first

assgn1/160050063_1.cpp

+#include"iomanip"
+#include"iostream"
+#include"limits"
+#include"cmath"
+#include"vector"
+#include"algorithm"
+#include"list"
+#include"queue"
+#include"stack"
+#include"set"
+#include"unordered_set"
+#include"map"
+#include"unordered_map"
+#include"string"
+#include"cstring"
+#include"assert.h"
+using namespace std;
+#define ff first
+#define ss second
+#define all(v) v.begin(),v.end()
+#define mp make_pair
+#define pb push_back
+#define mset(a,b) memset(a,b,sizeof(a))
+typedef long long ll;
+typedef long double ld;
+typedef pair<int,int> pii;
+typedef pair<ll,ll> pll;
+
+const int maxn=1e7+2;
+const ll inf=1e17;
+int n;
+list<int>adj[maxn];
+ll va[maxn],cap[maxn];
+int dep[maxn];
+
+void df0(int x,int p=-1)
+{
+    if(x!=1)
+    {
+        dep[x]=1+dep[p];
+    }
+    for(int v:adj[x])
+    {
+        df0(v,x);
+    }
+}
+
+void df1(int x)
+{
+    for(int v:adj[x])
+    {
+        df1(v);
+    }
+    if(adj[x].size()<2)return;
+    for(int v:adj[x])
+    {
+        if(v==mxc)continue;
+        ll mi=
+    }
+}
+
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    cin>>n;
+    for(int i=2;i<=n;++i)
+    {
+        cin>>va[i]>>cap[i];
+    }
+    cap[1]=inf;
+    for(int i=2;i<=n;++i)
+    {
+        int x;
+        cin>>x;
+        adj[x].pb(i);
+    }
+    df0(1);
+}

assgn1/gen.cpp

+#include"iomanip"
+#include"iostream"
+#include"limits"
+#include"cmath"
+#include"vector"
+#include"algorithm"
+#include"list"
+#include"queue"
+#include"stack"
+#include"set"
+#include"unordered_set"
+#include"map"
+#include"unordered_map"
+#include"string"
+#include"cstring"
+#include"assert.h"
+using namespace std;
+#define ff first
+#define ss second
+#define all(v) v.begin(),v.end()
+#define mp make_pair
+#define pb push_back
+#define mset(a,b) memset(a,b,sizeof(a))
+typedef long long ll;
+typedef long double ld;
+typedef pair<int,int> pii;
+typedef pair<ll,ll> pll;
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    int n;
+    cin>>n;
+    cout<<n<<'\n';
+    for(int i=0;i<n-1;++i)
+    {
+        cout<<"1 1000000000\n";
+    }
+    for(int i=2;i<=n;)
+    {
+        cout<<i-1<<'\n';
+        i++;
+        if(i<=n)
+            cout<<i-2<<'\n';
+        i++;
+    }
+}

assgn1/rr.cpp

+#include <bits/stdc++.h>
+using namespace std;
+typedef long long ll;
+#define pb push_back
+#define mp make_pair
+#define ff first
+#define ss second
+// #define MAX 100005
+#define MAX 10000005
+#define MOD 1000000007
+typedef vector<int> vi;
+typedef pair<int, int> ip;
+
+// Program assumes that maximum value of n is 10^7
+vector<int> children[MAX],vd[MAX];
+int depth[MAX],parent[MAX],temp[MAX],vis[MAX];
+int max_depth = 0;
+bool dead[MAX];
+ll have[MAX],cap[MAX];
+queue<int> q;
+
+// int total = 0;
+
+// DFS to calculate depths
+void initdfs(int u){
+	max_depth = max(max_depth, depth[u]);
+	vd[depth[u]].pb(u);
+	for(int v: children[u]){
+		depth[v] = 1+depth[u];
+		initdfs(v);
+	}
+}
+
+/*
+ For each depth, calculate contribution of vertices at that depth to the root. 
+ Meanwhile, also reduce the graph made by above vertices by compressing straight-line paths.
+*/ 
+void compute(int d){
+	for(int u: vd[d])
+		q.push(u);
+
+	int cnt = 0;
+	while(!q.empty()){
+		int u = q.front();
+		q.pop();
+		if(u == 1)
+		    continue;
+		if((have[u] <= cap[u]) && !dead[parent[u]]){
+			have[parent[u]] += have[u];
+			++vis[parent[u]];	
+			if(vis[parent[u]] == 1){
+				q.push(parent[u]);	
+				temp[cnt++] = parent[u];
+			}
+		}
+		else
+			dead[u] = 1;
+		have[u] = 0;
+	}
+
+	// total += cnt;
+
+	for(int u: vd[d]){
+		while(parent[u]!=1  && vis[parent[u]]==1){
+			cap[u] = min(cap[u],cap[parent[u]]);
+			dead[u] |= dead[parent[u]];
+			parent[u] = parent[parent[u]];
+		}
+	}
+
+	for(int i=0;i<cnt;i++)
+		vis[temp[i]] = 0;
+}
+
+int main(){
+	ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
+	
+	int n;
+	cin>>n;
+	for(int i=2;i<=n;i++)
+		cin>>have[i]>>cap[i];
+	for(int i=2;i<=n;i++){
+		cin>>parent[i];
+		children[parent[i]].pb(i);
+	}
+	
+	memset(vis,0,sizeof(vis));
+	memset(dead,0,sizeof(dead));
+	have[1] = 0;
+	cap[1] = 1000000000000000000LL;
+	depth[1] = 0;
+	vis[1] = 1;
+	initdfs(1);
+	
+	for(int d=1;d<=max_depth;d++)
+		compute(d);
+
+	// verify number of steps (should give WA if greater)
+	// if(total > 3*n){
+	// 	cout<<"-1\n";
+	// 	return 0;
+	// }
+
+	cout<<have[1]<<"\n";
+}

