Problem 4 DSU fucked

CP/JanuaryCookOff2018/prob3-dp.cpp

@@ -0,0 +1,118 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+typedef long long int ll;
+const ll inf=pow(10,14);
+bool apply(ll x,ll y,ll op)
+{
+if(op==0)
+{
+return x<y;
+}
+return x>y;
+}
+
+bool apply2(ll x,ll y,ll op)
+{
+if(op==1)
+{
+return x<y;
+}
+return x>y;
+}
+
+int main(){
+
+   ll t;
+cin>>t;
+while(t--)
+{
+ll n,arr[100005];
+cin>>n;
+for(ll i=0;i<n;i++)
+cin>>arr[i];
+
+ll dp[100005][2];
+for(ll i=0;i<100005;i++)
+{
+for(ll j=0;j<2;j++)
+dp[i][j]=inf;
+}
+
+if(n==2)
+{
+if(arr[0]==arr[1])
+cout<<-1<<endl;
+else
+cout<<0<<endl;
+continue;
+}
+
+ll x=ceil(1.0*n/2);
+dp[0][0]=0,dp[0][1]=1;
+for(ll i=1;i<x;i++)
+{
+ll val1=dp[i-1][0],val2=dp[i-1][1];
+if(!(apply(arr[i-1],arr[i],i%2) && apply(arr[n-i-1],arr[n-i],(n-i)%2)))
+{
+val1=inf;
+}
+if(!(apply(arr[n-i],arr[i],i%2) && apply(arr[n-i-1],arr[i-1],(n-i)%2)))
+{
+val2=inf;
+}
+dp[i][0]=min(val1,val2);
+
+val1=dp[i-1][0],val2=dp[i-1][1];
+if(!(apply(arr[i-1],arr[n-i-1],i%2) && apply(arr[i],arr[n-i],(n-i)%2)))
+{
+val1=inf;
+}
+if(!(apply(arr[n-i],arr[n-i-1],i%2) && apply(arr[i],arr[i-1],(n-i)%2)))
+{
+val2=inf;
+}
+dp[i][1]=min(val1,val2)+1;
+}
+
+ll dp2[100005][2];
+for(ll i=0;i<100005;i++)
+{
+for(ll j=0;j<2;j++)
+dp2[i][j]=inf;
+}
+
+
+dp2[0][0]=0,dp2[0][1]=1;
+for(ll i=1;i<x;i++)
+{
+ll val1=dp2[i-1][0],val2=dp2[i-1][1];
+if(!(apply2(arr[i-1],arr[i],i%2) && apply2(arr[n-i-1],arr[n-i],(n-i)%2)))
+{
+val1=inf;
+}
+if(!(apply2(arr[n-i],arr[i],i%2) && apply2(arr[n-i-1],arr[i-1],(n-i)%2)))
+{
+val2=inf;
+}
+dp2[i][0]=min(val1,val2);
+
+val1=dp2[i-1][0],val2=dp2[i-1][1];
+if(!(apply2(arr[i-1],arr[n-i-1],i%2) && apply2(arr[i],arr[n-i],(n-i)%2)))
+{
+val1=inf;
+}
+if(!(apply2(arr[n-i],arr[n-i-1],i%2) && apply2(arr[i],arr[i-1],(n-i)%2)))
+{
+val2=inf;
+}
+dp2[i][1]=min(val1,val2)+1;
+}
+ll res=min(min(dp[x-1][0],dp[x-1][1]),min(dp2[x-1][0],dp2[x-1][1]));
+if(res>pow(10,12))
+cout<<-1<<endl;
+else
+cout<<res<<endl;
+}
+   return 0;
+}

