Codeforces: 877E. Danil and a Part-time Job

0

Solution Idea:

Run a dfs on the given for getting the Euler tour order or inorder traversal order. Then the tree is converted to a liner 1D array. Now we can apply range query and update on this array.

Now use a range update query data structure. Here I have used segment tree. Now initialize the tree with the initial value and now our job is to just toggle a subtree of the given tree and perform query operation. Use a propagation for the update and answer the query.

```
#include &lt;bits/stdc++.h&gt;
#include &lt;ext/pb_ds/assoc_container.hpp&gt;
#include &lt;ext/pb_ds/tree_policy.hpp&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#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)             cerr&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#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(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define LINE_PRINT_CASE  printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;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;

//using namespace __gnu_pbds;
//typedef tree&lt;int, null_type, less&lt;int&gt;, rb_tree_tag, tree_order_statistics_node_update&gt; ordered_set;

/*----------------------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
/*------------------------------------------------*/

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

#define mx 200005
#define segment_tree int l=n*2,r=l+1,mid=(b+e)/2
pii info[mx];
vector&lt;int&gt;g[mx];
int cnt=0;
int maps[mx],ara[mx];

void dfs(int u, int par)
{
info[u].ff=++cnt;
maps[cnt]=u;
for(int i=0;i&lt;SZ(g[u]);i++)
{
int v=g[u][i];
if(v==par) continue;
dfs(v,u);
}
info[u].ss=cnt;
}

struct data
{
int val, prop;
};

data tree[3*mx];

void push_down(int n, int b, int e)
{
if(tree[n].prop%2)
{
segment_tree;
tree[l].val=(mid-b+1)-tree[l].val;
tree[l].prop++;
tree[r].val=(e-mid)-tree[r].val;
tree[r].prop++;
tree[n].prop=0;
}
}

void init(int n, int b, int e)
{
if(b==e)
{
tree[n].val=ara[maps[b]];
tree[n].prop=0;
return;
}
segment_tree;
init(l,b,mid);
init(r,mid+1,e);
tree[n].val=tree[l].val+tree[r].val;
}

void update(int n, int b, int e, int i, int j)
{
if(b&gt;j || e&lt;i) return;
if(b&gt;=i &amp;&amp; e&lt;=j)
{
tree[n].val=(e-b+1)-tree[n].val;
tree[n].prop++;
return;
}
push_down(n,b,e);
segment_tree;
update(l,b,mid,i,j);
update(r,mid+1,e,i,j);
tree[n].val=tree[l].val+tree[r].val;
}

int query(int n, int b, int e, int i, int j)
{
if(b&gt;j || e&lt;i) return 0;
if(b&gt;=i &amp;&amp; e&lt;=j) return tree[n].val;
push_down(n,b,e);
segment_tree;
int p=query(l,b,mid,i,j);
int q=query(r,mid+1,e,i,j);
return p+q;
}

char str[10];

int main()
{

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

int n;
sf(n);
for(int i=2;i&lt;=n;i++)
{
int a;
sf(a);
g[a].pb(i);
}

for(int i=1;i&lt;=n;i++) sf(ara[i]);
dfs(1,1);
init(1,1,n);
int q;
sf(q);
while(q--)
{
int a;
scanf(&quot; %s %d&quot;,str,&amp;a);
if(str[0]=='g')
{
int x=query(1,1,n,info[a].ff,info[a].ss);
printf(&quot;%d\n&quot;,x);
}
else
{
update(1,1,n,info[a].ff,info[a].ss);
}
}

return 0;
}

```

USACO: Cow Pedigrees

0

Solution Idea: http://zeffsalgo.blogspot.com/2013/12/usaco-training-problem-cow-pedigrees.html

```
/*
PROG: nocows
LANG: C++
*/
#include &lt;bits/stdc++.h&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#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&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#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(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define LINE_PRINT_CASE  printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;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
/*------------------------------------------------*/

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

int dp[205][102];

int func(int n, int level)
{
if(n==0 || level==0) return 0;
if(n==1) return 1;

int &amp;ret=dp[n][level];
if(ret!=-1) return ret;

int ans=0;

for(int i=1;i&lt;n-1;i++)
{
ans+=(func(i,level-1)*func(n-i-1,level-1))%9901;
ans%=9901;
}
return ret=ans;
}

int main()
{
freopen(&quot;nocows.in&quot;,&quot;r&quot;,stdin);
freopen(&quot;nocows.out&quot;,&quot;w&quot;,stdout);

int n,k;
sff(n,k);
ms(dp,-1);
printf(&quot;%d\n&quot;,(9901+func(n,k)-func(n,k-1))%9901);
return 0;
}