assgn1/tg.cpp

+//By Tushar Gautam
+#pragma GCC optimize ("-Ofast")
+#include <bits/stdc++.h>
+using namespace std;
+#define fastio ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0)
+#define pb push_back
+#define mp make_pair
+#define fi first
+#define se second
+#define all(x) x.begin(),x.end()
+#define memreset(a) memset(a,0,sizeof(a))
+#define testcase(t) int t;cin>>t;while(t--)
+#define forstl(i,v) for(auto &i: v)
+#define forn(i,e) for(int i = 0; i < e; i++)
+#define forsn(i,s,e) for(int i = s; i < e; i++)
+#define rforn(i,s) for(int i = s; i >= 0; i--)
+#define rforsn(i,s,e) for(int i = s; i >= e; i--)
+#define leadzero(a) __builtin_clz(a) // count leading zeroes
+#define trailzero(a) __builtin_ctz(a) // count trailing zeroes
+#define bitcount(a) __builtin_popcount(a) // count set bits (add ll)
+#define ln "\n"
+#define dbgarr(v,s,e) cerr<<#v<<" = "; forsn(i,s,e) cerr<<v[i]<<", "; cerr<<endl
+#define inputfile freopen("input.txt", "r", stdin)
+#define outputfile freopen("output.txt", "w", stdout)
+#define dbg(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); \
+stringstream _ss(_s); istream_iterator<string> _it(_ss); err(_it, args); }
+void err(istream_iterator<string> it) { cerr<<endl; }
+template<typename T, typename... Args>
+void err(istream_iterator<string> it, T a, Args... args) {
+	cerr << *it << " = " << a << "\t"; err(++it, args...);
+}
+template<typename T1,typename T2>
+ostream& operator <<(ostream& c,pair<T1,T2> &v){
+	c<<"("<<v.fi<<","<<v.se<<")"; return c;
+}
+template <template <class...> class TT, class ...T>
+ostream& operator<<(ostream& out,TT<T...>& c){
+    out<<"{ ";
+    forstl(x,c) out<<x<<" ";
+    out<<"}"; return out;
+}
+typedef long long int  ll;
+typedef long double  ld;
+typedef pair<ll,ll> p64;
+typedef pair<int,int> p32;
+typedef pair<int,p32> p96;
+typedef vector<ll> v64;
+typedef vector<int> v32; 
+typedef vector<v32> vv32;
+typedef vector<v64> vv64;
+typedef vector<p32> vp32;
+typedef vector<vp32> vvp32;
+typedef map<int,int> m32;
+const int LIM = 1e5+5, MOD = 1e9+7;
+int t,n,m,k,x,y;
+v64 v,c,best,totval,neig,blkin;
+vv32 g;
+int updsz(int i){
+	int curr=0;
+	forstl(it,g[i]){
+		auto l=1+updsz(it);
+		if(l>curr) best[i]=it,curr=l;
+	}
+	return curr;
+}
+void getneig(int i){
+	forstl(it,g[i]) if(it!=best[i]) neig[it]=best[i];
+	if(best[i]){
+		if(neig[i]) neig[best[i]]=best[neig[i]];
+		else neig[best[i]]=0;
+	}
+	forstl(it,g[i]) getneig(it);
+}
+ll fans=0,gin=0;
+void mainreduce(int i,ll cmin1,ll cmin){
+	// dbg("mainreduce",i,cmin);
+	// dbg(totval); dbg(c); dbg(blkin);
+	cmin=min(cmin,c[i]);
+	if(totval[i]>cmin) totval[i]=0,cmin=0;
+	if(neig[i]!=0){
+		//dbg(neig[i],totval[i],cmin1, gin);
+		if(c[neig[i]]<totval[neig[i]] && blkin[neig[i]]!=gin){
+			totval[neig[i]]=0; //dbg(2);
+			if(best[neig[i]]) c[best[neig[i]]]=0,blkin[best[neig[i]]]=blkin[neig[i]];
+			c[neig[i]]=cmin1; 
+		}
+		totval[neig[i]]+=totval[i];
+		if(totval[neig[i]]>cmin1){
+			c[neig[i]]=0; blkin[neig[i]]=gin; //dbg(1);
+		}else{
+			if(best[neig[i]]) c[best[neig[i]]]=min(c[best[neig[i]]],c[neig[i]]);
+			c[neig[i]]=cmin1; blkin[neig[i]]=gin;
+		}
+	}
+	if(best[i]) mainreduce(best[i],cmin1,cmin);
+}
+void reduce(int i,ll cmin){
+	//dbg("reduce",i,cmin);
+	//dbg(totval); dbg(c); dbg(blkin);
+	if(cmin==0 || v[i]>c[i]) c[i]=0,cmin=0,blkin[i]=-1;
+	else totval[i]=v[i],cmin=c[i];
+	c[i]=min(c[i],cmin);
+	forstl(it,g[i]) reduce(it,cmin);
+	if(g[i].size()>1){
+		gin=i;
+		forstl(it,g[i]) if(it!=best[i]) mainreduce(it,c[i],1e17);
+	}
+}
+void solve(int i,ll cmin){
+//	dbg(i,cmin);
+	if(cmin<totval[i]) totval[i]=0,cmin=0;
+	if(best[i]) solve(best[i],min(c[best[i]],cmin));
+	if(neig[i]==0) fans+=totval[i];
+}
+int main(){
+	fastio;
+	cin>>n;
+	v.resize(n); c.resize(n); c[0]=1e17; v[0]=0;
+	forsn(i,1,n) cin>>x>>y,v[i]=x,c[i]=y;
+	g.assign(n,v32(0)); best.assign(n,0); neig.assign(n,0);
+	forsn(i,1,n) cin>>x,--x,g[x].pb(i);
+	updsz(0); //dbg(best);
+	getneig(0); //dbg(neig);
+	totval.assign(n,0);blkin.assign(n,-2);
+	reduce(0,c[0]); solve(0,c[0]);
+	cout<<fans<<ln;
+	return 0;
+}

