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minimum-score-after-removals-on-a-tree.cpp
213 lines (203 loc) · 7.46 KB
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minimum-score-after-removals-on-a-tree.cpp
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// Time: O(n^2)
// Space: O(n)
// dfs with stack
class Solution {
public:
int minimumScore(vector<int>& nums, vector<vector<int>>& edges) {
vector<vector<int>> adj(size(nums));
for (const auto& e : edges) {
adj[e[0]].emplace_back(e[1]);
adj[e[1]].emplace_back(e[0]);
}
vector<int> left(size(nums)), right(size(nums));
const auto& is_ancestor = [&](int a, int b) {
return left[a] <= left[b] && right[b] <= right[a];
};
const auto& iter_dfs = [&]() {
int cnt = 0;
vector<tuple<int, int, int>> stk;
stk.emplace_back(1, 0, -1);
while (!empty(stk)) {
const auto [step, u, p] = stk.back(); stk.pop_back();
if (step == 1) {
left[u] = cnt++;
stk.emplace_back(2, u, p);
for (const auto& v : adj[u]) {
if (v == p) {
continue;
}
stk.emplace_back(1, v, u);
}
} else if (step == 2) {
for (const auto& v : adj[u]) {
if (v == p) {
continue;
}
nums[u] ^= nums[v];
}
right[u] = cnt;
}
}
};
iter_dfs();
int result = numeric_limits<int>::max();
for (int i = 1; i < size(nums); ++i) {
for (int j = i + 1; j < size(nums); ++j) {
int a, b, c;
if (is_ancestor(i, j)) {
tie(a, b, c) = tuple(nums[0] ^ nums[i], nums[i] ^ nums[j], nums[j]);
} else if (is_ancestor(j, i)) {
tie(a, b, c) = tuple(nums[0] ^ nums[j], nums[j] ^ nums[i], nums[i]);
} else {
tie(a, b, c) = tuple(nums[0] ^ nums[i] ^ nums[j], nums[i], nums[j]);
}
result = min(result, max({a, b, c}) - min({a, b, c}));
}
}
return result;
}
};
// Time: O(n^2)
// Space: O(n)
// dfs with recursion
class Solution2 {
public:
int minimumScore(vector<int>& nums, vector<vector<int>>& edges) {
vector<vector<int>> adj(size(nums));
for (const auto& e : edges) {
adj[e[0]].emplace_back(e[1]);
adj[e[1]].emplace_back(e[0]);
}
int cnt = 0;
vector<int> left(size(nums)), right(size(nums));
const auto& is_ancestor = [&](int a, int b) {
return left[a] <= left[b] && right[b] <= right[a];
};
function<void(int, int)> dfs = [&](int u, int p) {
left[u] = cnt++;
for (const auto& v : adj[u]) {
if (v == p) {
continue;
}
dfs(v, u);
nums[u] ^= nums[v];
}
right[u] = cnt;
};
dfs(0, -1);
int result = numeric_limits<int>::max();
for (int i = 1; i < size(nums); ++i) {
for (int j = i + 1; j < size(nums); ++j) {
int a, b, c;
if (is_ancestor(i, j)) {
tie(a, b, c) = tuple(nums[0] ^ nums[i], nums[i] ^ nums[j], nums[j]);
} else if (is_ancestor(j, i)) {
tie(a, b, c) = tuple(nums[0] ^ nums[j], nums[j] ^ nums[i], nums[i]);
} else {
tie(a, b, c) = tuple(nums[0] ^ nums[i] ^ nums[j], nums[i], nums[j]);
}
result = min(result, max({a, b, c}) - min({a, b, c}));
}
}
return result;
}
};
// Time: O(n^2)
// Space: O(n)
// dfs with recursion
class Solution3 {
public:
int minimumScore(vector<int>& nums, vector<vector<int>>& edges) {
vector<vector<int>> adj(size(nums));
for (const auto& e : edges) {
adj[e[0]].emplace_back(e[1]);
adj[e[1]].emplace_back(e[0]);
}
function<int(int, int, vector<int> *)> dfs = [&](int u, int p, vector<int> *result) {
int total = nums[u];
for (const auto& v : adj[u]) {
if (v == p) {
continue;
}
total ^= dfs(v, u, result);
}
result->emplace_back(total);
return total;
};
const int total = accumulate(cbegin(nums), cend(nums), 0,
[](int x, int y) {
return x ^ y;
});
int result = numeric_limits<int>::max();
for (const auto& e : edges) {
vector<vector<int>> xors(2);
dfs(e[0], e[1], &xors[0]);
dfs(e[1], e[0], &xors[1]);
for (auto& candidates : xors) {
const int total2 = candidates.back(); candidates.pop_back();
for (const auto& x : candidates) {
const auto& [a, b, c] = tuple(total ^ total2, x, total2 ^ x);
result = min(result, max({a, b, c}) - min({a, b, c}));
}
}
}
return result;
}
};
// Time: O(n^2)
// Space: O(n)
// dfs with stack
class Solution4_TLE {
public:
int minimumScore(vector<int>& nums, vector<vector<int>>& edges) {
vector<vector<int>> adj(size(nums));
for (const auto& e : edges) {
adj[e[0]].emplace_back(e[1]);
adj[e[1]].emplace_back(e[0]);
}
const auto& iter_dfs = [&](int u, int p, vector<int> *result) {
using RET = int;
RET ret = 0;
vector<tuple<int, int, int, shared_ptr<vector<shared_ptr<RET>>>, RET *>> stk;
stk.emplace_back(1, u, p, nullptr, &ret);
while (!empty(stk)) {
auto [step, u, p, new_rets, ret] = stk.back(); stk.pop_back();
if (step == 1) {
auto new_rets = make_shared<vector<shared_ptr<RET>>>();
stk.emplace_back(2, u, p, new_rets, ret);
for (const auto& v : adj[u]) {
if (v == p) {
continue;
}
new_rets->emplace_back(make_shared<RET>());
stk.emplace_back(1, v, u, nullptr, new_rets->back().get());
}
} else if (step == 2) {
*ret = nums[u];
for (const auto& x : *new_rets) {
*ret ^= *x;
}
result->emplace_back(*ret);
}
}
};
const int total = accumulate(cbegin(nums), cend(nums), 0,
[](int x, int y) {
return x ^ y;
});
int result = numeric_limits<int>::max();
for (const auto& e : edges) {
vector<vector<int>> xors(2);
iter_dfs(e[0], e[1], &xors[0]);
iter_dfs(e[1], e[0], &xors[1]);
for (auto& candidates : xors) {
const int total2 = candidates.back(); candidates.pop_back();
for (const auto& x : candidates) {
const auto& [a, b, c] = tuple(total ^ total2, x, total2 ^ x);
result = min(result, max({a, b, c}) - min({a, b, c}));
}
}
}
return result;
}
};