SPOJ KALTSUM – k Alternating Sum

0

Problem Link : http://www.spoj.com/problems/KALTSUM/

Solution Idea:

Break the problem into two cases: When k is greater than sqrt(n) and when k is less tahn or equal sqrt(n). Deal with them in different ways.

Case 1: For any k>sqrt(N) there will be less than sqrt(N) alternating segment. If you have an array, having cumulative sum, you can get the sum of a contiguous segment in O(1). So you can just loop over the alternating parts and get the sum in O(sqrt(N)) for a single query.

Case 2: Now when k <= sqrt(n), you need to do some preprocessing.

let arr[k][i] be the "k alternating sum" of a subarray which starts at position i and keeps alternating untill it reaches a position x such that if you add another segment of size k then it will go out of the array. [ This array can be computed in O(N) , and as you're doing it for every k < sqrt(n), the total complexity is O(N * sqrt(N))] With the help of this array, you can answer every query having k < sqrt(N) in O(1).

This solution idea is from this link.


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

ll dp[318][100005];
ll csum[100005];
ll ara[100005];

int main()
{

//    freopen("in.txt","r",stdin);
//	  freopen("out.txt","w",stdout);

    int n,q;

    sff(n,q);
    for(int i=1;i<=n;i++)
    {
        sfl(ara[i]);
        csum[i]=csum[i-1]+ara[i];
    }

    int root=ceil(sqrt(n));

    for(int i=1;i<=root;i++)
    {
        ll temp=0,sub=0;
        for(int j=n;j>=1;j--)
        {
            temp+=ara[j];
            if(j+i>n)
                sub=0;
            else
                sub=ara[j+i];
            temp-=sub;

            if(j+i-1>n)
                dp[i][j]=0;
            else
                dp[i][j]=temp-dp[i][j+i];
        }
    }
//
//    for(int i=1;i<=root;i++,cout<<endl)
//        for(int j=1;j<=n;j++)
//        cout<<dp[i][j]<<" ";

    while(q--)
    {
        int a,b,k;
        sfff(a,b,k);
        ll ans=0;
        if(k>root)
        {
            for(int i=a,j=0;i<=b;i+=k,j++)
            {
                if(j%2==0)
                    ans+=csum[i+k-1]-csum[i-1];
                else
                    ans-=csum[i+k-1]-csum[i-1];
            }
            pf("%lld\n",ans);
        }
        else
        {
            int turn=(b-a+1)/k;
            if(turn%2==1)
                pf("%lld\n",dp[k][a]+dp[k][b+1]);
            else
                pf("%lld\n",dp[k][a]-dp[k][b+1]);
        }
    }


    return 0;
}


Light OJ: 1348 – Aladdin and the Return Journey

0

Problem Link : http://lightoj.com:81/volume/problem/1348


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/


inline void inp( int &n )
{
    n=0;
    int ch=getchar_unlocked();
    int sign=1;
    while( ch < '0' || ch > '9' )
    {
        if(ch=='-')sign=-1;
        ch=getchar_unlocked();
    }
    while(  ch >= '0' && ch <= '9' )
        n = (n<<3)+(n<<1) + ch-'0', ch=getchar_unlocked();
    n=n*sign;
}


#define mx 30005

vector<int>g[mx];
int gini[mx];
int n;

int par[mx],level[mx], max_subtree[mx];
int sparse_par[mx][17];

int chain_head[mx],chain_indx[mx],chain_size[mx];
int node_serial[mx],serial_node[mx];
int chain_no,indx;

ll tree[mx];

int dfs(int u, int from, int cnt)
{
    sparse_par[u][0]=from;
    level[u]=cnt;
    int node=-1, maxi=0, total=1;
    for(int i=0; i<SZ(g[u]); i++)
    {
        int v=g[u][i];
        if(v!=from)
        {
            int temp=dfs(v,u,cnt+1);
            total+=temp;
            if(temp>maxi)
            {
                maxi=temp;
                node=v;
            }
        }
    }

    max_subtree[u]=node;
    return total;
}


void build_table(int n)
{
    for(int j=1; 1<<j<=n; j++)
    {
        for(int i=0; i<n; i++)
        {
            sparse_par[i][j]=sparse_par[sparse_par[i][j-1]][j-1];
        }
    }
}