assgn12/160050063_12.cpp

+#include"iomanip"
+#include"iostream"
+#include"limits"
+#include"cmath"
+#include"vector"
+#include"algorithm"
+#include"list"
+#include"queue"
+#include"stack"
+#include"set"
+#include"unordered_set"
+#include"map"
+#include"unordered_map"
+#include"string"
+#include"cstring"
+#include"assert.h"
+using namespace std;
+#define ff first
+#define ss second
+#define all(v) v.begin(),v.end()
+#define mp make_pair
+#define pb push_back
+#define mset(a,b) memset(a,b,sizeof(a))
+typedef long long ll;
+typedef long double ld;
+typedef pair<int,int> pii;
+typedef pair<ll,ll> pll;
+
+const int maxn = 1e5+3;
+
+int T[4*maxn];
+int a[maxn];
+
+void init(int v, int tl, int tr)
+{
+    if(tl == tr)
+    {
+        T[v] = a[tl];
+        return;
+    }
+    int tm = (tl + tr)/2;
+    init(2*v, tl, tm);
+    init(2*v+1, tm+1, tr);
+    T[v] = T[2*v];
+    if(T[2*v+1] < T[v])
+    {
+        T[v] = T[2*v+1];
+    }
+}
+void update(int v, int tl, int tr, int ind)
+{
+    if(ind<tl||ind>tr)return;
+    if(tl == tr && tr == ind)
+    {
+        T[v] = a[ind];
+        return;
+    }
+    int tm = (tl+tr)/2;
+    if(ind<=tm)update(2*v,tl,tm,ind);
+    else update(2*v+1,tm+1, tr, ind);
+    T[v] = T[2*v];
+    if(T[2*v+1] < T[v])
+    {
+        T[v] = T[2*v+1];
+    }
+}
+int query(int v,int tl, int tr, int l, int r, int x)
+{
+    //cout<<v<<' '<<tl<<' '<<tr<<' '<<l<<' '<<r<<' '<<x<<" v tl tr l r x\n";
+    if(T[v]>x)return -1;
+    if(tl == tr && tr == l && l == r)
+    {
+        if(T[v] <= x)
+        {
+            return tl;
+        }
+        else return -1;
+    }
+    int tm = (tl+tr)/2;
+    int ans1 = -1, ans2 = -1;
+    if(l>= tm+1)
+    {
+        return ans2 = query(2*v+1, tm+1, tr, l, r, x);
+    }
+    if(r<=tm)
+    {
+        return ans1 = query(2*v, tl, tm, l, r, x);
+    }
+    if(T[2*v+1]<=x)
+        return ans2 = query(2*v+1, tm+1, tr, tm+1, r, x);
+    else
+        return ans1 = query(2*v, tl, tm, l, tm, x);
+}
+
+void pr(int n)
+{
+    for(int i=0;i<n;++i)
+    {
+        cout<<a[i]<<' ';
+    }
+    cout<<'\n';
+}
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    int n,m;
+    cin>>n>>m;
+    for(int i=0;i<n;++i)cin>>a[i];
+    init(1,0,n-1);
+    while(m--)
+    {
+        char ch;
+        int i,x;
+        cin>>ch;
+        if(ch == 'A')
+        {
+            cin>>i>>x;
+            a[i] = x;
+            update(1, 0, n-1, i);
+        }
+        else if(ch == 'I')
+        {
+            cin>>i>>x;
+            cout<<query(1,0,n-1,0,i,x)<<'\n';
+        }
+        else
+        {
+            cin>>x;
+            cout<<"0\n";
+        }
+    }
+}
+
+
+

assgn12/test.py

+import random
+from datetime import datetime
+dt = datetime.now()
+see = dt.microsecond
+n = 100000
+m = 100000
+MAX = 10**9
+p = 0.1
+random.seed(see)
+print(n,m)
+a = [0 for _ in range(n)]
+for i in range(n):
+	a[i] = random.randint(0,MAX)
+	print(a[i])
+
+for i in range(m):
+	idx = random.randint(0,n-1)
+	x = random.randint(0,MAX)
+	if random.random() < p:
+		print("A",idx,x)
+	else:
+		print("I",idx,x)
+

assgn2/160050063_2.cpp

+#include"iomanip"
+#include"iostream"
+#include"limits"
+#include"cmath"
+#include"vector"
+#include"algorithm"
+#include"list"
+#include"queue"
+#include"stack"
+#include"set"
+#include"unordered_set"
+#include"map"
+#include"unordered_map"
+#include"string"
+#include"cstring"
+#include"assert.h"
+using namespace std;
+#define ff first
+#define ss second
+#define all(v) v.begin(),v.end()
+#define mp make_pair
+#define pb push_back
+#define mset(a,b) memset(a,b,sizeof(a))
+typedef long long ll;
+typedef long double ld;
+typedef pair<int,int> pii;
+typedef pair<ll,ll> pll;
+
+const int maxn=1e6+2;
+ll sho[maxn][21];
+list<pii> adj[maxn];
+int n,m,k,s,t;
+
+struct node
+{
+    ll len;
+    int ve,sk;
+    node()
+    {}
+    node(ll a,int b,int c):
+        len(a),ve(b),sk(c)
+    {}
+    bool operator<(const node & ob)const
+    {
+        return len>ob.len;
+    }
+};
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    cin>>n>>m>>k>>s>>t;
+    for(int i=0;i<m;++i)
+    {
+        int x,y,z;
+        cin>>x>>y>>z;
+        adj[x].pb(mp(y,z));
+    }
+    if(s==t)
+    {
+        cout<<"0\n";
+        return 0;
+    }
+    for(int i=1;i<=n;++i)
+    {
+        for(int j=0;j<21;++j)
+            sho[i][j]=1e17;
+    }
+    for(int i=0;i<=20;++i)
+    {
+        sho[s][i]=0;
+    }
+    priority_queue<node>qq;
+    qq.push(node(0,s,0));
+    while(!qq.empty())
+    {
+        auto xx=qq.top();
+        qq.pop();
+        if(xx.len!=sho[xx.ve][xx.sk])
+        {
+            continue;
+        }
+        int v=xx.ve;
+        for(auto ed:adj[v])
+        {
+            ll te1=sho[v][xx.sk]+ed.ss;
+            if(te1<sho[ed.ff][xx.sk])
+            {
+                sho[ed.ff][xx.sk]=te1;
+                qq.push(node(te1,ed.ff,xx.sk));
+            }
+            ll te2=sho[v][xx.sk];
+            if(xx.sk<20&&te2<sho[ed.ff][xx.sk+1])
+            {
+                sho[ed.ff][xx.sk+1]=te2;
+                qq.push(node(te2,ed.ff,xx.sk+1));
+            }
+        }
+    }
+    ll ans=sho[t][0];
+    for(int i=1;i<=k;++i)
+    {
+        if(sho[t][i]<ans)
+        {
+            ans=sho[t][i];
+        }
+    }
+    cout<<ans<<'\n';
+}

