线段树2020
单点更新，区间查询，维护区间和
#include<bits/stdc++.h>
using namespace std;
const int N = 1e6+10;
int n,m,a[N];
int sumv[N<<2];
//合并
void pushup(int o){
sumv[o] = sumv[o<<1] + sumv[o<<1|1];
}
//建树
void build(int o,int l,int r){
if(l == r) { //到最后一行了 [1,1] [2,2] ...
sumv[o] = a[l];
return;
}
int mid = (l+r)>>1;
build(o<<1,l,mid);
build(o<<1|1,mid+1,r);
pushup(o);//向上合并
}
//a[x] += y : change(1,1,n,x,y);
//单点修改 o为当前到达节点的编号
void change(int o,int l,int r,int pos,int v){
if(l == r){
sumv[o] += v;
return;
}
int mid = (l+r)>>1;
if(pos <= mid) change(o<<1,l,mid,pos,v);//前半段区间
else change(o<<1|1,mid+1,r,pos,v); //后半段区间
pushup(o); //向上更新 有一些线段树维护了多个值,所以pushup不止一条
}
//区间查询
int querysum(int o,int l,int r,int ql,int qr){
if(ql<=l && r<=qr) return sumv[o];//要查询的区间完全包含了[l,r]
int ans = 0;
int mid = (l+r)>>1;
if(ql<=mid) ans += querysum(o<<1,l,mid,ql,qr);
if(qr>mid) ans += querysum(o<<1|1,mid+1,r,ql,qr);
return ans;
}
int main(){
cin>>n>>m;
for(int i=1;i<=n;i++) cin>>a[i];
build(1,1,n);
while(m--){
int opt;
cin>>opt;
if(opt == 1){
int x,y;
cin>>x>>y;
change(1,1,n,x,y);
}
if(opt == 2){
int l,r;
cin>>l>>r;
cout<<querysum(1,1,n,l,r)<<endl;
}
}
}
单点更新，区间查询，维护区间最小值
#include<bits/stdc++.h>
using namespace std;
const int N = 1e6+10;
int n,m,a[N];
int minv[N<<2];
//建树
void build(int o,int l,int r){
if(l == r) { //到最后一行了 [1,1] [2,2] ...
minv[o] = a[l];
return;
}
int mid = (l+r)>>1;
build(o<<1,l,mid);
build(o<<1|1,mid+1,r);
pushup(o);//向上合并
}
void pushup(int o){
minv[o] = min(minv[o<<1],minv[o<<1|1]);
}
//a[x] += y : change(1,1,n,x,y);
//单点修改 o为当前到达节点的编号
void change(int o,int l,int r,int pos,int v){
if(l == r){
minv[o] += v;
return;
}
int mid = (l+r)>>1;
if(pos <= mid) change(o<<1,l,mid,pos,v);//前半段区间
else change(o<<1|1,mid+1,r,pos,v); //后半段区间
pushup(o); //向上更新 有一些线段树维护了多个值,所以pushup不止一条
}
//区间查询
int querymin(int o,int l,int r,int ql,int qr){
if(ql<=l && r<=qr) return minv[o];//要查询的区间完全包含了[l,r]
int ans = 1e9+7; //为了求区间最小 初始要设置一个比较大的值
int mid = (l+r)>>1;
if(ql<=mid) ans = min(ans,querymin(o<<1,l,mid,ql,qr));
if(qr>mid) ans = min(ans,querymin(o<<1|1,mid+1,r,ql,qr));
return ans;
}
int main(){
cin>>n>>m;
for(int i=1;i<=n;i++) cin>>a[i];
build(1,1,n);
while(m--){
int opt;
cin>>opt;
if(opt == 1){
int x,y;
cin>>x>>y;
change(1,1,n,x,y);
}
if(opt == 2){
int l,r;
cin>>l>>r;
cout<<querymin(1,1,n,l,r)<<endl;
}
}
}
区间修改，区间查询，标记下放
#include<bits/stdc++.h>
using namespace std;
const int N = 1e6+10;
int n,m,a[N];
int sumv[N<<2],addv[N<<2];
//合并
void pushup(int o){
sumv[o] = sumv[o<<1] + sumv[o<<1|1];
}
//建树
void build(int o,int l,int r){
if(l == r) { //到最后一行了 [1,1] [2,2] ...
