线段树维护区间Sum Max Min

最新推荐文章于 2024-01-09 10:00:09 发布

HHeyanjie

最新推荐文章于 2024-01-09 10:00:09 发布

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本文详细介绍了线段树这一数据结构，并通过实例展示了如何使用线段树来快速维护一个区间内的元素之和、最大值和最小值。线段树作为一种动态维护区间信息的工具，对于解决区间查询与更新问题具有高效的性能。

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#include <bits/stdc++.h>		//线段树维护区间和
#define ll long long
#define inf 0x3f3f3f3f 
using namespace std;
const int maxn = 1e5+7;
int a[10000];
struct node{
	int l,r;
	ll add;
	ll sum;
	ll maxx;
	ll minn;
}tree[maxn<<2];
void pushup(int index){		//更新值
	tree[index].sum = tree[index<<1].sum+tree[index<<1|1].sum;  
    tree[index].maxx = max(tree[index<<1].maxx,tree[index<<1|1].maxx);  
    tree[index].minn = min(tree[index<<1].minn,tree[index<<1|1].minn);  
}
void pushdown(int index){	//下推标记
	if(tree[index].add){
 		tree[index<<1].sum += (tree[index<<1].r-tree[index<<1].l+1)*tree[index].add;  
        tree[index<<1|1].sum +=(tree[index<<1|1].r-tree[index<<1|1].l+1)*tree[index].add;  
        
        tree[index<<1].maxx += tree[index].add;  
        tree[index<<1|1].maxx += tree[index].add;  
        
        tree[index<<1].minn += tree[index].add;  
        tree[index<<1|1].minn += tree[index].add;  
        
        tree[index<<1].add += tree[index].add;  
        tree[index<<1|1].add += tree[index].add;  
        
        tree[index].add = 0; 
	}
}
void build(int l, int r, int index){		//建树	数组a的l,r区间建树
	tree[index].l = l;
	tree[index].r = r;
	tree[index].add = 0;
	if(l == r){
		scanf("%lld",&tree[index].sum);
		tree[index].maxx = tree[index].minn = tree[index].sum;
		// tree[index].sum = tree[index].maxx = tree[index].minn = a[l];
		return;
	}
	int mid = (l+r)>>1;
	build(l,mid,index<<1);
	build(mid+1,r,index<<1|1);
	pushup(index);
}
void update(int l,int r,int index, ll w){	//修改a[L]的值 更新sum
	if(l <= tree[index].l && r >= tree[index].r){	
        tree[index].sum += (tree[index].r-tree[index].l+1)*w;  
        tree[index].maxx += w;  
        tree[index].minn += w;  
        tree[index].add += w;
		return;
	}
	pushdown(index);
	int mid = (tree[index].l + tree[index].r)>>1;
	if(l <= mid) update(l,r,index<<1,w);
	if(r > mid) update(l,r,index<<1|1,w);
	pushup(index);
}
ll query(int l,int r,int index){	//查询
	if(l <= tree[index].l && r >= tree[index].r){
		return tree[index].sum;
		// return tree[index].maxx;
		// return tree[index].minn;
	}
	pushdown(index);
	int mid = (tree[index].l + tree[index].r)>>1;
	ll sum = 0;
	ll maxx = 0;
	ll minn = inf;
 	if(l <= mid){
 		sum += query(l,r,index<<1);
 		maxx = max(maxx,query(l,r,index<<1));
 		minn = min(minn,query(l,r,index<<1));
 	}
	if(r > mid){
		sum += query(l,r,index<<1|1);
 		maxx = max(maxx,query(l,r,index<<1|1));
 		minn = min(minn,query(l,r,index<<1|1));
	}
	return sum;
	// return maxx;
	// return minn;
}
int main(){
	int n,m,q,x,y;
	ll z; 
    while(~scanf("%d %d", &n, &m)){  
        build(1,n,1);  
        while(m--){  
            scanf("%d",&q);  
            if(q == 1){  
                cout<<"query from x to y"<<endl;  
                scanf("%d %d",&x,&y);  
                cout<<query(x,y,1)<<endl;  
            }  
            else{  
                cout<<"add z from x to y:"<<endl;  
                scanf("%d %d %lld", &x, &y, &z);  
                update(x,y,1,z);  
                for(int i = 1; i <= n; i ++){  
                    printf("a[%d] = %lld\n",i,query(i,i,1));  
                }
            }  
        }  
    }

	return 0;
}