assgn2/in

+4 4 1 1 4
+1 2 1
+1 3 2
+2 4 4
+3 4 2

assgn2/in1

+4 3 1 1 4
+1 2 1
+2 3 1
+3 4 1

assgn3/160050063_3.cpp

+#include"iomanip"
+#include"iostream"
+#include"limits"
+#include"cmath"
+#include"vector"
+#include"algorithm"
+#include"list"
+#include"queue"
+#include"stack"
+#include"set"
+#include"unordered_set"
+#include"map"
+#include"unordered_map"
+#include"string"
+#include"cstring"
+#include"assert.h"
+using namespace std;
+#define ff first
+#define ss second
+#define all(v) v.begin(),v.end()
+#define mp make_pair
+#define pb push_back
+#define mset(a,b) memset(a,b,sizeof(a))
+typedef long long ll;
+typedef long double ld;
+typedef pair<int,int> pii;
+typedef pair<ll,ll> pll;
+
+const int maxn = 100+3;
+int n;
+pll re[maxn];
+ll grundy[maxn];
+list<pair<ll,pll> > ans;
+ll grnd(ll x, ll y)
+{
+    assert(x>=y);
+    if(y==0)
+    {
+        return x;
+    }
+    if(y==1)
+    {
+        if(x%2==1)
+        {
+            return x+1;
+        }
+        return x-1;
+    }
+    if(y==2)
+    {
+        x-=y;
+        if(x%2==0)
+        {
+            x/=2;
+            return 2*x+3;
+        }
+        x/=2;
+        if(x==0||x==1)
+        {
+            return 3*x+1;
+        }
+        return 2*x+2;
+    }
+    else
+    {
+        x-=y;
+        if(x%2==0)
+        {
+            ll init = y*2 -(y/2);
+            return init + x;
+        }
+        x/=2;
+        ll terms=(y+2)/2;
+        if(x<terms)
+        {
+            return 3*x+1;
+        }
+        ll lastterm=(terms-1)*3+1;
+        ll xleft = x -terms;
+        return lastterm + (xleft+1)*2;
+    }
+}
+void ne(int i, ll x, ll y)
+{
+    ans.pb(mp(i,mp(x,y)));
+}
+void calc(int i, ll x, ll y, ll newgr)
+{
+    ll posonxy=  (newgr*2)/3;
+    if(posonxy<= y && posonxy<x && grnd(posonxy,posonxy)==newgr)
+    {
+        ne(i,posonxy,posonxy);
+    }
+    if(x>y)
+    {
+        ll in1=y+1,in2=y+2;
+        ll hi = x-1;
+        if(in1%2!=hi%2)hi--;
+        while(in1<=hi)
+        {
+            ll m=(in1+hi)/2;
+            if(m%2!=in1%2)m--;
+            ll val = grnd(m,y);
+            if(val==newgr)
+            {
+                ne(i,m,y);
+                break;
+            }
+            if(val<newgr)
+            {
+                in1=m+2;
+            }
+            else
+            {
+                hi = m - 2;
+            }
+        }
+        hi = x-1;
+        if(in2%2!=hi%2)hi--;
+        while(in2<=hi)
+        {
+            ll m=(in2+hi)/2;
+            if(m%2!=in2%2)m--;
+            ll val = grnd(m,y);
+            if(val==newgr)
+            {
+                ne(i,m,y);
+                break;
+            }
+            if(val<newgr)
+            {
+                in2 = m+2;
+            }
+            else
+            {
+                hi = m-2;
+            }
+        }
+    }
+    ll hi1 = y-1,hi2=y-2;
+    if(hi1<0)return;
+    if(hi1%2!=(x-1)%2)
+    {
+        swap(hi1,hi2);
+    }
+    ll lo=0;
+    if(lo%2!=hi1%2)lo++;
+    while(lo<=hi1)
+    {
+        ll m=(lo+hi1)/2;
+        if(m%2!=lo%2)m--;
+        ll val = grnd(x,m);
+        if(val == newgr)
+        {
+            ne(i,x,m);
+            break;
+        }
+        if(val>newgr)
+        {
+            lo = m+2;
+        }
+        else
+        {
+            hi1 = m-2;
+        }
+    }
+    lo = 0;
+    if(hi2<0)return;
+    if(lo%2!=hi2%2)lo++;
+    while(lo<=hi2)
+    {
+        ll m=(lo+hi2)/2;
+        if(m%2!=lo%2)m--;
+        ll val =grnd(x,m);
+        if(val == newgr)
+        {
+            ne(i,x,m);
+            break;
+        }
+        if(val>newgr)
+        {
+            hi2 = m-2;
+        }
+        else
+        {
+            lo = m+2;
+        }
+    }
+}
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    /*
+    int i;ll x,y,newg;
+    cin>>i>>x>>y>>newg;
+    calc(i,x,y, newg);
+    for(auto &f:ans)
+    {
+        cout<<f.ff<<' '<<f.ss.ff<<' '<<f.ss.ss<<'\n';
+    }
+    return 0;
+    */
+    /*
+    int m;
+    cin>>m;
+    for(int j=m-1;j>=0;--j)
+    {
+        for(int i=0;i<m;++i)
+        {
+            if(i>=j)
+            {
+                if(grnd(i,j)<10)
+                {
+                    cout<<' '<<grnd(i,j)<<' ';
+                }
+                else
+                {
+                    cout<<grnd(i,j)<<' ';
+                }
+            }
+            else cout<<"   ";
+        }
+        cout<<'\n';
+    }
+    return 0;
+    */
+    cin>>n;
+    ll gxor=0;
+    for(int i=0;i<n;++i)
+    {
+        ll x,y;
+        cin>>x>>y;
+        re[i].ff=x;
+        re[i].ss=y;
+        grundy[i]=grnd(x,y);
+        gxor = gxor^grundy[i];
+    }
+    if(gxor==0)
+    {
+        cout<<"0\n";
+        return 0;
+    }
+    for(int i=0;i<n;++i)
+    {
+        ll newgr=gxor^grundy[i];
+        calc(i,re[i].ff,re[i].ss,newgr);
+    }
+    cout<<ans.size()<<'\n';
+    for(auto &x:ans)
+    {
+        ll a=x.ss.ff, b=x.ss.ss;
+        assert(a>=b);
+        cout<<x.ff<<' '<<a<<' '<<b<<'\n';
+    }
+}

assgn3/Assignment3/Assignment3/Input/i1.txt

+100
+1692768257 492739943
+783279169 498237273
+1848774861 835107658
+2127360904 418200384
+1920723587 1099474625
+627145005 576359559
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+1351474472 273131673
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+1890880920 1572614134
+1844506509 1694452318
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+1474270931 405218231
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+948789114 913251289
+1232560023 1009047599
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+855535484 327533535
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+401086167 104040836
+953495417 562641994
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+1447153164 430042817
+2050925073 637683914
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+636857449 604648695
+2027121358 437999261
+1565711969 604251
+1803936292 583131298
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+1611285775 35744584
+1954311973 1111231755
+580093799 358949346
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+1925725560 943442983
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+1942670347 1522149573
+1150401083 119153041
+2008590856 995728040
+2091069599 1036867238
+1945357308 181749981
+1064727739 950184633
+2045362569 1637959654
+462820324 0