sumv[o] = a[l];
return;
}
int mid = (l+r)>>1;
build(o<<1,l,mid);
build(o<<1|1,mid+1,r);
pushup(o);//向上合并
}
void puttag(int o,int l,int r,int v){
addv[o] += v;
sumv[o] += (r-l+1)*v;
}
void pushdown(int o,int l,int r){
if(addv[o] == 0) return;
addv[o<<1] += addv[o];
addv[o<<1|1] += addv[o];
int mid = (l+r)>>1;
sumv[o<<1] += addv[o] * (mid-l+1);
sumv[o<<1|1] += addv[o] * (r-mid);
addv[o] = 0;
}
void optadd(int o,int l,int r,int ql,int qr,int v){
if(ql<=l&&r<=qr){ //1.完全覆盖(l,r)这个子区间 就先更新好值,打上标记(为后面作标记准备)
puttag(o,l,r,v); //在puttag这里更新区间的值 打上标记
return;
}
int mid = (l+r)>>1;
pushdown(o,l,r);//标记下放 因为接下来要更新子区间了
if(ql <= mid) optadd(o<<1,l,mid,ql,qr,v);
if(qr > mid) optadd(o<<1|1,mid+1,r,ql,qr,v);
pushup(o);
}
int querysum(int o,int l,int r,int ql,int qr){
if(ql<=l&&r<=qr) return sumv[o];
int ans = 0;
int mid = (l+r)>>1;
pushdown(o,l,r);
if(ql<=mid) ans+=querysum(o<<1,l,mid,ql,qr);
if(qr>mid) ans+=querysum(o<<1|1,mid+1,r,ql,qr);
return ans;
}
int main(){
cin>>n>>m;
for(int i=1;i<=n;i++) cin>>a[i];
build(1,1,n);
while(m--){
int opt;
cin>>opt;
if(opt == 1){ //区间加
int l,r,v;
cin>>l>>r>>v;
optadd(1,1,n,l,r,v);
}
if(opt == 2){
int l,r;
cin>>l>>r;
cout<<querysum(1,1,n,l,r)<<endl;
}
}
}
线段树2019
单点更新区间查询，维护最小值
#include <iostream>
using namespace std;
const int inf = 0x3f3f3f3f;
const int maxn = 110;
int a[maxn];//原数组
int minv[4 * maxn];//维护最小值
/*
单点更新
区间查询
*/
//维护
void pushup(int id) {
minv[id] = min(minv[id << 1], minv[id << 1 | 1]);
}
//建树
void build(int id, int l, int r) {
if (l == r) {
minv[id] = a[l];
return;
}
int mid = (l + r) >> 1;
build(id << 1, l, mid);
build(id << 1 | 1, mid + 1, r);
pushup(id);
}
//更新
void update(int id, int l, int r, int x, int v) {
if (l == r) {
minv[id] = v;
return;
}
int mid = (l + r) >> 1;
if (x <= mid) {
update(id << 1, l, mid, x, v);
} else {
update(id << 1 | 1, mid + 1, r, x, v);
}
pushup(id);
}
//查询
int query(int id,int l,int r,int x,int y){
if(x <= l && r <= y){
return minv[id];
}
int mid = (l + r) >> 1;
int ans = inf;
if( x <= mid){
ans = min(ans,query(id << 1, l, mid, x,y));
}
if( y > mid){
ans = min(ans,query( id<< 1 | 1,mid + 1,r,x,y));
}
return ans;
}
int main() {
int n;
cin >> n;
for (int i = 1; i <= n; ++i) {
cin >> a[i];
}
build(1, 1, n);
int q;
cin >> q;
for (int i = 0; i < q; ++i) {
int x, v;
cin >> x >> v;
update(1, 1, n, x, v);
}
int p;
cin >> p;
for (int i = 0; i < p; ++i) {
int l, r;
cin >> l >> r;
cout << query(1, 1, n, l, r) << endl;
}
return 0;
}
区间更新，区间查询，维护赋值修改
void up(int p)
{
if (!p) return;
s[p] = s[p * 2] + s[p * 2 + 1];
}
void down(int p, int l, int r)
{
if (col[p])
{
int mid = (l + r) / 2;
s[p * 2] = col[p] * (mid - l + 1);
s[p * 2 + 1] = col[p] * (r - mid);
col[p * 2] = col[p * 2 + 1] = col[p];
col[p] = 0;
}
}
void modify(int p, int l, int r, int x, int y, int c)
{
if (x <= l && r <= y)
{
s[p] = (r - l + 1) * c; //仅修改该结点
col[p] = c; //增加标记，子结点待修改
return;
}
down(p, l, r); //下传lazy标记
int mid = (l + r) / 2;
if (x <= mid) modify(p * 2, l, mid, x, y, c);
if (y > mid) modify(p * 2 + 1, mid + 1, r, x, y, c);
up(p);
}
