret;        x=x/16;    }    return ret;}ll toLL(char buf[]){    ll ret=0;    int len=strlen(buf);    rep(i,0,len) ret=ret*16+toInt(buf[i]);    return ret;}//dp i j len-i start-j tot-valll dp[9][17];//dp[i][0] no-leading-zeros//dp[i][16] start with 0 and have leading-zerosvoid init(){    mem(dp,0);    rep(i,0,16) dp[1][i]=val[i];    dp[1][16]=val[0];    rep(i,2,9){        rep(j,0,16) dp[i][0]+=dp[i-1][j];        ll num=pow16(i-1);        rep(j,1,16){            dp[i][j]=val[j]*num+num/16*(i-1)*78;        }        dp[i][16]=val[0]*num+num/16*(i-1)*78;    }    rep(i,1,5) rep(j,0,17) printf("%d %d %lld\n",i,j,dp[i][j]);}ll st,ed;ll LIM=0xFFFFFFFF;void debugHex(int x){    printf("%08X\n",x);}ll cal(ll x){    if(x<0) return 0;    if(x==0) return 6;    string buf=toHex(x);    bool flag=true;    int pos=0;    while(buf[pos]=='0') pos++;    int num;    ll base=0;    ll ret=0;    for(;pos<8;pos++){        int i=8-pos;        num=toInt(buf[pos]);        if(num){            if(flag){                ret+=dp[i][0];            }else ret+=dp[i][16]+base*pow16(i-1);            flag=false;        }        rep(j,1,num){            ret+=dp[i][j]+base*pow16(i-1);        }        if(pos==7) ret+=dp[i][num]+base*pow16(i-1);        base+=val[num];        printf("i:%d pos:%d num:%d base:%lld ret:%lld\n",i,pos,num,base,ret);    }    return ret;}int main(){#ifndef ONLINE_JUDGE    //freopen("in.txt","r",stdin);    //freopen("out.txt","w",stdout);#endif    init();    char buf[233];    while(~scanf("%s",buf)){        st=toLL(buf);        cout<<"= ="<<cal(st)<<" normal "<<bruteForce(st)<<endl;    }    int T; sc(T);    while(T--){        int n;        scanf("%d %s",&n,buf);        st=toLL(buf);        ed=(st+n-1)%LIM;        debugHex(st);        debugHex(ed);        ll ans;        if(st<=ed){            ans=cal(ed)-cal(st-1);        }else{            ans=cal(LIM)-cal(st-1)+cal(ed-1);        }        printf("%lld\n",ans);    }    return 0;}

代码（按照题意）

#include <bits/stdc++.h>#define mem(a,b) memset(a,b,sizeof(a))#define rep(i,a,b) for(int i=a;i<b;i++)#define sc(a) scanf("%d",&a)const int INF=0x3f3f3f3f;const int maxn=2e5+50;const int mod=1e9+7;const double eps=1e-8;#define pii pair<int,int>typedef long long ll;typedef unsigned int ui;using namespace std;ll val[16]={6,2,5,5,4,5,6,3,7,6,6,5,4,5,5,4};inline ll pow16(ll i){    return (1ll<<(i*4));}inline char toChar(int x){    assert(x>=0 && x<16);    if(x>=0 && x<=9) return x+'0';    return x+'A'-10;}inline int toInt(char x){    if(x>='0' && x<='9') return x-'0';    return x-'A'+10;}ll bruteForce(int x){    ll ret=0;    while(x>=0){        char buf[66]={0};        sprintf(buf,"%08X",x);        rep(pos,0,8) ret+=val[toInt(buf[pos])];        x--;    }    return ret;}string toHex(ll x){    string ret="";    for(int i=0;i<8;i++){        ret=toChar(x%16)+ret;        x=x/16;    }    return ret;}ll toLL(char buf[]){    ll ret=0;    int len=strlen(buf);    rep(i,0,len) ret=ret*16+toInt(buf[i]);    return ret;}//dp i j len-i start-j tot-valll dp[9][16];//dp[i][0] start with 0 and have leading-zerosvoid init(){    mem(dp,0);    rep(i,0,16) dp[1][i]=val[i];    dp[1][16]=val[0];    rep(i,2,9){        ll num=pow16(i-1);        rep(j,0,16) dp[i][j]=val[j]*num+num/16*(i-1)*78;    }    //rep(i,1,5) rep(j,0,16) printf("%d %d %lld\n",i,j,dp[i][j]);}ll st,ed;ll LIM=0xFFFFFFFF;void debugHex(int x){    printf("%08X\n",x);}ll cal(ll x){    if(x<0) return 0;    if(x==0) return 6;    string buf=toHex(x);    int pos=0,num;    ll base=0,ret=0;    while(buf[pos]=='0') {        pos++;        base+=val[0];    }    for(;pos<8;pos++){        int i=8-pos;        num=toInt(buf[pos]);        ll sz=pow16(i-1);        rep(j,0,num){            ret+=dp[i][j]+base*sz;        }        if(pos==7) ret+=dp[i][num]+base*sz;        base+=val[num];        //printf("i:%d pos:%d num:%d base:%lld ret:%lld\n",i,pos,num,base,ret);    }    return ret;}int main(){#ifndef ONLINE_JUDGE    //freopen("in.txt","r",stdin);    //freopen("out.txt","w",stdout);#endif    init();    char buf[233];//    while(~scanf("%s",buf)){//        st=toLL(buf);//        cout<<"= ="<<cal(st)<<" normal "<<bruteForce(st)<<endl;//    }    int T; sc(T);    while(T--){        int n;        scanf("%d %s",&n,buf);        st=toLL(buf);        ed=(st+n-1)%LIM;//        debugHex(st);//        debugHex(ed);        ll ans;        if(st<=ed){            ans=cal(ed)-cal(st-1);        }else{            ans=cal(LIM)-cal(st-1)+cal(ed-1);        }        printf("%lld\n",ans);    }    return 0;}