Line Segment tree --- Analysis & template Summary

Line Segment tree: (convert)

Data Structure topic --- line tree: http://blog.csdn.net/metalseed/article/details/8039326

Summary of line tree: http://blog.csdn.net/shiqi_614/article/details/8228102

 

Overview:

A line segment tree, similar to an interval tree, is a complete binary tree. It stores a line segment (a subarray in an array) on each node and is mainly used to efficiently solve the dynamic query problem of consecutive intervals, due to the characteristics of the binary structure, it can basically maintain the complexity of each operation as O (lgn )!

Nature: the father's range is [a, B], (C = (a + B)/2) the left son's range is [a, c], the range of the right son is [C + 1, B]. The space required by the line segment tree is four times the size of the array.

 

 

HDU 1066 enemy army deployment

· Application of the classic line segment tree:

Code:

 1 #include <cstdio> 2 #include <algorithm> 3 using namespace std; 4  5 #define lson l , m , rt << 1 6 #define rson m + 1 , r , rt << 1 | 1 7 #define root 1 , n , 1 8 #define LL long long 9 #define maxn 50000*510 11 LL ad[maxn<<2];12 LL su[maxn<<2];13 void PushUp(int rt) {14     su[rt] = su[rt<<1] + su[rt<<1|1];15 }16 void PushDown(int rt,int m) {17     if (ad[rt]) {18         ad[rt<<1] += ad[rt];19         ad[rt<<1|1] += ad[rt];20         su[rt<<1] += ad[rt] * (m - (m >> 1));21         su[rt<<1|1] += ad[rt] * (m >> 1);22         ad[rt] = 0;23     }24 }25 void build(int l,int r,int rt) {26     ad[rt] = 0;27     if (l == r) {28         scanf("%lld",&su[rt]);29         return ;30     }31     int m = (l + r) >> 1;32     build(lson);33     build(rson);34     PushUp(rt);35 }36 void update(int L,int R,int c,int l,int r,int rt) {37     if (L <= l && r <= R) {38         ad[rt] += c;39         su[rt] += (LL)c * (r - l + 1);40         return ;41     }42     PushDown(rt , r - l + 1);43     int m = (l + r) >> 1;44     if (L <= m) update(L , R , c , lson);45     if (m < R) update(L , R , c , rson);46     PushUp(rt);47 }48 LL query(int L,int R,int l,int r,int rt) {49     if (L <= l && r <= R) {50         return su[rt];51     }52     PushDown(rt , r - l + 1);53     int m = (l + r) >> 1;54     LL ret = 0;55     if (L <= m) ret += query(L , R , lson);56     if (m < R) ret += query(L , R , rson);57     return ret;58 }59 int main() {60     int n,number=1;61     int T;62     scanf("%d",&T);63     while(T--){64         printf("Case %d:\n",number++);65         scanf("%d",&n);66         build(root);67         char op[20];68         int a , b ;69         while (scanf("%s",op) && op[0]!=‘E‘) {70             if (op[0] == ‘Q‘) {71                 scanf("%d%d",&a,&b);72                 printf("%lld\n",query(a , b ,root));73             } else {74                 scanf("%d%d",&a,&b);75                 if(op[0]==‘A‘)76                     update(a , a , b , root);77                 else78                     update(a , a , -b , root);79 80             }81         }82     }83     return 0;84 }

 

Line Segment tree --- Analysis & template Summary