int LCA_query(int p, int q)
{
    if(level[p]<=level[q]) swap(p,q);
    int log=log2(level[p]);

    for(int i=log; i>=0; i--)
    {
        if(level[p]-(1<<i)>=level[q])
            p=sparse_par[p][i];
    }
    if(p==q) return p;

    for(int i=log; i>=0; i--)
    {
        if(sparse_par[p][i]!=sparse_par[q][i])
        {
            p=sparse_par[p][i];
            q=sparse_par[q][i];
        }
    }

    return sparse_par[p][0];
}


void HLD(int u, int sz)
{
    if(chain_head[chain_no]==-1)
        chain_head[chain_no]=u;
    chain_indx[u]=chain_no;
    chain_size[chain_no]=sz;

    node_serial[u]=indx;
    serial_node[indx]=u;
    indx++;
    if(max_subtree[u]==-1) return ;

    HLD(max_subtree[u],sz+1);

    for(int i=0; i<SZ(g[u]); i++)
    {
        int v=g[u][i];
        if(v!=sparse_par[u][0] && v!=max_subtree[u])
        {
            chain_no++;
            HLD(v,1);
        }
    }
}


void update(int idx, int val)
{
    while(idx<=indx)
    {
        tree[idx]+=val;
        idx+=(idx&-idx);
    }
}

ll query(int a, int b)
{
    ll ret=0;
    ll ret2=0;
    while(b)
    {
        ret+=tree[b];
        b-=(b & -b);
    }
    a--;
    while(a)
    {
        ret2+=tree[a];
        a-=(a&-a);
    }
    return ret-ret2;
}


ll query_tree(int a, int b)
{
    ll ret=0;
    while(chain_indx[a]!=chain_indx[b])
    {
        ret+=query(node_serial[chain_head[chain_indx[a]]],node_serial[a]);
        a=sparse_par[chain_head[chain_indx[a]]][0];
    }
    ret+=query(node_serial[b],node_serial[a]);
    return ret;
}

void update_tree(int a, int val)
{
    update(node_serial[a],gini[a]*-1);
    update(node_serial[a],val);
    gini[a]=val;
}

inline void allclear(int n)
{
    chain_no=1;
    indx=1;
    for(int i=0; i<=n; i++)
    {
        g[i].clear();
    }

    ms(tree,0);
    ms(chain_head,-1);
}



int main()
{

//    freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);

    int t;
    scanf("%d",&t);
    TEST_CASE(t)
    {
        scanf("%d",&n);
        for(int i=0; i<n; i++) scanf("%d",&gini[i]);
        allclear(n+2);
        for(int i=1; i<n; i++)
        {
            int a,b;
            scanf("%d %d",&a,&b);
            g[a].pb(b);
            g[b].pb(a);
        }

        dfs(0,0,1);
        build_table(n);
        HLD(0,1);

        for(int i=1; i<indx; i++)
        {
            update(i,gini[serial_node[i]]);
        }


        int m;
        scanf("%d",&m);
        LINE_PRINT_CASE;
        while(m--)
        {
            int a,b;
            scanf("%d",&a);
            if(a==0)
            {
                scanf("%d %d",&a,&b);
                int lca=LCA_query(a,b);
                ll ans=query_tree(a,lca);
                ans+=query_tree(b,lca);
                ans-=gini[lca];
                printf("%lld\n",ans);
            }
            else
            {
                scanf("%d %d",&a,&b);
                update_tree(a,b);
            }
        }
    }


    return 0;
}


UVa : 10938 – Flea circus

0

Problem Link : http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=1879

Solution Idea: Find the LCA. Then find the middle node and middle+1 node on the path connection two nodes which are given in the query. Here I use an extra DFS to find the path on a reverse graph g2.


