洛谷 P3372 【模板】线段树 1

题意： 区间更新区间查询

思路：直接线段树实现就行，难点还是手撕线段树的结构跟细节。 说一下merge：直接对两个区间的sum求和。applyLazy：lazy值*区间长度。

struct Node{
bool is_lazy;
long long sum = 0;
long long lazy_val = 0;

Node(): is_lazy(false){}

Node operator + (const Node& other){
Node res = *this;
res.sum += other.sum;
return res;
}

void operator |= (const Node& other){
this->lazy_val += other.lazy_val;
this->is_lazy = true;
}

void applyLazy(Node& lazy, int length){
this->sum += lazy.lazy_val * length;
}
};

template
class SegmentTree{
public:
SegmentTree(int sz): sz_(sz), flag_{}{
st_.resize(4 * sz_);
lazy_.resize(4 * sz_);
}

SegmentTree(const vector& s): SegmentTree(int(s.size() - 1)){
function<void(int, int, int)> build = [&](int p, int l, int r){
if (l == r){
st_[p] = s[l];
}
else{
int mid = (l + r) >> 1;
build(p << 1, l, mid);
build(p << 1 | 1, mid + 1, r);
st_[p] = merge(st_[p << 1], st_[p << 1 | 1]);
}
};
build(1, 1, sz_);
}

void update(int i, int j, T val){
update(1, 1, sz_, i, j, val);
}

T query(int i, int j){
return query(1, 1, sz_, i, j);
}

private:
int sz_;
vector st_;
vector lazy_;
const T flag_;

T merge(T a, T b){
return a + b;
}

void pushDown(int p, int l, int r){
if (lazy_[p].is_lazy){
st_[p].applyLazy(lazy_[p], r - l + 1);
if (l != r){
lazy_[p << 1] |= lazy_[p];
lazy_[p << 1 | 1] |= lazy_[p];
}
lazy_[p] = flag_;
}
}

void update(int p, int l, int r, int i, int j, T val){
pushDown(p, l, r);
if (i > j){
return;
}
if (l >= i && r <= j){
lazy_[p] = val;
lazy_[p].is_lazy = true;
pushDown(p, l, r);
}
else{
int mid = (l + r) >> 1;
update(p << 1, l, mid, i, min(mid, j), val);
update(p << 1 | 1, mid + 1, r, max(i, mid + 1), j, val);
st_[p] = merge(st_[p << 1], st_[p << 1 | 1]);
}
}

T query(int p, int l, int r, int i, int j){
pushDown(p, l, r);
if (l >= i && r <= j){
return st_[p];
}
int mid = (l + r) >> 1;
if (j <= mid){
return query(p << 1, l, mid, i, j);
}
else if (i > mid){
return query(p << 1 | 1, mid + 1, r, i, j);
}
return merge(query(p << 1, l, mid, i, mid), query(p << 1 | 1, mid + 1, r, mid + 1, j));
}
};

void solve(){
int n, q;
cin >> n >> q;

vector a(n + 1);
for (int i = 1; i <= n; ++i){
cin >> a[i].sum;
}
SegmentTree st(a);

while (q --){
int t;
cin >> t;
int x, y;
cin >> x >> y;
if (t & 1){
Node k;
cin >> k.lazy_val;
st.update(x, y, k);
}
else{
cout << st.query(x, y).sum << '\n';
}
}
}

总结：
1 build里面忘记合并子区间。
2 query忘记写返回值
3 |=重载多写了返回值，导致lazy_val没有有向下传递到子区间

感觉在空间复杂度上还可以优化，室友有更好的存储lazy值的方式