CP/JanuaryCookOff2018/prob4.cpp

@@ -0,0 +1,157 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+const int N = 1005;
+
+int A[N][N];
+vector<int> adj[N];
+bool visited[N];
+int ans[N][N];
+bool myParity[N];
+
+int p[N], sz[N];
+
+int par(int x){
+	if(p[x] != x)	p[x] = par(p[x]);
+	return p[x];
+}
+
+void join(int a, int b){
+	int p1 = par(a), p2 = par(b);
+	if(p1 == p2)	return ;
+	if(sz[p2] > sz[p1])	swap(p1, p2);
+	sz[p1] += sz[p2];
+	p[p2] = p1;
+}
+
+bool BipartiteCheck(int u, int parity) {
+	visited[u] = 1;
+	myParity[u] = parity;
+	for(auto v : adj[u]) {
+		if(A[u][v] == 1)	continue;
+		if(visited[v] == 1 and myParity[v] == myParity[u])	return 0;
+	}
+	for(auto v : adj[u]){
+		if(visited[v] == 1 or A[u][v] == 1)	continue;
+		if(BipartiteCheck(v, parity^1) == 0)	return 0;
+	}
+	return 1;
+}
+
+void dfs_assign(int u, int val, int col_number) {
+	visited[u] = 1;
+	ans[u][col_number] = val;
+	for(auto v : adj[u]) {
+		if(visited[v])	continue;
+		dfs_assign(v, val * A[u][v], col_number);
+	}
+}
+
+void solve() {
+	int n;
+	scanf("%d", &n);
+	//assert(n >= 1 and n <= 1000);
+	for(int i = 1; i <= n; i++) {
+		for(int j = 1; j <= n; j++) {
+			scanf("%d", &A[i][j]);
+			assert(A[i][j] >= -1 and A[i][j] <= 1);
+		}
+	}
+
+	for(int i = 1; i <= n; i++) {
+		p[i] = i, sz[i] = 1;
+		visited[i] = 0;
+		adj[i].clear();
+    for(int j = 1; j <= n; j++) ans[i][j] = 0;
+	}
+
+	for(int i = 1; i <= n; i++) {
+		for(int j = 1; j <= n; j++) {
+			if(A[i][j] != A[j][i]) {
+				cout<<-1<<endl;
+				//cout<<"non symmetric"<<endl;
+				return ;
+			}
+		}
+	}
+
+	// ^ensured matrix is symmetric.
+
+	for(int i = 1; i <= n; i++) {
+		if(A[i][i] == -1) {
+			cout<<-1<<endl;
+			//cout<<"diagonal fucked"<<endl;
+			return ;
+		}
+	}
+
+	// ^ensured none of the diagonal entries is -1.
+
+	for(int i = 1; i <= n; i++) {
+		for(int j = i + 1; j <= n; j++) {
+			if(A[i][j] != 0) {
+				if(A[i][i] == 0 or A[j][j] == 0) {
+					cout<<-1<<endl;
+					//cout<<"involve zero row"<<endl;
+					return ;
+				}
+				join(i, j);
+				adj[i].push_back(j);
+				adj[j].push_back(i);
+			}
+		}
+	}
+
+	// ^joined the rows, which have non - zero entries in dsu
+	// and added edges between those rows which have opposite parities.
+	// also verified that no pure zero row is involved.
+
+	for(int i = 1; i <= n; i++) {
+		for(int j = i + 1; j <= n; j++) {
+			if(A[i][j] == 0 and par(i) == par(j)) {
+				cout<<-1<<endl;
+				//cout<<"non - transitive"<<endl;
+				return ;
+			}
+		}
+	}
+
+  //cout<<"BC"<<endl;
+
+	// ^ensured that all the pair of rows which are not connected are not indirectly in the same dsu.
+
+	for(int i = 1; i <= n; i++) {
+		if(visited[i])	continue;
+		if(!BipartiteCheck(i, 0)) {
+			cout<<-1<<endl;
+			//cout<<"non - bipartite"<<endl;
+			return ;
+		}
+	}
+
+	// ^ensured there are no parity issues and that all the graphs are bipartite in nature.
+
+	for(int i = 1; i <= n; i++) {
+		visited[i] = (A[i][i] == 0);
+	}
+
+	int colNumber = 1;
+
+	for(int i = 1; i <= n; i++) {
+		if(visited[i])	continue;
+		dfs_assign(i, -1, colNumber++);
+	}
+
+	for(int i = 1; i <= n; i++) {
+		for(int j = 1; j <= n; j++) {
+			cout<<ans[i][j]<<" ";
+		}
+		cout<<endl;
+	}
+}
+
+int main() {
+  int t;
+  scanf("%d", &t);
+  while(t--) solve();
+}