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213 | struct SegmentTree {
public:
explicit SegmentTree(int n)
: n(n), treeIntervalCounts(4 * n), treeIntervalLengths(4 * n) {}
// Adds val to intervalCounts[i] and updates intervalLengths[i] accordingly.
void add(int i, int val) {
add(0, 0, n - 1, i, val);
}
// Returns sum(intervalCounts[i..n - 1]).
int queryIntervalCounts(int i) const {
return query(treeIntervalCounts, 0, 0, n - 1, i, n - 1);
}
// Returns sum(intervalLengths[i..n - 1]).
int queryIntervalLengths(int i) const {
return query(treeIntervalLengths, 0, 0, n - 1, i, n - 1);
}
private:
const int n;
vector<int> treeIntervalCounts;
vector<int> treeIntervalLengths;
void add(int treeIndex, int lo, int hi, int i, int val) {
if (lo == hi) {
treeIntervalCounts[treeIndex] += val;
treeIntervalLengths[treeIndex] = treeIntervalCounts[treeIndex] * i;
return;
}
const int mid = (lo + hi) / 2;
if (i <= mid)
add(2 * treeIndex + 1, lo, mid, i, val);
else
add(2 * treeIndex + 2, mid + 1, hi, i, val);
treeIntervalCounts[treeIndex] =
merge(treeIntervalCounts[2 * treeIndex + 1],
treeIntervalCounts[2 * treeIndex + 2]);
treeIntervalLengths[treeIndex] =
merge(treeIntervalLengths[2 * treeIndex + 1],
treeIntervalLengths[2 * treeIndex + 2]);
}
int query(const vector<int>& tree, int treeIndex, int lo, int hi, int i,
int j) const {
if (i <= lo && hi <= j) // [lo, hi] lies completely inside [i, j].
return tree[treeIndex];
if (j < lo || hi < i) // [lo, hi] lies completely outside [i, j].
return 0;
const int mid = (lo + hi) / 2;
return merge(query(tree, treeIndex * 2 + 1, lo, mid, i, j),
query(tree, treeIndex * 2 + 2, mid + 1, hi, i, j));
}
int merge(int left, int right) const {
return left + right;
}
};
class Solution {
public:
vector<int> numberOfAlternatingGroups(vector<int>& colors,
vector<vector<int>>& queries) {
const int n = colors.size();
vector<int> ans;
vector<int> arr{colors};
SegmentTree tree(2 * n - 1);
set<pair<int, int>> intervals;
arr.insert(arr.end(), colors.begin(), colors.end());
// Insert all intervals, each of them is an alternating sequence.
int start = 0;
for (int i = 1; i < 2 * n - 1; ++i)
if (arr[i] == arr[i - 1]) {
insert(intervals, {start, i - 1}, tree, n);
start = i;
}
insert(intervals, {start, 2 * n - 2}, tree, n);
for (const vector<int>& query : queries)
if (query[0] == 1) {
const int sz = query[1];
const pair<int, int>& intervalWithN = findInterval(intervals, n);
const int numAlternatingGroups =
getNumAlternatingGroups(sz, intervalWithN, tree, n);
ans.push_back(numAlternatingGroups);
} else {
const int index = query[1];
const int color = query[2];
if (arr[index] == color)
continue;
update(intervals, index, color, arr, tree, n);
if (index < n - 1)
update(intervals, index + n, color, arr, tree, n);
}
return ans;
}
private:
// Returns the number of alternating groups of size `sz`.
int getNumAlternatingGroups(int sz, const pair<int, int>& intervalWithN,
const SegmentTree& tree, int n) {
const int numIntervals = tree.queryIntervalCounts(sz);
const int sumIntervals = tree.queryIntervalLengths(sz);
// The number of alternating groups for an interval is |interval| - sz + 1.
// Therefore, the number of alternating groups for all intervals is
// sum(|intervals[i]| - sz + 1)
// = sum(|intervals[i]) - numIntervals * sz + numIntervals
const int numAlternatingGroups =
sumIntervals - numIntervals * sz + numIntervals;
// We need to check if the interval (l, r) contains n, and if it does, we
// need to adjust the number of alternating groups to avoid duplicates.
const auto& [l, r] = intervalWithN;
// 1. For an interval with l >= n, it wasn't being considered in `insert`
// and `remove`.
// 2. For an interval with r - l + 1 < sz, it's impossible to form a group
// of size `sz`.
if (l >= n || r - l + 1 < sz)
return numAlternatingGroups;
// 3. For an interval with r >= n, it's possible to duplicately count the
// groups starting from n.
if (r >= n) { // l < n && r - 1 + 1 >= sz
// Groups starting from [l..n) are non-duplicately counted.
const int nonDuplicateGroups = n - l;
// The number of groups of size `sz` in the interval [l..r].
const int numGroups = (r - l + 1) - sz + 1;
return numAlternatingGroups - max(0, numGroups - nonDuplicateGroups);
}
return numAlternatingGroups;
}
// Inserts an interval into `intervals` and updates `tree`.
void insert(set<pair<int, int>>& intervals, const pair<int, int>& interval,
SegmentTree& tree, int n) {
intervals.insert(interval);
if (interval.first < n)
tree.add(interval.second - interval.first + 1, 1);
}
// Removes an interval from `intervals` and updates `tree`.
void remove(set<pair<int, int>>& intervals, const pair<int, int>& interval,
SegmentTree& tree, int n) {
intervals.erase(interval);
if (interval.first < n)
tree.add(interval.second - interval.first + 1, -1);
}
// Returns the interval containing the target.
pair<int, int> findInterval(const set<pair<int, int>>& intervals,
int target) {
auto it = intervals.upper_bound({target, INT_MAX});
return (*--it);
}
// Updates the color of the index-th element in `arr` and updates `intervals`
// and `tree`.
void update(set<pair<int, int>>& intervals, int index, int color,
vector<int>& arr, SegmentTree& tree, int n) {
arr[index] = color;
const pair<int, int> intervalWithIndex = findInterval(intervals, index);
remove(intervals, intervalWithIndex, tree, n);
auto [start, end] = intervalWithIndex;
// interval [s..i - 1|i|i + 1..e]
// index ^
if (start < index && index < end) {
insert(intervals, {start, index - 1}, tree, n);
insert(intervals, {index, index}, tree, n);
insert(intervals, {index + 1, end}, tree, n);
return;
}
// interval [s|s + 1..e]
// index ^
if (start == index && index < end)
insert(intervals, {start + 1, end}, tree, n);
// interval [s..e - 1|e]
// index ^
if (start < index && index == end)
insert(intervals, {start, end - 1}, tree, n);
start = index;
end = index;
vector<pair<int, int>> intervalsToRemove;
auto it = intervals.upper_bound({index, INT_MAX});
for (auto lit = it; lit != intervals.begin();) {
--lit;
if (arr[lit->second] == arr[start]) // [..lit->second|start..]
break;
intervalsToRemove.push_back(*lit);
start = lit->first;
}
for (auto rit = it; rit != intervals.end(); ++rit) {
if (arr[rit->first] == arr[end]) // [..end|rit->first..]
break;
intervalsToRemove.push_back(*rit);
end = rit->second;
}
for (const pair<int, int>& interval : intervalsToRemove)
remove(intervals, interval, tree, n);
insert(intervals, {start, end}, tree, n);
}
};
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