assgn3/Assignment3/Assignment3/Input/i2.txt

+35
+1692835485 1622640939
+831428520 143044611
+1582136302 1116576084
+1516313475 822310560
+1359739835 492135376
+1773919118 743144925
+1512513892 271863523
+1910169151 1057053305
+1479881854 218720624
+1693007551 219586907
+1220240403 111624371
+1855881545 1317579566
+1748637787 1041576914
+1643986901 963242805
+1490092549 31179729
+1261782657 51695435
+1759191540 380102074
+197075352 177360884
+1931910463 825657390
+1813892648 415882124
+1819070730 1544560418
+644620390 79895615
+1029585211 628321930
+1962897398 772782972
+1828759214 182313348
+1170153834 120248812
+1626339674 239671457
+1046765245 719041902
+797436491 69663310
+1529291211 452663555
+1713095981 690897338
+1448523933 467480437
+1467119539 470857119
+2071728190 218359838
+2345210196 0

assgn3/Assignment3/Assignment3/Input/i3.txt

+5
+1692936327 1170008786
+1977394370 1757739265
+1538778723 108436640
+1673484155 1428475824
+1895304845 0

assgn3/Assignment3/Assignment3/Input/i4.txt

+100
+1696717902 302430401
+2001440805 31763027
+1265250333 679274137
+1124933714 537353107
+1175182862 314903010
+891260175 711323400
+1482787418 170920951
+1807894538 537378763
+1890066376 1556134106
+1165675574 767475008
+1495670184 16060637
+1707340707 1432694353
+598771335 441457503
+1081956326 20252536
+2125034947 1695931933
+1407268591 661820972
+1725804526 1682532100
+1962535050 252341004
+1353855657 1125251077
+1662787234 1260343427
+1960767228 1478237781
+504073124 134007653
+1703761915 579556307
+1764512604 1561654005
+1422959334 173728401
+1299633546 884833985
+560071330 80530420
+2041400849 698018509
+1625324671 839755657
+1508588746 510799115
+1860822132 1659117540
+1033221263 796997599
+1283140054 704104404
+1984322851 1247823058
+1680366513 93118847
+837228719 362542294
+1862290220 990225089
+2085056162 900762988
+1511311613 177702975
+1651631495 596915343
+1990587226 1460054664
+1748225594 151770769
+1739532537 556300104
+687303199 480979101
+1245932277 190328380
+1917184748 270737642
+1279420048 458989325
+1270934245 472325251
+1719502653 993651292
+1464425572 290510337
+1376904328 347260624
+1696238669 837895958
+1467092727 20227835
+1449175487 666806619
+1680369382 410761577
+1657383181 628737830
+1577165570 1031080069
+1449043004 1317172040
+1601211248 1439864579
+2034421324 1958244857
+284564934 236763869
+1375416816 3148392
+1613954789 1116450204
+872193466 232208640
+1918417490 752825881
+794063739 523278372
+1874221622 1365878915
+1391520876 752666758
+1194447102 395311158
+1827712335 755127657
+1949661076 1648218406
+1215186989 1078241153
+1532045085 752816065
+1753439978 147622465
+1130310781 747156970
+492954905 101178209
+1842593886 1761252262
+1944822016 452177186
+1922515572 680265842
+442443050 25069866
+1551955436 378636390
+747760669 539261639
+989376333 482150010
+1865316075 1039417939
+1489048825 1400993619
+1884804789 1816663284
+382811826 57353170
+1862054334 268003807
+2118982274 1066776490
+2013760917 937455299
+1871175901 1102841439
+1199770330 524708016
+1815974627 1047964825
+1631424728 284198600
+522239272 509779215
+1546998622 821325725
+2144060806 454369782
+264940706 141077342
+1124845511 979958836
+1629492965 1116067809

assgn3/Assignment3/Assignment3/Input/i5.txt

+87
+1714806646 1696801937
+1524756582 661514023
+882846850 543344042
+1971737163 1042490827
+1166341684 473953172
+1993546931 714115081
+1854002628 503408823
+1930023984 234450826
+1972725021 172611153
+1883388634 589401914
+279901441 203814858
+1314331957 960408257
+1804344874 1094484547
+1660906775 1007718031
+1867723719 1064077034
+1846381869 1001373133
+248904792 44694788
+1713509113 1191955921
+1475705031 885816814
+1566551894 888170238
+1290872906 318359769
+1821129148 1780653392
+1360015032 109454752
+2104187803 323706225
+1813923825 954445724
+1719472456 939873963
+1364377403 486130313
+1681774652 260629555
+1888332049 406814350
+1683412177 11409614
+835644521 635337915
+2075104072 134413067
+1713171375 1139710824
+1958044296 811076244
+1679725399 324757531
+1443876490 666956330
+1817884617 936912050
+1592744764 1330724546
+877588693 715475655
+1238394032 276989100
+1758740651 1189204049
+550523511 322148914
+2056752571 1289098101
+2033904278 1943678685
+184507400 49485532
+911323069 627164935
+1675256441 753450279
+1764657487 376908070
+1849218939 1439368389
+455808763 61230468
+1076517815 703710892
+605191451 485190730
+1863357331 970164765
+1804087472 692637916
+1468183803 976529911
+1178072991 73534397
+2005366356 1089513354
+1900439906 1583989274
+1576782927 1169218311
+1287389737 1042450109
+1261566234 1037648007
+1528889562 35356362
+1405032179 645650041
+660747643 205370796
+1033005006 547697264
+1457333494 1353039623
+832605678 600186294
+1259722687 600353299
+1979434718 117924636
+1690129749 1244492574
+1843453085 1169424326
+744309738 521522791
+1352784930 846947721
+1918208566 1128734531
+2080728517 1306859998
+1830924111 1180477471
+1758645210 1048355714
+1732610809 111613543
+1230598701 1135593370
+475439092 257363450
+2065652404 1199316626
+633022440 574161842
+1573860892 1294052523
+1323931745 1242771648
+1599784201 837137214
+1077805767 656963524
+1798946860 1372518641