```

UVa 438 – The Circumference of the Circle

0

```
#include &lt;bits/stdc++.h&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#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&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#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(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define LINE_PRINT_CASE  printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;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
/*------------------------------------------------*/

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

double dist(double x1, double y1, double x2, double y2)
{
return sqrt(sqr(x1-x2)+sqr(y1-y2));
}

int main()
{

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

double x1,y1,x2,y2,x3,y3;
while(cin&gt;&gt;x1&gt;&gt;y1&gt;&gt;x2&gt;&gt;y2&gt;&gt;x3&gt;&gt;y3)
{
double a,b,c;

//calculating the three side of the triangle

a=dist(x1,y1,x2,y2);
b=dist(x2,y2,x3,y3);
c=dist(x1,y1,x3,y3);

// calculating the sub perimeter

double s=(a+b+c)/2.0;

// calculating the area of the triangle.

double area=sqrt(s*(s-a)*(s-b)*(s-c));

// calculating radius using formula area= (a*b*c)/(2*R) ; here R = diameter

double r=(a*b*c)/(4.0*area);

cout&lt;&lt;setprecision(2)&lt;&lt;fixed&lt;&lt;Pi*2.0*r&lt;&lt;endl;

}

return 0;
}

```

Light OJ : 1296 – Again Stone Game

0

Solution Idea: Just Find the pattern for smaller input and get AC 😛

```

#include &lt;bits/stdc++.h&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#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&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#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(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define LINE_PRINT_CASE  printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;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
/*------------------------------------------------*/

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

int main()
{

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

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

int ans=0;

for(int i=0;i&lt;n;i++)
{
int a;
sf(a);
while(a%2)
{
a/=2;
}
ans^=a/2;
}

PRINT_CASE;
if(ans)
pf(&quot;Alice\n&quot;);
else
pf(&quot;Bob\n&quot;);

}

return 0;
}

```

Light OJ: 1199 – Partitioning Game

0

```
#include &lt;bits/stdc++.h&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#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&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#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(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define LINE_PRINT_CASE  printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;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
/*------------------------------------------------*/

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

int dp[10005];

int func(int n)
{
if(n==1 || n==2) return 0;

if(dp[n]!=-1) return dp[n];

set&lt;int&gt;st;

int mid=n/2;
if(n%2==0) mid--;

for(int i=1;i&lt;=mid;i++)
{
st.insert(func(i)^func(n-i));
}

int ret=0;
while(st.find(ret)!=st.end()) ret++;
return dp[n]=ret;
}

int main()
{

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

ms(dp,-1);

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

int ans=0;

for(int i=0;i&lt;n;i++)
{
int a;
sf(a);
ans^=func(a);
}

PRINT_CASE;

if(ans)
pf(&quot;Alice\n&quot;);
else
pf(&quot;Bob\n&quot;);

}

return 0;
}

```

UVa : 10938 – Flea circus

0

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 &lt;bits/stdc++.h&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#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&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#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(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define LINE_PRINT_CASE  printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;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
/*------------------------------------------------*/

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

#define mx 5005
int n,q;

vector&lt;int&gt;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&lt;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&lt;=n;i++)
{
sparse_par[i][0]=par[i];
sparse_dis[i][0]=1;
}
sparse_dis[1][0]=0;

for(int j=1; 1&lt;&lt;j&lt;=n;j++)
{
for(int i=1;i&lt;=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]&lt;=level[q]) swap(p,q);

int log=log2(level[p]);

int ret=0;

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

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

for(int i=log;i&gt;=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&lt;int&gt;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&lt;SZ(g2[u]);i++)
return dfs1(g2[u][i],cnt-1);
}

int main()
{

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

while(sf(n) &amp;&amp; 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(&quot;The fleas jump forever between %d and %d.\n&quot;,min(aa,bb),max(aa,bb));

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

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

}

return 0;
}

```

UVa : 12238 – Ants Colony

0

```
#include &lt;bits/stdc++.h&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#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&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#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(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define LINE_PRINT_CASE  printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;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
/*------------------------------------------------*/

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

#define mx 100005

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

vector&lt;int&gt;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&lt;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&lt;n;i++)
{
sparse_par[i][0]=par[i];
sparse_sum[i][0]=dis[i];
}

for(int j=1;1&lt;&lt;j&lt;n;j++)
{
for(int i=0;i&lt;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]&lt;=level[q]) swap(p,q);

int log=log2(level[p]);

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

if(p==q) return ret;

for(int i=log;i&gt;=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(&quot;in.txt&quot;,&quot;r&quot;,stdin);
///freopen(&quot;out.txt&quot;,&quot;w&quot;,stdout);

while(sf(n) &amp;&amp; n)
{
for(int i=1;i&lt;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(&quot;%lld&quot;,ans);
test=0;
}
else
{
printf(&quot; %lld&quot;,ans);
}

}

printf(&quot;\n&quot;);

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

}

return 0;
}

```

Light OJ: 1081 – Square Queries

0

Solution Idea: Build a 2D sparse table for the given array. Then query the answer form the sparse table.