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

#define mx 5005
int n,q;

vector<int>g1[mx],g2[mx];

int sparse_par[mx][14],sparse_dis[mx][14];

int level[mx],par[mx];

void dfs(int u, int cnt, int from)
{
    par[u]=from;
    level[u]=cnt;
    g2[u].pb(from);

    for(int i=0;i<SZ(g1[u]);i++)
    {
        int v=g1[u][i];
        if(v!=from)
        {
            dfs(v,cnt+1,u);
        }
    }
}


void build_talbe()
{
    for(int i=1;i<=n;i++)
    {
        sparse_par[i][0]=par[i];
        sparse_dis[i][0]=1;
    }
    sparse_dis[1][0]=0;

    for(int j=1; 1<<j<=n;j++)
    {
        for(int i=1;i<=n;i++)
        {
            sparse_par[i][j]=sparse_par[sparse_par[i][j-1]][j-1];
            sparse_dis[i][j]=sparse_dis[i][j-1]+sparse_dis[sparse_par[i][j-1]][j-1];
        }
    }
}

int LCA;

int query(int p, int q)
{
    if(level[p]<=level[q]) swap(p,q);

    int log=log2(level[p]);

    int ret=0;

    for(int i=log;i>=0;i--)
    {
        if(level[p]-(1<<i)>=level[q])
        {
            ret+=sparse_dis[p][i];
            p=sparse_par[p][i];
        }
    }


    if(p==q){LCA=p; return ret;}

    for(int i=log;i>=0;i--)
    {
        if(sparse_par[p][i]!=sparse_par[q][i])
        {
            ret+=sparse_dis[p][i];
            ret+=sparse_dis[q][i];
            p=sparse_par[p][i];
            q=sparse_par[q][i];
        }
    }
    ret+=2;
    LCA=par[p];
    return ret;
}


vector<int>temp;

int dfs1(int u, int cnt)
{
    if(u==LCA) return u;
    temp.pb(u);
    if(cnt==0) return u;
    for(int i=0;i<SZ(g2[u]);i++)
        return dfs1(g2[u][i],cnt-1);
}

int main()
{

//    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);

    while(sf(n) && n)
    {
        loop(i,n-1)
        {
            int a,b;
            sff(a,b);
            g1[a].pb(b);
            g1[b].pb(a);
        }

        dfs(1,0,1);

        build_talbe();

        sf(q);

        while(q--)
        {
            int a,b;
            sff(a,b);

            int dis=query(a,b)+1;

            if(dis%2==0)
            {
                temp.clear();
                dfs1(a,n);
                temp.pb(LCA);
                int x=SZ(temp);
                dfs1(b,n);
                reverse(temp.begin()+x,temp.end());
                int aa=temp[(dis/2)-1];
                int bb=temp[dis/2];
                pf("The fleas jump forever between %d and %d.\n",min(aa,bb),max(aa,bb));

            }
            else
            {
                int p;
                if(level[a]>level[b])
                    p=a;
                else
                    p=b;
                pf("The fleas meet at %d.\n",dfs1(p,dis/2));
            }
        }

        for(int i=0;i<=n;i++)
        {
            g1[i].clear();
            g2[i].clear();
        }

    }


    return 0;
}


UVa : 12238 – Ants Colony

0

Problem Link : http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=3390


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

#define mx 100005

int n;
int level[mx],par[mx],dis[mx];

vector<int>g[mx],cost[mx];

ll sparse_par[mx][20],sparse_sum[mx][20];

void dfs(int u, int cnt, int from)
{
    par[u]=from;
    level[u]=cnt;

    for(int i=0;i<SZ(g[u]);i++)
    {
        int v=g[u][i];

        if(v!=from)
        {
            dis[v]=cost[u][i];
            dfs(v,cnt+1,u);
        }

    }

}


void build_table()
{
    for(int i=0;i<n;i++)
    {
        sparse_par[i][0]=par[i];
        sparse_sum[i][0]=dis[i];
    }

    for(int j=1;1<<j<n;j++)
    {
        for(int i=0;i<n;i++)
        {
            sparse_par[i][j]=sparse_par[sparse_par[i][j-1]][j-1];
            sparse_sum[i][j]=sparse_sum[i][j-1]+sparse_sum[sparse_par[i][j-1]][j-1];
//            D(i);
//            D(j);
//            D(sparse_par[i][j]);
//            D(sparse_sum[i][j]);
        }
    }