assgn3/Assignment3/Assignment3/Input/i6.txt

+45
+1696902779 1262174493
+523238785 128725030
+1556630835 965546681
+2128907843 1648656091
+1779961191 1329074634
+1360534427 96241333
+472897540 151977233
+923298748 165224414
+2071915395 230370527
+1234707660 597160659
+1288113382 538965867
+313303623 64089317
+1259843672 3835884
+1496653855 45192978
+1508914456 785383674
+690874569 84801854
+1483102217 656270390
+1126254425 460433738
+2042157120 1037256317
+1451069486 1300555870
+1353947924 1066035056
+750151173 395119271
+2061756721 149081855
+1652804583 985652536
+994591026 173319594
+1432548433 78665734
+1402346914 611557773
+1679719945 594756269
+569643343 233092153
+791775032 513567475
+1554286012 893921576
+1890844922 344333420
+1635561552 967595748
+1980160692 1092322864
+1275007129 1006672885
+1452987337 1321622922
+1973941893 1093089133
+1714016795 1134632707
+1360802871 117121189
+1611064526 313012347
+1687667106 657040966
+831267929 526602688
+1738958968 1578423153
+692441080 643348467
+761233085 177522224

assgn3/Assignment3/Assignment3/Input/i7.txt

+5
+1696970007 244591842
+1921016015 571388136
+1289992276 1247015107
+2052766267 1517860414
+1218977439 721735385

assgn3/Assignment3/Assignment3/Input/i8.txt

+1
+1697020428 1092017589

assgn3/Assignment3/Assignment3/Output/o1.txt

+0

assgn3/Assignment3/Assignment3/Output/o2.txt

+0

assgn3/Assignment3/Assignment3/Output/o3.txt

+0

assgn3/Assignment3/Assignment3/Output/o4.txt

+26
+8 565025544 565025544
+11 1190752235 1190752235
+11 157575291 1707340707
+14 2125034947 1283867758
+16 1725804526 618385669
+30 505312025 505312025
+37 2085056162 508603481
+40 493046929 493046929
+69 419532723 1827712335
+70 1949661076 883399053
+76 1842593886 854763083
+77 250901368 1944822016
+78 344805912 1922515572
+83 166952089 1865316075
+84 673917402 673917402
+84 1065406761 1489048825
+88 559750782 559750782
+88 2118982274 879459855
+89 592607390 592607390
+89 2013760917 471877494
+90 595007584 595007584
+90 1871175901 172306298
+92 634569055 634569055
+92 175465075 1815974627
+99 673266345 673266345
+99 780612139 1629492965

assgn3/Assignment3/Assignment3/Output/o5.txt

+21
+3 1302711336 1042490827
+5 88418646 88418646
+9 612082627 589401914
+13 1039335208 1007718031
+15 1093011692 1001373133
+17 1308867596 1191955921
+21 191749194 191749194
+23 53350217 53350217
+33 981185071 811076244
+37 58890607 58890607
+40 1363320304 1189204049
+42 194828612 194828612
+48 1739010824 1439368389
+52 91499877 91499877
+53 44412525 44412525
+56 225611543 225611543
+57 399129059 399129059
+58 1202779128 1169218311
+75 109142007 109142007
+76 131640171 131640171
+80 1524089367 1199316626

assgn3/Assignment3/Assignment3/Output/o6.txt

+18
+2 330774233 330774233
+5 339439688 96241333
+13 337533700 45192978
+14 290527194 290527194
+16 72530595 72530595
+18 1344277586 1037256317
+19 357465282 357465282
+20 1353947924 785456431
+24 15944884 15944884
+25 256478802 78665734
+26 22178368 22178368
+27 310103849 310103849
+30 602752391 602752391
+31 1117752161 344333420
+32 681996603 681996603
+34 484624479 484624479
+39 224820999 224820999
+40 327328330 327328330

assgn3/Assignment3/Assignment3/Output/o7.txt

+3
+0 216318115 216318115
+1 536421381 536421381
+4 93109621 93109621

assgn3/Assignment3/Assignment3/Output/o8.txt

+1
+0 0 0

assgn3/Assignment3/Assignment3/testcases.cpp

+#include <stdio.h>
+#include <stdlib.h> 
+#include <time.h>
+#include <algorithm>
+
+using namespace std;
+
+// long int grundy(long int x,long int y){
+// 	long int a = y/2;
+// 	if((x-y)%2==0) return 3*a+2*(y%2)+x-y;
+// 	else{
+// 		long int k = (x-y-1)/2;
+// 		if(k==0) return 1;
+// 		else if(k<=a) return 1+3*k;
+// 		else return 1+3*a+2*(k-a);
+// 	}
+// }
+
+int main(){
+	srand(time(0));
+	int n;
+	scanf("%d",&n);
+	printf("%d\n",n);
+	long int c,d;
+	// long int g;
+	for(int i=0;i<n;i++){				// make i<n-1 and uncomment every other comment leaving this one for testcases which should give output 0.
+		c = rand();d = rand();
+		printf("%ld %ld\n", max(c,d), min(c,d));
+		// if(i==0)g = grundy(max(c,d), min(c,d));
+		// else g = g^grundy(max(c,d), min(c,d));
+	}
+	// printf("%ld %d\n", g, 0);
+}
\ No newline at end of file

assgn3/input/i1.txt

+100
+1692768257 492739943
+783279169 498237273
+1848774861 835107658
+2127360904 418200384
+1920723587 1099474625
+627145005 576359559
+1723860143 1215541724
+1655046433 597821357
+152593708 9719840
+1792900106 546975838
+1929030485 654742636
+553276024 305943858
+922570488 810260476
+1788572634 854014505
+450449330 64168932
+1157002294 822033635
+1351474472 273131673
+1672532114 296916585
+1876844808 1833784415
+1890880920 1572614134
+1844506509 1694452318
+879465759 51069212
+1474270931 405218231
+1763141196 832163780
+2134719866 227497433
+1028464771 311531494
+1412391545 344688272
+1927946524 1763962932
+948789114 913251289
+1232560023 1009047599
+652045968 384636034
+855535484 327533535
+1581862923 522597001
+1292338558 79679577
+969479257 684538548
+1079442610 250096414
+744932919 257907623
+1031420115 589874221
+1231517795 672190779
+1746439433 601063235
+1000890899 306715157
+733932542 58165026
+1862576468 474532597
+1821561896 453575357
+1644354470 463914440
+1948043427 698524047
+1276493342 230195427
+1688261988 661965464
+2065288152 1519784203
+1111418903 842602403
+804741115 431910999
+1037589552 633433333
+1439971050 1200386824
+1948181368 1600219307
+401086167 104040836
+953495417 562641994
+874499605 336781167
+1708225080 1661663924
+1447153164 430042817
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assgn3/input/i2.txt