```
#include &lt;bits/stdc++.h&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#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&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#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(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;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
/*------------------------------------------------*/

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

int n,q;

int ara[505][505];
int sparse[505][505][16];

void build()
{
for(int k=0; (1&lt;&lt;k)&lt;=n; k++)
{
for(int i=0; i+(1&lt;&lt;k)-1&lt;n; i++)
for(int j=0; j+(1&lt;&lt;k)-1&lt;n; j++)
{
if(k==0)
sparse[i][j][k]=ara[i][j];
else
{
int a=1&lt;&lt;(k-1);
sparse[i][j][k]=max(max(sparse[i][j][k-1],sparse[i+a][j][k-1]),max(sparse[i][j+a][k-1],sparse[i+a][j+a][k-1]));
}
}
}
}

int main()
{

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

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

loop(i,n) loop(j,n) sf(ara[i][j]);

build();

PRINT_CASE;

while(q--)
{
int i,j,s;
sfff(i,j,s);
int k=log2(s);
int a=1&lt;&lt;k;
i--;
j--;
int ans=max(max(sparse[i][j][k],sparse[i+s-a][j][k]),max(sparse[i][j+s-a][k],sparse[i+s-a][j+s-a][k]));
pf(&quot;%d\n&quot;,ans);

}

}

return 0;
}

```

Light OJ: 1255 – Substring Frequency(Hash)

0

```
#include &lt;bits/stdc++.h&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#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&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#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(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;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
/*------------------------------------------------*/

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

/*---------------------Hashing---------------------*/

#define MH 1000006

#define Base1 10000019
#define Base2 10000079

#define MOD1 1000000007
#define MOD2 1000000009

ll B1[MH],B2[MH];

void init_hash()
{
B1[0]=B2[0]=1;
for(int i=1;i&lt;MH;i++)
{
B1[i]=(B1[i-1]*Base1)%MOD1;
B2[i]=(B2[i-1]*Base2)%MOD2;
}
}

struct Hash
{
pll H[MH];
int digit[MH];
int len;

Hash()
{
len=0;
H[0]=pll(0,0);
}

void clear()
{
len=0;
H[0]=pll(0,0);
}

void insert(char ch)
{
len++;
digit[len]=ch-'a'+1;
H[len].ff=(((H[len-1].ff*Base1)%MOD1)+digit[len])%MOD1;
H[len].ss=(((H[len-1].ss*Base2)%MOD2)+digit[len])%MOD2;
}

pll substr(int l, int r)
{
int sub_len=r-l+1;
pll ans;
ans.ff=(H[r].ff-((H[l-1].ff*B1[sub_len])%MOD1)+MOD1)%MOD1;
ans.ss=(H[r].ss-((H[l-1].ss*B2[sub_len])%MOD2)+MOD2)%MOD2;
return ans;
}

pll concate(pll h, int l, int r)
{
pll x=substr(l,r);
int sub_len=r-l+1;
h.ff=(((h.ff*B1[sub_len])%MOD1)+x.ff)%MOD1;
h.ss=(((h.ss*B2[sub_len])%MOD2)+x.ss)%MOD2;
return h;
}

bool operator==(const Hash&amp; p) const
{
return len==p.len &amp;&amp; H[len]==p.H[len];
}

pll &amp; operator[](int index)
{
return H[index];
}
};

Hash h1,h2;

int lcp(int id1, int id2, int l)
{
int lo=1,hi=l;
while(lo&lt;=hi)
{
int mid=(lo+hi)/2;
if(h1.substr(id1,id1+mid)==h2.substr(id2,id2+mid))
lo=mid+1;
else
hi=mid-1;
}
return hi;
}

/*------------------Hashing End---------- ----------*/

char text[MH],pattern[MH];

int main()
{

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

init_hash();
int t;
sf(t);
getchar();

TEST_CASE(t)
{
sc(&quot;%s %s&quot;,text,pattern);
int l1=strlen(text);
int l2=strlen(pattern);

h1.clear();
h2.clear();

for(int i=0;i&lt;l1;i++)
h1.insert(text[i]);
for(int i=0;i&lt;l2;i++)
h2.insert(pattern[i]);
int ans=0;

for(int i=0;i&lt;=l1-l2;i++)
{
if(h1.substr(i+1,i+l2)==h2[l2])
ans++;
}

PRINT_CASE;
pf(&quot;%d\n&quot;,ans);

}

return 0;
}

```