From 585da08a4eeea343cd345d6a82a39df468628326 Mon Sep 17 00:00:00 2001
From: zscoder <zisong.yeoh@gmail.com>
Date: Sat, 22 Oct 2016 09:17:10 +0800
Subject: [PATCH] Added Min Cost Flow and Gaussian Elimination

---
 Data Structures Class Template.cpp | 168 +++++++++++++++++++++++++++++
 1 file changed, 168 insertions(+)

diff --git a/Data Structures Class Template.cpp b/Data Structures Class Template.cpp
index 51ca8e9..c28e011 100644
--- a/Data Structures Class Template.cpp	
+++ b/Data Structures Class Template.cpp	
@@ -1349,6 +1349,7 @@ struct Tree
 		for(int i = 0; i < adj[u].size(); i++)
 		{
 			int v = adj[u][i].v;
+			if(v == p) continue;
 			dfsstartend(v, u);
 		}
 		en[u] = ++timer;
@@ -2960,6 +2961,173 @@ struct plane
 };
 //End Geometry
 
+//Start MinCostFlow (yunkai version)
+struct Edge{
+    int u, v;
+    long long cap, cost;
+ 
+    Edge(int _u, int _v, long long _cap, long long _cost){
+        u = _u; v = _v; cap = _cap; cost = _cost;
+    }
+};
+ 
+struct MinCostFlow{
+    int n, s, t;
+    long long flow, cost;
+    vector<vector<int> > graph;
+    vector<Edge> e;
+    vector<long long> dist, potential;
+    vector<int> parent;
+    bool negativeCost;
+ 
+    MinCostFlow(int _n){
+        // 0-based indexing
+        n = _n;
+        graph.assign(n, vector<int> ());
+        negativeCost = false;
+    }
+ 
+    void addEdge(int u, int v, long long cap, long long cost, bool directed = true){
+        if(cost < 0)
+            negativeCost = true;
+ 
+        graph[u].push_back(e.size());
+        e.push_back(Edge(u, v, cap, cost));
+ 
+        graph[v].push_back(e.size());
+        e.push_back(Edge(v, u, 0, -cost));
+ 
+        if(!directed)
+            addEdge(v, u, cap, cost, true);
+    }
+ 
+    pair<long long, long long> getMinCostFlow(int _s, int _t){
+        s = _s; t = _t;
+        flow = 0, cost = 0;
+ 
+        potential.assign(n, 0);
+        if(negativeCost){
+            // run Bellman-Ford to find starting potential
+            dist.assign(n, 1LL<<62);
+            for(int i = 0, relax = false; i < n && relax; i++, relax = false){
+                for(int u = 0; u < n; u++){
+                    for(int k = 0; k < graph[u].size(); k++){
+                        int eIdx = graph[u][i];
+                        int v = e[eIdx].v, cap = e[eIdx].cap, w = e[eIdx].cost;
+ 
+                        if(dist[v] > dist[u] + w && cap > 0){
+                            dist[v] = dist[u] + w;
+                            relax = true;
+            }   }   }   }
+ 
+            for(int i = 0; i < n; i++){
+                if(dist[i] < (1LL<<62)){
+                    potential[i] = dist[i];
+        }   }   }
+ 
+        while(dijkstra()){
+            flow += sendFlow(t, 1LL<<62);
+        }
+ 
+        return make_pair(flow, cost);
+    }
+ 
+    bool dijkstra(){
+        parent.assign(n, -1);
+        dist.assign(n, 1LL<<62);
+        priority_queue<ii, vector<ii>, greater<ii> > pq;
+ 
+        dist[s] = 0;
+        pq.push(ii(0, s));
+ 
+ 
+        while(!pq.empty()){
+            int u = pq.top().second;
+            long long d = pq.top().first;
+            pq.pop();
+ 
+            if(d != dist[u]) continue;
+ 
+            for(int i = 0; i < graph[u].size(); i++){
+                int eIdx = graph[u][i];
+                int v = e[eIdx].v, cap = e[eIdx].cap;
+                int w = e[eIdx].cost + potential[u] - potential[v];
+ 
+                if(dist[u] + w < dist[v] && cap > 0){
+                    dist[v] = dist[u] + w;
+                    parent[v] = eIdx;
+ 
+                    pq.push(ii(dist[v], v));
+        }   }   }
+ 
+        // update potential
+        for(int i = 0; i < n; i++){
+            if(dist[i] < (1LL<<62))
+                potential[i] += dist[i];
+        }
+ 
+        return dist[t] != (1LL<<62);
+    }
+ 
+    long long sendFlow(int v, long long curFlow){
+        if(parent[v] == -1)
+            return curFlow;
+        int eIdx = parent[v];
+        int u = e[eIdx].u, w = e[eIdx].cost;
+ 
+        long long f = sendFlow(u, min(curFlow, e[eIdx].cap));
+ 
+        cost += f*w;
+        e[eIdx].cap -= f;
+        e[eIdx^1].cap += f;
+ 
+        return f;
+    }
+};
+//End mincostflow
+
+//Start Z_{2} gausselim
+struct gausselim
+{
+	ll cnt[61][2];
+	int rank;
+	ll cyc[61];
+	ll tmp;
+	void init()
+	{
+		for(int i = 0; i < 61; i++)
+		{
+			cyc[i] = cnt[i][0] = cnt[i][1] = 0;
+		}
+		rank = tmp = 0;
+	}
+	void addval(ll x)
+	{
+		for(int i = 0; i < 61; i++)
+		{
+			cnt[i][(x>>i)&1]++;
+		}
+	}
+	void add(ll x)
+	{
+		tmp|=x;
+		for(int i = 60; i >= 0; i--)
+		{
+			if(x&(1LL<<i))
+			{
+				if(cyc[i]==0)
+				{
+					cyc[i] = x;
+					rank++;
+					break;
+				}
+			}
+			x = min(x, (x^cyc[i]));
+		}	
+	}
+};
+//End Z_{2} gausselim
+
 /* TO-DO LIST :
 1. SQRT DECOMP (MO)
 2. SQRT DECOMP (REAL)