+35
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assgn3/input/i3.txt

+5
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+1895304845 0

assgn3/input/i4.txt

+100
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assgn3/input/i5.txt

+87
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assgn3/input/i6.txt

+45
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+831267929 526602688
+1738958968 1578423153
+692441080 643348467
+761233085 177522224

assgn3/input/i7.txt

+5
+1696970007 244591842
+1921016015 571388136
+1289992276 1247015107
+2052766267 1517860414
+1218977439 721735385

assgn3/input/i8.txt

+1
+1697020428 1092017589

assgn3/out

+26
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+4 1195575200 1195575200
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+5 339439688 96241333
+12 163367499 3835884
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+35 1452987337 453648648
+38 430982884 117121189
+39 224820999 224820999
+40 654656660 654656660
+42 860582838 860582838

assgn3/output/o1.txt

+0

assgn3/output/o2.txt

+0

assgn3/output/o3.txt

+0

assgn3/output/o4.txt

+31
+8 565025544 565025544
+11 1190752235 1190752235
+11 157575291 1707340707
+14 2125034947 1283867758
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+84 1065406761 1489048825
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+90 1871175901 172306298
+92 634569055 634569055
+92 175465075 1815974627
+99 673266345 673266345
+99 780612139 1629492965

assgn3/output/o5.txt

+30
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+3 1302711336 1042490827
+5 88418646 88418646
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+33 981185071 811076244
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+56 225611543 225611543
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+76 131640171 131640171
+78 781066530 781066530
+80 1524089367 1199316626
+82 865781297 865781297
+86 928081782 928081782

assgn3/output/o6.txt

+26
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+4 597787600 597787600
+4 26803217 1779961191
+5 339439688 96241333
+13 337533700 45192978
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+35 565351552 1321622922
+35 1452987337 635545328
+39 224820999 224820999
+40 327328330 327328330
+42 430291419 430291419

assgn3/output/o7.txt

+5
+0 216318115 216318115
+1 536421381 536421381
+2 15645036 1289992276
+3 2052766267 963656992
+4 93109621 93109621

assgn3/output/o8.txt

+1
+0 0 0

assgn3/output/r1.txt

+0

assgn3/output/r2.txt

+0

assgn3/output/r3.txt

+0

assgn3/output/r4.txt

+25
+8 1130051088 1130051088
+8 1890066376 389979487
+11 1190752235 1190752235
+11 1707340707 157575291
+14 2125034947 1283867758
+16 1725804526 129352481
+27 2041400849 174440312
+30 1010624050 1010624050
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+37 2085056162 508603481
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+69 1827712335 419532723
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+77 1944822016 250901368
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+83 1865316075 166952089
+84 1347834804 1347834804
+84 1489048825 1065406761
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+89 2013760917 471877494
+90 1871175901 172306298
+92 1815974627 175465075
+96 2144060806 283743155
+99 1629492965 780612139

assgn3/output/r5.txt

+24
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+3 1302711336 1042490827
+5 176837292 176837292
+9 612082627 589401914
+13 1039335208 1007718031
+15 1093011692 1001373133
+17 1308867596 1191955921
+21 383498388 383498388
+23 53350217 53350217
+33 981185071 811076244
+37 58890607 58890607
+40 1363320304 1189204049
+42 389657224 389657224
+43 2033904278 622081330
+48 1739010824 1439368389
+52 91499877 91499877
+53 44412525 44412525
+56 225611543 225611543
+57 399129059 399129059
+58 1202779128 1169218311
+75 218284014 218284014
+76 131640171 131640171
+80 1524089367 1199316626

assgn3/output/r6.txt

+26
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+4 1195575200 1195575200
+4 1779961191 26803217
+5 339439688 96241333
+12 163367499 3835884
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+16 72530595 72530595
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+20 1353947924 785456431
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+23 1652804583 756387947
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+25 256478802 78665734
+26 44356736 44356736
+27 1227689682 594756269
+30 602752391 602752391
+31 1117752161 344333420
+32 681996603 681996603
+34 484624479 484624479
+35 1452987337 453648648
+38 430982884 117121189
+39 224820999 224820999
+40 654656660 654656660
+42 860582838 860582838

assgn3/output/r7.txt

+5
+0 216318115 216318115
+1 536421381 536421381
+2 1289992276 15645036
+3 2052766267 838204710
+4 186219242 186219242

assgn3/output/r8.txt

+1
+0 0 0

assgn3/sim.cpp

+#include"iomanip"
+#include"iostream"
+#include"limits"
+#include"cmath"
+#include"vector"
+#include"algorithm"
+#include"list"
+#include"queue"
+#include"stack"
+#include"set"
+#include"unordered_set"
+#include"map"
+#include"unordered_map"
+#include"string"
+#include"cstring"
+#include"assert.h"
+using namespace std;
+#define ff first
+#define ss second
+#define all(v) v.begin(),v.end()
+#define mp make_pair
+#define pb push_back
+#define mset(a,b) memset(a,b,sizeof(a))
+typedef long long ll;
+typedef long double ld;
+typedef pair<int,int> pii;
+typedef pair<ll,ll> pll;
+const int maxn=60;
+int gr[maxn][maxn];
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    for(int y=0;y<maxn;++y)
+    {
+        for(int x=y;x<maxn;++x)
+        {
+            set<int>me;
+            for(int y1=0;y1<y;++y1)
+            {
+                me.insert(gr[x][y1]);
+            }
+            for(int x1=y;x1<x;++x1)
+            {
+                me.insert(gr[x1][y]);
+            }
+            for(int x1=0;x1<x;++x1)
+            {
+                me.insert(gr[x1][x1]);
+            }
+            int f=0;
+            while(me.find(f)!=me.end())
+            {
+                f++;
+            }
+            gr[x][y]=f;
+        }
+    }
+    for(int j=maxn-1;j>=0;--j)
+    {
+        for(int i=0;i<maxn;++i)
+        {
+            if(i>=j)
+            {
+                if(gr[i][j]<10)
+                {
+                    cout<<' '<<gr[i][j]<<' ';
+                }
+                else
+                {
+                    cout<<gr[i][j]<<' ';
+                }
+            }
+            else cout<<"   ";
+        }
+        cout<<'\n';
+    }
+}
+

