[pull] master from wisdompeak:master

Readme.md

@@ -1132,7 +1132,8 @@
 [1168.Optimize-Water-Distribution-in-a-Village](https://github.com/wisdompeak/LeetCode/tree/master/Union_Find/1168.Optimize-Water-Distribution-in-a-Village) (H-)   
 [1489.Find-Critical-and-Pseudo-Critical-Edges-in-Minimum-Spanning-Tree](https://github.com/wisdompeak/LeetCode/tree/master/Union_Find/1489.Find-Critical-and-Pseudo-Critical-Edges-in-Minimum-Spanning-Tree) (H)   
 [1579.Remove-Max-Number-of-Edges-to-Keep-Graph-Fully-Traversable](https://github.com/wisdompeak/LeetCode/tree/master/Union_Find/1579.Remove-Max-Number-of-Edges-to-Keep-Graph-Fully-Traversable) (H-)  
-[1584.Min-Cost-to-Connect-All-Points](https://github.com/wisdompeak/LeetCode/tree/master/Union_Find/1584.Min-Cost-to-Connect-All-Points) (H-)  
+[1584.Min-Cost-to-Connect-All-Points](https://github.com/wisdompeak/LeetCode/tree/master/Union_Find/1584.Min-Cost-to-Connect-All-Points) (H-)      
+[3600.Maximize-Spanning-Tree-Stability-with-Upgrades](https://github.com/wisdompeak/LeetCode/tree/master/Union_Find/3600.Maximize-Spanning-Tree-Stability-with-Upgrades) (H)      
 
 #### [Recursion](https://github.com/wisdompeak/LeetCode/tree/master/Recursion)
 [087.Scramble-String](https://github.com/wisdompeak/LeetCode/tree/master/Recursion/087.Scramble-String) (H-)  
@@ -1704,7 +1705,8 @@
 [Graph](https://github.com/wisdompeak/LeetCode/tree/master/Template/Graph)  
 [Bit_Manipulation](https://github.com/wisdompeak/LeetCode/tree/master/Template/Bit_manipulation)  
 [RB_Tree](https://github.com/wisdompeak/LeetCode/tree/master/Template/RB_Tree)        
-[Binary_Lift](https://github.com/wisdompeak/LeetCode/tree/master/Template/Binary_Lift)      
+[Binary_Lift](https://github.com/wisdompeak/LeetCode/tree/master/Template/Binary_Lift)         
+[Union_Find](https://github.com/wisdompeak/LeetCode/tree/master/Template/Union_Find)    
 [二维子矩阵求和](https://github.com/wisdompeak/LeetCode/tree/master/Template/Sub_Rect_Sum_2D)          
 [二维差分数组](https://github.com/wisdompeak/LeetCode/tree/master/Template/Diff_Array_2D)    
 [CPP_LANG](https://github.com/wisdompeak/LeetCode/tree/master/Template/CPP_LANG)

Template/Union_Find/union_find.cpp

@@ -0,0 +1,23 @@
+struct DSU {
+    vector<int> p, r;
+    DSU(int n): p(n,-1), r(n,0) {
+        iota(p.begin(), p.end(), 0);
+    }
+    int find(int x) {
+        return p[x]==x ? x : p[x]=find(p[x]);
+    }
+    bool unite(int a, int b) {
+        a = find(a); b = find(b);
+        if (a == b) return false;
+        if (r[a] < r[b]) swap(a,b);
+        p[b] = a;
+        if (r[a]==r[b]) ++r[a];
+        return true;
+    }
+};
+
+int main {
+  DSU dsu(n);
+  dsu.unite(u,v);
+  if (dsu.find(u)==dsu.find(v) {}
+}

Union_Find/3600.Maximize-Spanning-Tree-Stability-with-Upgrades/3600.Maximize-Spanning-Tree-Stability-with-Upgrades.cpp

@@ -0,0 +1,75 @@
+class Solution {
+public:
+    struct DSU {
+        vector<int> p, r;
+        DSU(int n): p(n,-1), r(n,0) {
+            iota(p.begin(), p.end(), 0);
+        }
+        int find(int x) {
+            return p[x]==x ? x : p[x]=find(p[x]);
+        }
+        bool unite(int a, int b) {
+            a = find(a); b = find(b);
+            if (a == b) return false;
+            if (r[a] < r[b]) swap(a,b);
+            p[b] = a;
+            if (r[a]==r[b]) ++r[a];
+            return true;
+        }
+    };
+
+    bool isOK(int T, int n, vector<vector<int>>& edges, int k) {
+        DSU dsu(n);
+        int count = 0;
+        int upgrade = 0;
+
+        vector<vector<int>>candidates; // upgrade, u,v
+        for (auto& e: edges) {
+            int u = e[0], v = e[1], s = e[2], must = e[3];
+            if (must) {
+                if (s<T) return false;
+                dsu.unite(u,v);
+                count++;
+            } else {
+                if (s>=T)
+                    candidates.push_back({0, u, v});
+                else if (2*s>=T)
+                    candidates.push_back({1, u, v});
+            }
+        }
+
+        sort(candidates.begin(), candidates.end());
+
+        for (auto& cand: candidates) {
+            int u = cand[1], v = cand[2];
+            if (count==n-1) break;
+            if (dsu.find(u)!=dsu.find(v)) {
+                dsu.unite(u,v);
+                count++;
+                upgrade += cand[0];
+                if (upgrade > k) return false;
+            }
+        }
+
+        for (int i=0; i<n; i++)
+            if (dsu.find(i)!=dsu.find(0))
+                return false;
+
+        return count==n-1;
+    }
+
+    int maxStability(int n, vector<vector<int>>& edges, int k) {
+        int lo = 1, hi = 1e5*2;
+        while (lo < hi) {
+            int mid = hi-(hi-lo)/2;
+            if (isOK(mid, n, edges, k))
+                lo = mid;
+            else
+                hi = mid-1;
+        }
+        if (isOK(lo, n, edges, k))
+            return lo;
+        else
+            return -1;        
+    }
+};

Union_Find/3600.Maximize-Spanning-Tree-Stability-with-Upgrades/Readme.md

@@ -0,0 +1,7 @@
+### 3600.Maximize-Spanning-Tree-Stability-with-Upgrades
+
+突破口是二分搜值。如果猜测全局最小的stability是T的话，尝试能否用最小生成树的方法构造出一棵树来。
+
+当固定全局最小的stability是T之后，那么哪些edge能用哪些不能用就一目了然了。对于must的那些边，如果存在stability小于T的，那么显然无解。对于非must的边，如果`2*stability<T`，那么必然排除作为构造树的候选；反之就可以作为候选，同时我们需要根据2s和T的比较，标注这条边“是否需要upgrade”。
+
+有了所有的候选边，我们就可以用Kruskal算法构造“最小生成树”。只不过这里优化的不是总边的权重，而是“upgrade的次数”。我们将所有边按照“是否需要upgrade”排序即可（其实就是0或者1），优先选用不需要upgrade的边实现更多的union。如果发现一个候选边的两个端点已经union在一起了，那么这条边其实就可以放心地舍弃而没有任何副作用。注意处理完所有的边之后还需要判断两点：是否恰好用到了n-1条边（否则说明可能有环），是否所有的点的find都相同（否则说明可能有不联通的区域）。