专题七：线段树 / 线段树
  • 题意
    • 输出区间最大值与最小值的差
  • 题解
    • 线段树的区间查询或者直接上ST即可
    • 注意ST初始化f数组要看数据范围
  • 线段树代码：
  • #include<algorithm>
#include <iostream>
#include   <fstream>
#include  <cstdlib>
#include  <cstring>
#include  <cassert>
#include   <cstdio>
#include   <vector>
#include   <string>
#include    <cmath>
#include    <queue>
#include    <stack>
#include      <set>
#include      <map>
using namespace std;
#define P(a,b,c) make_pair(a,make_pair(b,c))
#define rep(i,a,n) for (int i=a;i<=n;i++)
#define per(i,a,n) for (int i=n;i>=a;i--)
#define CLR(vis) memset(vis,0,sizeof(vis))
#define MST(vis,pos) memset(vis,pos,sizeof(vis))
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef pair<int,pair<int,int> >pii;
typedef long long ll;
typedef unsigned long long ull;
const ll mod = 1000000007;
const int INF = 0x3f3f3f3f;
ll gcd(ll a, ll b) {
	return b ? gcd(b, a%b) : a;
}
template<class T>inline void gmax(T &A, T B) {
	(A<B)&&(A=B);//if(B>A)A=B;
}
template<class T>inline void gmin(T &A, T B) {
	(A>B)&&(A=B);//if(B<A)A=B;
}
template <class T>
inline bool scan(T &ret) {
	char c;
	int sgn;
	if(c=getchar(),c==EOF) return 0; //EOF
	while(c!='-'&&(c<'0'||c>'9')) c=getchar();
	sgn=(c=='-')?-1:1;
	ret=(c=='-')?0:(c-'0');
	while(c=getchar(),c>='0'&&c<='9') ret=ret*10+(c-'0');
	ret*=sgn;
	return 1;
}
inline void outt(int x) {
	if(x>9) outt(x/10);
	putchar(x%10+'0');
}
const int maxn=1e6+10;
int a[maxn];
struct SegmentTree {
	int l,r;
	int dat;
	int mi;
} t[maxn * 4];
void build(int p,int l,int r) { //build(1，1，n) 1为根节点
	t[p].l=l,t[p].r=r;
	if(l==r) {
		t[p].dat=a[l];
		t[p].mi=a[l];
		return;
	}
	int mid=(l+r)/2;
	build(p*2,l,mid);
	build(p*2+1,mid+1,r);
	t[p].dat=max(t[p*2].dat,t[p*2+1].dat);
	t[p].mi=min(t[p*2].mi,t[p*2+1].mi);
}
void change(int p,int x,int v) { //change(1,x,v) 1为根节点
	if(t[p].l==t[p].r) {
		t[p].dat=v;
		t[p].mi=v;
		return ;
	}
	int mid=(t[p].l+t[p].r)/2;
	if(x<=mid)change(p*2,x,v);
	else change(p*2+1,x,v);
	t[p].dat=max(t[p*2].dat,t[p*2+1].dat);
	t[p].mi=min(t[p*2].mi,t[p*2+1].mi);
}
int ask_max(int p,int l,int r) { //ask(1,l,r) 1为根节点
	if(l<=t[p].l && r>=t[p].r)return t[p].dat;
	int mid=(t[p].l + t[p].r)/2;
	int val=-(1<<30);
	if(l<=mid)val=max(val,ask_max(p*2,l,r));
	if(r>mid) val=max(val,ask_max(p*2+1,l,r));
	return val;
}
int ask_min(int p,int l,int r) { //ask(1,l,r) 1为根节点
	if(l<=t[p].l && r>=t[p].r)return t[p].mi;
	int mid=(t[p].l + t[p].r)/2;
	int val=1<<30;
	if(l<=mid)val=min(val,ask_min(p*2,l,r));
	if(r>mid) val=min(val,ask_min(p*2+1,l,r));
	return val;
}
string cmd;
int main() {
	int m,n;
	while(scan(n)) {
		scan(m);
		rep(i,1,n)scan(a[i]);
		build(1,1,n);
		while(m--) {
			int x,y;
			scan(x);
			scan(y);