assgn4/160050063_4.cpp

+#include"iomanip"
+#include"iostream"
+#include"limits"
+#include"cmath"
+#include"vector"
+#include"algorithm"
+#include"list"
+#include"queue"
+#include"stack"
+#include"set"
+#include"unordered_set"
+#include"map"
+#include"unordered_map"
+#include"string"
+#include"cstring"
+#include"assert.h"
+using namespace std;
+#define ff first
+#define ss second
+#define all(v) v.begin(),v.end()
+#define mp make_pair
+#define pb push_back
+#define mset(a,b) memset(a,b,sizeof(a))
+typedef long long ll;
+typedef long double ld;
+typedef pair<int,int> pii;
+typedef pair<ll,ll> pll;
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+}

assgn7/160050063.cpp

+#include"iomanip"
+#include"iostream"
+#include"limits"
+#include"cmath"
+#include"vector"
+#include"algorithm"
+#include"list"
+#include"queue"
+#include"stack"
+#include"set"
+#include"map"
+#include"string"
+#include"cstring"
+#include"assert.h"
+using namespace std;
+#define ff first
+#define ss second
+#define all(v) v.begin(),v.end()
+#define mp make_pair
+#define pb push_back
+#define mset(a,b) memset(a,b,sizeof(a))
+typedef long long ll;
+typedef long double ld;
+typedef pair<int,int> pii;
+typedef pair<ll,ll> pll;
+
+
+#define INF 2100000000
+struct edge
+{
+    int a,b;ll cap,flow; int back;
+    edge(int a,int b,int c,int d,int e):
+        a(a),b(b),cap(c),flow(d),back(e)
+    {
+
+    }
+};
+struct max_flow
+{
+    vector<vector<edge> >g;
+    vector<ll>ex;
+    vector<int>h;
+    vector<int>active;
+    vector<int>count;
+    int size;
+    max_flow(int n):
+        g(n),ex(n),h(n),count(2*n),active(n)
+    {
+    }
+    void addEdge(int a,int b,int cap)
+    {
+        if(a!=b)
+        {
+            g[a].pb(edge(a,b,cap,0,g[b].size()));
+            g[b].pb(edge(b,a,0,0,g[a].size()-1));
+        }
+    }
+    ll maximum_flow(int s,int t)
+    {
+        h[s]=g.size();
+        count[g.size()]++;
+        count[0]=g.size()-1;
+        queue<int>qq;
+        active[s]=1;
+        active[t]=1;
+        for(int i=0;i<g[s].size();++i)
+        {
+            if(g[s][i].cap>g[s][i].flow)
+            {
+                int vert = g[s][i].b;
+                g[s][i].flow+=g[s][i].cap;
+                g[g[s][i].b][g[s][i].back].flow=-g[s][i].cap;
+                ex[g[s][i].b]+=g[s][i].flow;
+                if(active[vert]==0&&ex[vert]>0)
+                {
+                    qq.push(vert);
+                    active[vert]=1;
+                }
+            }
+        }
+        for(;;)
+        {
+            if(qq.empty())
+                break;
+            int v=qq.front();
+            active[v]=0;
+            qq.pop();
+            for(int j=0;j<g[v].size()&&ex[v]>0;++j)
+            {
+                int vert = g[v][j].b;
+                if(h[v]==h[vert]+1)
+                {
+                    int tob=min(g[v][j].cap-g[v][j].flow,ex[v]);
+                    if(tob>0)
+                    {
+                        g[v][j].flow+=tob;
+                        g[vert][g[v][j].back].flow=-g[v][j].flow;
+                        ex[v]-=tob;
+                        ex[vert]+=tob;
+                        if(active[vert]==0&&ex[vert]>0)
+                        {
+                            active[vert]=1;
+                            qq.push(vert);
+                        }
+                    }
+                }
+            }
+            if(ex[v]>0)
+            {
+                if(count[h[v]]==1)
+                {
+                    int k=h[v];
+                    for(int i=0;i<g.size();++i)
+                    {
+                        if(h[i]>=k)
+                        {
+                            count[h[i]]--;
+                            h[i]=max(h[i],(int)g.size()+1);
+                            count[h[i]]++;
+                            if(active[i]==0&&ex[i]>0)
+                            {
+                                qq.push(i);
+                                active[i]=1;
+                            }
+                        }
+                    }
+                }
+                else
+                {
+                    count[h[v]]--;
+                    h[v]=INF;
+                    for(int i=0;i<g[v].size();++i)
+                    {
+                        if(g[v][i].flow<g[v][i].cap)
+                        {
+                            h[v]=min(h[v],h[g[v][i].b]+1);
+                        }
+                    }
+                    count[h[v]]++;
+                    if(active[v]==0&&ex[v]>0)
+                    {
+                        qq.push(v);
+                        active[v]=1;
+                    }
+                }
+            }
+        }
+        ll ans=0;
+        for(int i=0;i<g[s].size();++i)
+        {
+            ans+=g[s][i].flow;
+        }
+        return ans;
+    }
+    void bfs(int s)
+    {
+        int n = g.size();
+        for(int i=0;i<n;++i)
+        {
+            active[i]=0;
+            h[i]=0;
+        }
+        queue<int>qq;
+        qq.push(s);
+        h[s]=1;
+
+        while(!qq.empty())
+        {
+            int vert = qq.front();
+            qq.pop();
+            for(edge &ed : g[vert])
+            {
+                if(ed.flow<ed.cap&&h[ed.b]==0)
+                {
+                    qq.push(ed.b);
+                    h[ed.b]=1;
+                }
+            }
+        }
+    }
+};
+
+int main()
+{
+    int n;
+    scanf("%d",&n);
+    max_flow ob(n+2);//0 money sink  1-n items   n+1-n+m vouchers  n+m+1 source node
+    for(int i=1;i<=n;++i)
+    {
+        int pa;
+        scanf("%d",&pa);
+        ob.addEdge(0,i,pa);
+        ob.addEdge(i,n+1,10000-pa);
+    }
+    for(int i=1;i<=n;++i)
+    {
+        for(int j=i+1;j<=n;++j)
+        {
+            int pij;
+            scanf("%d",&pij);
+            ob.addEdge(i,j,pij);
+            ob.addEdge(j,i,pij);
+        }
+    }
+    ll ans=ob.maximum_flow(0,n+1);
+    ob.bfs(0);
+    for(int i=1;i<=n;++i)
+    {
+        printf(ob.h[i]==1?"A":"B");
+    }
+    printf("\n");
+}
+
+