算法1
树状数组 + 线段树
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long ll;
const int N = 500010;
ll trr[N]; // 树状数组 维护a数组的差分数组
ll a[N]; // 原数组
struct Node
{
int l, r;
ll d; // 序列差分的最大公约数
} tr[N << 2];
int n, m;
int lowbit(int x)
{
return x & -x;
}
void add(int x, ll v)
{
for(int i = x; i <= n; i += lowbit(i))
trr[i] += v;
}
ll sum(int x)
{
ll res = 0;
for(int i = x; i; i -= lowbit(i))
res += trr[i];
return res;
}
ll gcd(ll a, ll b)
{
return b ? gcd(b, a % b) : a;
}
void pushup(Node &fa, Node &l, Node &r)
{
fa.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)
{
tr[u] = {l, r, a[r] - a[r - 1]};
}
else
{
tr[u] = {l, r};
int mid = l + r >> 1;
build(u << 1, l, mid);
build(u << 1 | 1, mid + 1, r);
pushup(u);
}
}
void modify(int u, int x, ll v)
{
if(tr[u].l == x && tr[u].r == x)
{
tr[u].d += v;
}
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);
}
}
Node query(int u, int l, int r)
{
if(l <= tr[u].l && r >= tr[u].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
{
Node res;
auto left = query(u << 1, l, r);
auto right = query(u << 1 | 1, l, r);
pushup(res, left, right);
return res;
}
}
}
int main()
{
scanf("%d%d", &n, &m);
for(int i = 1; i <= n; i ++)
{
scanf("%lld", &a[i]);
add(i, a[i]), add(i + 1, -a[i]);
}
build(1, 1, n);
while(m --)
{
char op[2];
int l, r;
scanf("%s%d%d", op, &l, &r);
if(*op == 'Q')
{
// gcd(a[l] ~ a[r]) = gcd(sum(a[l]), gcd(b[l + 1] ~ b[r]))
ll res = 0;
if(l == r)
res = abs(sum(l));
else
res = abs(gcd(sum(l), query(1, l + 1, r).d));
printf("%lld\n", res);
}
else
{
ll x;
scanf("%lld", &x);
modify(1, l, x);
if(r < n)
modify(1, r + 1, -x);
add(l, x);
add(r + 1, -x);
}
}
return 0;
}
算法2
线段树 (同时维护 差分序列的区间和 + 差分序列的最大公约数)
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long ll;
const int N = 500010;
struct Node
{
int l, r;
ll sum; // 区间[l, r]的和(原序列的差分序列的区间和)
ll d; // 区间[l, r]差分序列的最大公倍数
} tr[N << 2];
ll a[N];
int n, m;
ll gcd(ll a, ll b)
{
return b ? gcd(b, a % b) : a;
}
void pushup(Node &fa, Node &l, Node &r)
{
fa.d = gcd(l.d, r.d);
fa.sum = l.sum + r.sum;
}
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 = a[r] - a[r - 1];
tr[u] = {l, r, b, b};
}
else
{
tr[u] = {l, r};
int mid = l + r >> 1;
build(u << 1, l, mid);
build(u << 1 | 1, mid + 1, r);
pushup(u);
}
}
void modify(int u, int x, ll v)
{
if(tr[u].l == x && tr[u].r == x)
{
tr[u].d += v;
tr[u].sum += v;
}
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);
}
}
Node query(int u, int l, int r)
{
if(l <= tr[u].l && r >= tr[u].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
{
Node res;
auto left = query(u << 1, l, r);
auto right = query(u << 1 | 1, l, r);
pushup(res, left, right);
return res;
}
}
}
int main()
{
scanf("%d%d", &n, &m);
for(int i = 1; i <= n; i ++) scanf("%lld", &a[i]);
build(1, 1, n);
while(m --)
{
char op[2];
int l, r;
scanf("%s%d%d", op, &l, &r);
if(*op == 'Q')
{
// gcd(a[l ~ r]) = gcd(a[l], gcd(b[l + 1 ~ r]));
// a[l] = query(1, 1, l).sum;
// gcd(b[l + 1 ~ r]) = query(1, l + 1, r).d;
ll res = 0;
if(l == r)
res = query(1, 1, l).sum;
else
res = abs(gcd(query(1, 1, l).sum, query(1, l + 1, r).d));
printf("%lld\n", res);
}
else
{
ll x;
scanf("%lld", &x);
modify(1, l, x);
if(r < n)
modify(1, r + 1, -x);
}
}
return 0;
}