}


ll query(int p, int q)
{
    ll ret=0;
    if(level[p]<=level[q]) swap(p,q);

    int log=log2(level[p]);

    for(int i=log;i>=0;i--)
    {
        if(level[p]-(1<<i)>=level[q])
        {
            ret+=sparse_sum[p][i];
            p=sparse_par[p][i];
        }
    }

    if(p==q) return ret;

    for(int i=log;i>=0;i--)
    {
        if(sparse_par[p][i]!=sparse_par[q][i])
        {
            ret+=sparse_sum[p][i];
            ret+=sparse_sum[q][i];
            p=sparse_par[p][i];
            q=sparse_par[q][i];
        }
    }


    ret+=dis[p];
    ret+=dis[q];
    return ret;

}

int main()
{

//    freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);

    while(sf(n) && n)
    {
        for(int i=1;i<n;i++)
        {
            int a,b;
            sff(a,b);
            g[i].pb(a);
            g[a].pb(i);
            cost[a].pb(b);
            cost[i].pb(b);
        }

        dis[0]=0;

        dfs(0,0,0);

        build_table();

        int q;
        sf(q);

        bool test=1;

        while(q--)
        {
            int a,b;
            sff(a,b);

            ll ans=query(a,b);

            if(test)
            {
                printf("%lld",ans);
                test=0;
            }
            else
            {
                printf(" %lld",ans);
            }

        }

        printf("\n");

        for(int i=0;i<=n;i++)
        {
            g[i].clear();
            cost[i].clear();
        }

    }

    return 0;
}

SPOJ: LCA – Lowest Common Ancestor

0

Problem Link : http://www.spoj.com/problems/LCA/


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

int n,q;
int par[1005],level[1005];
vector<int>g[1005];
int sparse_par[1005][12];


void dfs(int u, int cnt, int from)
{
    par[u]=from;
    level[u]=cnt;

    for(int i=0;i<SZ(g[u]);i++)
    {
        int v=g[u][i];
        if(v!=from)
        {
            dfs(v,cnt+1,u);
        }
    }
}

void build_table()
{
    for(int i=1;i<=n;i++)
    {
        sparse_par[i][0]=par[i];
    }

    for(int j=1;1<<j<=n;j++)
    {
        for(int i=1;i<=n;i++)
        {
            sparse_par[i][j]=sparse_par[sparse_par[i][j-1]][j-1];
//            D(i);
//            D(j);
//            D(sparse_par[i][j]);
        }
    }
}

int query(int p, int q)
{
    if(level[p]<=level[q]) swap(p,q);
    int log=log2(level[p]);

    for(int i=log;i>=0;i--)
    {
        if(level[p]-(1<<i)>=level[q])
            p=sparse_par[p][i];
    }

    if(p==q) return p;

    for(int i=log;i>=0;i--)
    {
        if(sparse_par[p][i]!=sparse_par[q][i])
        {
            p=sparse_par[p][i];
            q=sparse_par[q][i];
        }
    }

    return par[p];

}

int main()
{

//    freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);

    int t;
    sf(t);
    TEST_CASE(t)
    {
        sf(n);

        for(int i=1;i<=n;i++)
        {
            int m,a;
            sf(m);
            for(int j=0;j<m;j++)
            {
                sf(a);
                g[a].pb(i);
                g[i].pb(a);
            }
        }

        dfs(1,0,1);

        build_table();

        sf(q);
        LINE_PRINT_CASE;
        while(q--)
        {
            int a,b;
            sff(a,b);
            printf("%d\n",query(a,b));
        }

        for(int i=0;i<=n;i++)
            g[i].clear();


    }

    return 0;
}


Light OJ: 1128 – Greatest Parent

0

Problem Link : http://lightoj.com:81/volume/problem/1128


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

int n,q;

int par[100005];
ll dis[100005];

int sparse_par[100005][20];


void build_talbe()
{
    ms(sparse_par,-1);
    for(int i=0; i<n; i++)
    {
        sparse_par[i][0]=par[i];
    }

    for(int j=1; 1<<j <n; j++)
    {
        for(int i=0; i<n; i++)
        {
            sparse_par[i][j]=sparse_par[sparse_par[i][j-1]][j-1];
        }
    }
}

ll query(int p, ll v)
{

    int log=log2(n);

    for(int i=log; i>=0; i--)
    {

//        int a=sparse_par[p][i];
//        int b=dis[sparse_par[p][i]];

        if(dis[sparse_par[p][i]]>=v)
        {
            p=sparse_par[p][i];
        }
    }

    return p;

