1、求区间和
1 #include <cstdio> 2 #include <iostream> 3 using namespace std; 4 const int maxn=50000+5; 5 int a[maxn]; 6 struct Node 7 { 8 int l,r,sum; 9 } node[maxn<<2]; 10 11 //参数含义：节点区间，节点编号 12 void InitTree(int l,int r,int k) 13 { 14 node[k].r=r;//节点k的右子树 15 node[k].l=l; 16 node[k].sum=0;//权值 17 if(l==r)//到达叶子节点 18 { 19 node[k].sum=a[r]; 20 return; 21 } 22 int mid=(l+r)>>1; 23 InitTree(l,mid,k<<1);//递归建左子树 24 InitTree(mid+1,r,k<<1|1);//递归建右子树 25 26 node[k].sum=node[k<<1].sum+node[k<<1|1].sum; 27 //父节点的值为两子节点值的和 28 //此为线段树的核心所在，求最值修改这一句即可 29 } 30 void UpdateTree(int l,int r,int k,int sum) 31 { 32 if(node[k].l==l&&node[k].r==r) 33 { 34 node[k].sum+=sum; 35 return; 36 } 37 int mid=(node[k].l+node[k].r)>>1; 38 if(l>mid) 39 UpdateTree(l,r,k<<1|1,sum);//更新下一层的右子树 40 else 41 UpdateTree(l,r,k<<1,sum); 42 43 node[k].sum=node[k<<1].sum+node[k<<1|1].sum; 44 //注意：每次更新后也要更新父节点的值 45 } 46 //查询l到r的k 47 int SearchTree(int l,int r,int k) 48 { 49 if(node[k].l==l&&node[k].r==r) 50 { 51 return node[k].sum; 52 } 53 int mid=(node[k].l+node[k].r)>>1; 54 if(l>mid) 55 { 56 return SearchTree(l,r,k<<1|1);//查询右子树 57 } 58 else if(r<=mid) 59 { 60 return SearchTree(l,r,k<<1); 61 } 62 else 63 { 64 //查询区间横跨左右子树，两棵子树一起查询 65 return SearchTree(mid+1,r,k<<1|1)+SearchTree(l,mid,k<<1); 66 } 67 } 68 int main() 69 { 70 int T,kase=0; 71 cin>>T; 72 while(T--) 73 { 74 printf("Case %d: ",++kase); 75 int n,x,y; 76 scanf("%d",&n); 77 for(int i=1;i<=n;i++) 78 { 79 scanf("%d",&a[i]); 80 } 81 InitTree(1,n,1); 82 char ch[10]; 83 while(scanf("%s",ch)) 84 { 85 if(ch[0]=='E') 86 break; 87 scanf("%d%d",&x,&y); 88 if(ch[0]=='A') 89 UpdateTree(x,x,1,y); 90 else if(ch[0]=='S') 91 UpdateTree(x,x,1,-y); 92 else if(ch[0]=='Q') 93 cout<<SearchTree(x,y,1)<<endl; 94 } 95 } 96 return 0; 97 }
2、求区间最大值
1 #include <cstdio> 2 #include <iostream> 3 using namespace std; 4 const int maxn=200000+5; 5 int a[maxn]; 6 struct Node 7 { 8 int l,r,sum; 9 } node[maxn<<2]; 10 11 //参数含义：节点区间，节点编号 12 void InitTree(int l,int r,int k) 13 { 14 node[k].r=r;//节点k的右子树 15 node[k].l=l; 16 node[k].sum=0;//权值 17 if(l==r)//到达叶子节点 18 { 19 node[k].sum=a[r]; 20 return; 21 } 22 int mid=(l+r)>>1; 23 InitTree(l,mid,k<<1);//递归建左子树 24 InitTree(mid+1,r,k<<1|1);//递归建右子树 25 26 node[k].sum=max(node[k<<1].sum,node[k<<1|1].sum); 27 //父节点的值为两子节点值的和 28 ///此为线段树的核心所在，求最值修改这一句即可 29 } 30 void UpdateTree(int l,int r,int k,int sum) 31 { 32 if(node[k].l==l&&node[k].r==r) 33 { 34 node[k].sum=sum; 35 return; 36 } 37 int mid=(node[k].l+node[k].r)>>1; 38 if(l>mid) 39 UpdateTree(l,r,k<<1|1,sum);//更新下一层的右子树 40 else 41 UpdateTree(l,r,k<<1,sum); 42 43 node[k].sum=max(node[k<<1].sum,node[k<<1|1].sum); 44 //注意：每次更新后也要更新父节点的值 45 } 46 //查询l到r的k 47 int SearchTree(int l,int r,int k) 48 { 49 if(node[k].l==l&&node[k].r==r) 50 { 51 return node[k].sum; 52 } 53 int mid=(node[k].l+node[k].r)>>1; 54 if(l>mid) 55 { 56 return SearchTree(l,r,k<<1|1);//查询右子树 57 } 58 else if(r<=mid) 59 { 60 return SearchTree(l,r,k<<1); 61 } 62 else 63 { 64 //查询区间横跨左右子树，两棵子树一起查询 65 return max(SearchTree(mid+1,r,k<<1|1),SearchTree(l,mid,k<<1)); 66 } 67 } 68 int main() 69 { 70 int n,m; 71 while(scanf("%d%d",&n,&m)!=EOF) 72 { 73 int x,y; 74 for(int i=1;i<=n;i++) 75 { 76 scanf("%d",&a[i]); 77 } 78 InitTree(1,n,1); 79 char ch; 80 while(m--) 81 { 82 getchar(); 83 scanf("%c",&ch); 84 scanf("%d%d",&x,&y); 85 if(ch=='U') 86 UpdateTree(x,x,1,y); 87 else if(ch=='Q') 88 printf("%d ",SearchTree(x,y,1)); 89 } 90 } 91 return 0; 92 }
3、更新版本（源自网络）（上面两个为更新结点，这个是更新区间）