				printf("%d\n", ask_max(1,x,y)-ask_min(1,x,y));
		}
	}
	return 0;
}
  • ST代码
  • #include<algorithm>
#include <iostream>
#include  <fstream>
#include  <cstdlib>
#include  <cstring>
#include  <cassert>
#include   <cstdio>
#include   <vector>
#include   <string>
#include    <cmath>
#include    <queue>
#include    <stack>
#include      <set>
#include      <map>
using namespace std;
#define P(a,b,c) make_pair(a,make_pair(b,c))
#define rep(i,a,n) for (int i=a;i<=n;i++)
#define per(i,a,n) for (int i=n;i>=a;i--)
#define CLR(vis) memset(vis,0,sizeof(vis))
#define MST(vis,pos) memset(vis,pos,sizeof(vis))
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef pair<int,pair<int,int> >pii;
typedef long long ll;
typedef unsigned long long ull;
const ll mod = 1000000007;
const int INF = 0x3f3f3f3f;
ll gcd(ll a, ll b) {
	return b ? gcd(b, a%b) : a;
}
template<class T>inline void gmax(T &A, T B) {
	(A<B)&&(A=B);//if(B>A)A=B;
}
template<class T>inline void gmin(T &A, T B) {
	(A>B)&&(A=B);//if(B<A)A=B;
}
template <class T>
inline bool scan(T &ret) {
	char c;
	int sgn;
	if(c=getchar(),c==EOF) return 0; //EOF
	while(c!='-'&&(c<'0'||c>'9')) c=getchar();
	sgn=(c=='-')?-1:1;
	ret=(c=='-')?0:(c-'0');
	while(c=getchar(),c>='0'&&c<='9') ret=ret*10+(c-'0');
	ret*=sgn;
	return 1;
}
inline void outt(int x) {
	if(x>9) outt(x/10);
	putchar(x%10+'0');
}
const int maxn=1e5+10;
int f[2*maxn][32];
int f2[2*maxn][32];
int a[maxn];
int n;
//void ST_prework(){
//	rep(i,1,n)f1[i][0]=a[i],f2[i][0]=a[i];
//	int t=log(n)/log(2)+1;
//	rep(j,1,t-1){
//		rep(i,1,n-(1<<j)+1){
//			f1[i][j]=max(f1[i][j-1],f1[i+(i<<(j-1))][j-1]);
//			f2[i][j]=min(f2[i][j-1],f2[i+(i<<(j-1))][j-1]);
//		}
//	}
//}
//int ST_query(int l,int r){
//	int k = log(r-l+1)/log(2);
//	cout<< max(f1[l][k],f1[r-(1<<k)+1][k]) << " " << min(f2[l][k],f2[r-(1<<k)+1][k]) << endl;
//	return max(f1[l][k],f1[r-(1<<k)+1][k])-min(f2[l][k],f2[r-(1<<k)+1][k]);
//}
//
void ST_prework()
{
    for(int i=1;i<=n;i++)f[i][0]=a[i],f2[i][0]=a[i];
    int t=log(n)/log(2)+1;
    for(int j=1;j<t;j++)
        for(int i=1;i<=n-(1<<j)+1;i++){
        	f[i][j]=max(f[i][j-1],f[i+(1<<(j-1))][j-1]);
            f2[i][j]=min(f2[i][j-1],f2[i+(1<<(j-1))][j-1]);
		}
            
}
int ST_query(int l,int r)
{
    int k=log(r-l+1)/log(2);
    return max(f[l][k],f[r-(1<<k)+1][k])-min(f2[l][k],f2[r-(1<<k)+1][k]);
}
 
int main() {
	int m;
	while(scan(n)) {
		scan(m);
//		memset(a,0x3f,sizeof(f2));
		rep(i,1,n){
			rep(j,1,30){
				f2[i][j]=0x3f3f3f3f;
			}
		}
		rep(i,1,n)scan(a[i]);
		ST_prework();
		while(m--) {
			int x,y;
			scan(x);
			scan(y);
			printf("%d\n", ST_query(x,y));
		}
	}
	return 0;
}

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