算法提高之区间最大公约数

• 核心思想：线段树

  • 1.在区间上加一个数
    • 差分
  • 2.求一段区间的最gcd
    • 求[l,r]的gcd 可以拆解为求**[1,l].sum(差分数组 求出来时l点的值)和[l+1,r]**做gcd

•   #include <iostream>#include <cstring>#include <algorithm>using namespace std;typedef long long LL;const int N = 500010;int n,m;LL w[N];struct Node{int l,r;LL sum,d;}tr[N*4];LL gcd(LL a,LL b){return b?gcd(b,a%b):a;}void pushup(Node &u,Node &l,Node &r){u.sum = l.sum + r.sum;u.d = gcd(l.d,r.d);}void pushup(int u){pushup(tr[u],tr[u<<1],tr[u<<1|1]);}void build(int u,int l,int r){if(l == r){LL b = w[r] - w[r-1];  //差分tr[u] = {l, r, b, b};}else{tr[u].l = l,tr[u].r = r;int mid = l+r>>1;build(u<<1,l,mid),build(u<<1|1,mid+1,r);pushup(u);}}Node query(int u,int l,int r){if(tr[u].l >= l && tr[u].r <= r) return tr[u];else{int mid = tr[u].l + tr[u].r >> 1;if(r <= mid) return query(u<<1,l,r);else if(l > mid) return query(u<<1|1,l,r);else{auto left = query(u << 1, l, r);auto right = query(u << 1 | 1, l, r);Node res;pushup(res,left,right);return res;}}}void modify(int u,int x, LL v){if(tr[u].l == x && tr[u].r == x){LL b = tr[u].sum + v;  //当前值+vtr[u] = {x,x,b,b};}else{int mid = tr[u].l + tr[u].r >> 1;if(x <= mid) modify(u<<1,x,v);else modify(u<<1|1,x,v);pushup(u);}}int main(){cin>>n>>m;for(int i=1;i<=n;i++) cin>>w[i];build(1,1,n);int l,r;LL d;char op[2];while (m -- ){cin>>op>>l>>r;if(op[0] == 'Q'){auto left = query(1,1,l);  //求[1,l].sumNode right({0, 0, 0, 0});if(l + 1 <= r) right = query(1,l+1,r);  //求[l+1,r].dcout<<abs(gcd(left.sum,right.d))<<endl;}else{cin>>d;modify(1,l,d);if(r + 1 <= n) modify(1,r+1,-d);}}}