1 #include <string.h> 2 #include <algorithm> 3 #include <stdio.h> 4 #include <math.h> 5 #include <queue> 6 #define MAXN 100010 7 #define inf 0x3f3f3f3f 8 9 using namespace std; 10 11 struct node{ 12 long long l,r;//区间[l,r] 13 long long add;//区间的延时标记 14 long long sum;//区间和 15 // long long mx; //区间最大值 16 // long long mn; //区间最小值 17 }tree[MAXN<<2];//一定要开到4倍多的空间 18 19 void pushup(long long index){ 20 tree[index].sum = tree[index<<1].sum+tree[index<<1|1].sum; 21 // tree[index].mx = max(tree[index<<1].mx,tree[index<<1|1].mx); 22 // tree[index].mn = min(tree[index<<1].mn,tree[index<<1|1].mn); 23 } 24 void pushdown(long long index){ 25 //说明该区间之前更新过 26 //要想更新该区间下面的子区间，就要把上次更新该区间的值向下更新 27 if(tree[index].add){ 28 //替换原来的值 29 /* 30 tree[index<<1].sum = (tree[index<<1].r-tree[index<<1].l+1)*tree[index].add; 31 tree[index<<1|1].sum = (tree[index<<1|1].r-tree[index<<1|1].l+1)*tree[index].add; 32 tree[index<<1].mx = tree[index].add; 33 tree[index<<1|1].mx = tree[index].add; 34 tree[index<<1].mn = tree[index].add; 35 tree[index<<1|1].mn = tree[index].add; 36 tree[index<<1].add = tree[index].add; 37 tree[index<<1|1].add = tree[index].add; 38 tree[index].add = 0;*/ 39 //在原来的值的基础上加上val 40 41 tree[index<<1].sum += (tree[index<<1].r-tree[index<<1].l+1)*tree[index].add; 42 tree[index<<1|1].sum +=(tree[index<<1|1].r-tree[index<<1|1].l+1)*tree[index].add; 43 // tree[index<<1].mx += tree[index].add; 44 // tree[index<<1|1].mx += tree[index].add; 45 // tree[index<<1].mn += tree[index].add; 46 // tree[index<<1|1].mn += tree[index].add; 47 tree[index<<1].add += tree[index].add; 48 tree[index<<1|1].add += tree[index].add; 49 tree[index].add = 0; 50 51 } 52 } 53 void build(long long l,long long r,long long index){ 54 tree[index].l = l; 55 tree[index].r = r; 56 tree[index].add = 0;//刚开始一定要清0 57 if(l == r){ 58 scanf("%d",&tree[index].sum); 59 // tree[index].mn = tree[index].mx = tree[index].sum; 60 return ; 61 } 62 long long mid = (l+r)>>1; 63 build(l,mid,index<<1); 64 build(mid+1,r,index<<1|1); 65 pushup(index); 66 } 67 void updata(long long l,long long r,long long index,long long val){ 68 if(l <= tree[index].l && r >= tree[index].r){ 69 /*把原来的值替换成val,因为该区间有tree[index].r-tree[index].l+1 70 个数，所以区间和 以及 最值为： 71 */ 72 /*tree[index].sum = (tree[index].r-tree[index].l+1)*val; 73 tree[index].mn = val; 74 tree[index].mx = val; 75 tree[index].add = val;//延时标记*/ 76 //在原来的值的基础上加上val,因为该区间有tree[index].r-tree[index].l+1 77 //个数，所以区间和 以及 最值为： 78 tree[index].sum += (tree[index].r-tree[index].l+1)*val; 79 // tree[index].mn += val; 80 // tree[index].mx += val; 81 tree[index].add += val;//延时标记 82 83 return ; 84 } 85 pushdown(index); 86 long long mid = (tree[index].l+tree[index].r)>>1; 87 if(l <= mid){ 88 updata(l,r,index<<1,val); 89 } 90 if(r > mid){ 91 updata(l,r,index<<1|1,val); 92 } 93 pushup(index); 94 } 95 long long query(long long l,long long r,long long index){ 96 if(l <= tree[index].l && r >= tree[index].r){ 97 return tree[index].sum; 98 //return tree[index].mx; 99 //return tree[index].mn; 100 } 101 pushdown(index); 102 long long mid = (tree[index].l+tree[index].r)>>1; 103 long long ans = 0; 104 // long long Max = 0; 105 // long long Min = inf; 106 if(l <= mid){ 107 ans += query(l,r,index<<1); 108 // Max = max(query(l,r,index<<1),Max); 109 // Min = min(query(l,r,index<<1),Min); 110 } 111 if(r > mid){ 112 ans += query(l,r,index<<1|1); 113 // Max = max(query(l,r,index<<1|1),Max); 114 // Min = min(query(l,r,index<<1|1),Min); 115 } 116 return ans; 117 // return Max; 118 //return Min; 119 } 120 int main() 121 { 122 long long n,m,x,y,z; 123 char q; 124 scanf("%lld%lld",&n,&m); 125 build(1,n,1); 126 getchar(); 127 while(m--){ 128 scanf("%c",&q); 129 if(q == 'Q'){ 130 scanf("%lld%lld",&x,&y); 131 printf("%lld ",query(x,y,1)); 132 } 133 else{ 134 scanf("%lld%lld%lld",&x,&y,&z); 135 updata(x,y,1,z); 136 /* for(int i = 1; i <= n; ++i){ 137 printf("a[%d] = %d ",i,query(i,i,1)); 138 }*/ 139 } 140 getchar(); 141 } 142 return 0; 143 }