}

int main()
{

//    freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);

    int t;
    sf(t);

    TEST_CASE(t)
    {
        sff(n,q);

        par[0]=0;
        dis[0]=1;

        loop1(i,n-1)
        {
            ll a,b;
            sffl(a,b);
            par[i]=a;
            dis[i]=b;
        }


        build_talbe();

        PRINT_CASE;

        while(q--)
        {
            ll a,b;
            sffl(a,b);
            printf("%d\n",query(a,b));
        }


    }

    return 0;
}


Light OJ: 1101 – A Secret Mission

0

Problem Link : http://lightoj.com:81/volume/problem/1101


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

typedef pair<int,pii > piii;

vector< piii > g1;

vector<int>g[50005],cost[50005];

int n,m;

int par[50004];

int find_par(int u)
{
    return par[u]=(par[u]==u)?u:find_par(par[u]);
}


int dis[50005],level[50005];

void dfs(int u, int cnt, int from)
{
    level[u]=cnt;
    par[u]=from;

    for(int i=0; i<SZ(g[u]); i++)
    {
        int v=g[u][i];

        if(level[v]==-1)
        {
            dis[v]=cost[u][i];
            dfs(v,cnt+1,u);
        }
    }

}

int sparse_par[50005][16];
int sparse_max[50005][16];

void build_table()
{

    ms(sparse_par,-1);

    for(int i=1; i<=n; i++)
        sparse_par[i][0]=par[i],sparse_max[i][0]=dis[i];

    for(int i=1; 1<<i <=n; i++)
    {
        for(int j=1; j<=n; j++)
            if(sparse_par[j][i-1]!=-1)
            {
                sparse_par[j][i]=sparse_par[sparse_par[j][i-1]][i-1];
                sparse_max[j][i]=max(sparse_max[j][i-1],sparse_max[sparse_par[j][i-1]][i-1]);
            }
    }


}

int query(int p, int q)
{
    int a=p,b=q;

    if(level[p]<level[q]) swap(p,q);

    int log=log2(level[p]);

    int ret=0;

    for(int i=log; i>=0; i--)
    {
        if(level[p]-(1<<i) >=level[q])
        {
            ret=max(ret,sparse_max[p][i]);
            p=sparse_par[p][i];
        }
    }

    if(p==q) return ret;

    for(int i=log; i>=0; i--)
        if(sparse_par[p][i]!=-1 && sparse_par[p][i]!=sparse_par[q][i])
        {
            ret=max(ret,max(sparse_max[p][i],sparse_max[q][i]));
            p=sparse_par[p][i],q=sparse_par[q][i];
        }
    ret=max(ret,max(dis[p],dis[q]));
    return ret;

}

int main()
{

    freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);



    int t;
    sf(t);
    TEST_CASE(t)
    {

        g1.clear();

        sff(n,m);
        for(int i=0; i<m; i++)
        {
            int a,b,c;
            sfff(a,b,c);
            g1.pb(piii(c,pii(a,b)));
        }

        sort(all(g1));

//        reverse(all(g1));

        int cnt=0;

        for(int i=1; i<=n; i++) par[i]=i,g[i].clear(),cost[i].clear();

        for(int i=0; i<SZ(g1) && cnt<n-1; i++)
        {
            int a=g1[i].ss.ff;
            int b=g1[i].ss.ss;
            int c=g1[i].ff;
            int u=find_par(a);
            int v=find_par(b);

            if(u!=v)
            {
                par[v]=u;
                g[a].pb(b);
                g[b].pb(a);
                cost[a].pb(g1[i].ff);
                cost[b].pb(g1[i].ff);
                cnt++;
            }
        }


        ms(level,-1);
        dis[1]=0;

        dfs(1,0,1);

        build_table();

        int q;
        sf(q);
        PRINT_CASE;

        while(q--)
        {
            int a, b;
            sff(a,b);
            printf("%d\n",query(a,b));
        }



    }

    return 0;
}