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Problem solution · C++

Minimum Edge Toggles on a Tree

Minimum Edge Toggles on a Tree: a C++ solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Direct simulation
Source
Kamyu LeetCode Solutions
Length
123 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Direct simulation

For Minimum Edge Toggles on a Tree, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 123 lines of C++ from the credited upstream file minimum-edge-toggles-on-a-tree.cpp.
  • The implementation visibly relies on sequence storage.
  • 12 loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from Kamyu LeetCode Solutions by kamyu104 and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeMinimum Edge Toggles on a Tree · C++C++
Use this to learn the idea, then write your own version.
// Time:  O(n)// Space: O(n) // greedy, topological sort, bitmasksclass Solution {public:    vector<int> minimumFlips(int n, vector<vector<int>>& edges, string start, string target) {        vector<int> diff(n);        for (int i = 0; i < n; ++i) {            if (start[i] != target[i]) {                diff[i] = 1;            }        }        if (accumulate(cbegin(diff), cend(diff), 0) % 2) {            return {-1};        }        vector<int> degree(n), adj(n), edge(n);        for (int idx = 0; idx < size(edges); ++idx) {            const auto& u = edges[idx][0], &v = edges[idx][1];            ++degree[u];            ++degree[v];            adj[u] ^= v;            adj[v] ^= u;            edge[u] ^= idx;            edge[v] ^= idx;        }        vector<bool> lookup(size(edges));        for (int i = 0; i < n; ++i) {            int u = i;            while (degree[u] == 1) {                const auto v = adj[u];                const auto idx = edge[u];                --degree[u];                --degree[v];                adj[u] ^= v;                adj[v] ^= u;                edge[u] ^= idx;                edge[v] ^= idx;                if (diff[u]) {                    diff[u] ^= 1;                    diff[v] ^= 1;                    lookup[idx] = true;                }                u = v;            }        }        vector<int> result;        for (int i = 0; i < size(lookup); ++i) {            if (lookup[i]) {                result.emplace_back(i);            }        }        return result;    }}; // Time:  O(n)// Space: O(n)// greedy, topological sortclass Solution2 {public:    vector<int> minimumFlips(int n, vector<vector<int>>& edges, string start, string target) {        vector<int> diff(n);        for (int i = 0; i < n; ++i) {            if (start[i] != target[i]) {                diff[i] = 1;            }        }        if (accumulate(cbegin(diff), cend(diff), 0) % 2) {            return {-1};        }        vector<int> degree(n);        vector<vector<pair<int, int>>> adj(n);        const auto& topological_sort = [&]() {            vector<bool> lookup(size(adj));            vector<int> q;            for (int u = 0; u < size(adj); ++u) {                if (size(adj[u]) == 1) {                    q.emplace_back(u);                }            }            while (!empty(q)) {                vector<int> new_q;                for (const auto& u : q) {                    for (const auto& [v, idx] : adj[u]) {                        if (degree[v] == 0) {                            continue;                        }                        --degree[u];                        --degree[v];                        if (degree[v] == 1) {                            new_q.emplace_back(v);                        }                        if (diff[u]) {                            diff[u] ^= 1;                            diff[v] ^= 1;                            lookup[idx] = true;                        }                    }                }                q = move(new_q);            }            return lookup;        };         for (int idx = 0; idx < size(edges); ++idx) {            const auto& u = edges[idx][0], &v = edges[idx][1];            ++degree[u];            ++degree[v];            adj[u].emplace_back(v, idx);            adj[v].emplace_back(u, idx);        }        const auto& lookup = topological_sort();        vector<int> result;        for (int i = 0; i < size(lookup); ++i) {            if (lookup[i]) {                result.emplace_back(i);            }        }        return result;    }};

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