线段树基本操作（单点更新，区间极值，区间求和）

做了一部分题目，总结一下线段树的几个基本操作。

#include<iostream>#include<cstdio>#include<cstring>#include<cstdlib>#include<algorithm>#include<cmath>#include<queue>using namespace std;const int INF=1<<29;int max_tree[300000];int min_tree[300000];int sum_tree[300000]; int a[300000];void build(int node,int begin,int end){//建树 if(begin==end) min_tree[node]=a[begin],max_tree[node]=a[begin],sum_tree[node]=a[begin];else{build(2*node,begin,(begin+end)/2);build(2*node+1,(begin+end)/2+1,end);max_tree[node]=max(max_tree[2*node],max_tree[2*node+1]);min_tree[node]=min(min_tree[2*node],min_tree[2*node+1]);sum_tree[node]=sum_tree[2*node]+sum_tree[2*node+1];}}int findmin(int node,int begin,int end,int z,int y){//找到z--y的最小值 int p1=INF,p2=INF;if(begin>=z&&end<=y) return min_tree[node];int fz=(begin + end) / 2;if(z<=fz)p1=findmin(2*node,begin,fz, z, y) ;if(y>fz)p2=findmin(2*node+1,fz+1,end,z,y);return min(p1,p2);}int findmax(int node,int begin,int end,int z,int y){//找到z--y的最大值 int p1=-INF,p2=-INF;if(begin>=z&&end<=y) return max_tree[node];int fz=(begin + end) / 2;if(z<=fz)p1=findmax(2*node,begin,fz, z, y) ;if(y>fz)p2=findmax(2*node+1,fz+1,end,z,y);return max(p1,p2);}int getsum(int node,int begin,int end,int z,int y){//求z--y的和 if(begin>=z&&end<=y) return sum_tree[node];int fz=(begin + end) / 2;int sum=0;if(z<=fz) sum+=getsum(2*node,begin,fz,z,y);if(y>fz) sum+=getsum(2*node+1,fz+1,end,z,y);return sum;}void updata(int node,int begin,int end,int x,int num){//单点更新 if(begin==end){min_tree[node]=num;max_tree[node]=num;sum_tree[node]=num;return;}int fz=(begin+end)/2;if(x<=fz) updata(node*2,begin,fz,x,num);else updata(node*2+1,fz+1,end,x,num);min_tree[node]=min(min_tree[2*node],min_tree[2*node+1]);max_tree[node]=max(max_tree[2*node],max_tree[2*node+1]);sum_tree[node]=sum_tree[2*node]+sum_tree[2*node+1];}int main(){a[1]=2,a[2]=3,a[3]=8,a[4]=1,a[5]=5,a[6]=7;// 2 3 8 1 5 7 build(1,1,6);cout<<"2 3 8 1 5 7"<<endl; /*寻找2--5区间最小值 */ cout<<"2--5区间最小值:"<<findmin(1,1,6,2,5)<<endl;/*寻找2--5区间最大值 */ cout<<"2--5区间最大值:"<<findmax(1,1,6,2,5)<<endl;/* 求2--5区间和 */cout<<"2--5区间和 :"<<getsum(1,1,6,2,5)<<endl;/* 更新a[3]=0,a[4]=10 */updata(1,1,6,3,0);updata(1,1,6,4,10);cout<<"2 3 0 10 5 7"<<endl; //查询更新后的结果 /*寻找2--5区间最小值 */ cout<<"2--5区间最小值:"<<findmin(1,1,6,2,5)<<endl;/*寻找2--5区间最大值 */ cout<<"2--5区间最大值:"<<findmax(1,1,6,2,5)<<endl;/* 求2--5区间和 */cout<<"2--5区间和 :"<<getsum(1,1,6,2,5)<<endl;return 0;}