Tree array _ poj tree Array

From: http://blog.csdn.net/svitter

The tree array is used to calculate the value in the interval and change the value of a single element. Note that the tree array starts from array subscript 1.

Basic Algorithms:

Obtain all lowbit values to prevent repeated calculation.

void getLowbit(){    for(int i = 0; i < 1000; i++)        lowbit[i] = i & (-i);}

Evaluate the range and 1 ~ I:

int Sum(int i){    int sum = 0;    while(i > 0)    {        sum += C[i];        i = i - lowbit[i];    }    return sum;}

Change the I value of an element:

void Change(int i, int inc){while(i <= n){C[i] += inc;i = i + lowbit[i];}}

Cn method:

sum(n) - sum(n - lowbit(n));

Question: poj3321

A. Apple tree contains multiple apples, one branch and one apple, and the number of apples at or above a node is calculated. You can add or delete apple. (If there is an apple, add it. If not, delete it. At the beginning, there were all apples ).

Test data: the first row is N, which indicates the number of branches. Then enter the branch relationship. The second behavior is m, which indicates the number of operations. Then, enter Q or C and add a number, indicating the sum or the tree is deleted or added.

Train of Thought: the sparse graph is stored in an adjacent table. STL _ sparse graph, and tree _ uses a vector adjacent table for storage. Calculate the sum between segments and change only one element. You can use a tree array. Take the root as 1 and the upstream node as the other side. Use deep search to count the number of apples.

C [I] is sum (I)-sum (I-lowbit [I]), that is, I-(I-lowbit [I]); C [time];

Q: Use start [N] and end [N] to store the access time. Use (end [N]-start [N] + 1) /2 obtain the final result (except for the Apple Node Selected, the other Apple went twice ).

C: Modify the apple node by combining the modify of the tree array. The query function does not calculate the value of apple.

#include <iostream>#include <stdio.h>#include <string.h>#include <vector>using namespace std;#define MY_MAX 220000typedef vector<int> VCT_INT;vector <VCT_INT> G(MY_MAX/2);int C[MY_MAX];int lowbit[MY_MAX];bool HasApple[MY_MAX];int start[MY_MAX];int end[MY_MAX];int nCount = 0;void DFS(int v){    start[v] = ++ nCount;    for(int i = 0; i < G[v].size(); i++)        DFS(G[v][i]);    end[v] = ++ nCount;}int QuerySum(int p){    int nSum = 0;    while(p > 0)    {        nSum += C[p];        p -= lowbit[p];    }    return nSum;}void Modify(int p, int val){    while(p <= nCount)    {        C[p] += val;        p += lowbit[p];    }}void getLowbit(){    for(int i = 1; i < MY_MAX; i++)        lowbit[i] = i & (-i);}int main(){    int n, m;    scanf("%d", &n);    int x, y, i, j ,k;    int a, b;    getLowbit();    //build map    for(i = 0; i < n - 1; i++)    {        scanf("%d%d", &a, &b);         G[a].push_back(b);     }     nCount = 0; DFS(1);     for(i = 1; i <= n; i++)        HasApple[i] = 1;    for(i = 1; i <= nCount; i++)        C[i] = i - (i - lowbit[i]);    scanf("%d", &m);    while(m--)    {        char cmd[10];        scanf("%s%d", cmd, &a);        if(cmd[0]== 'C')        {    if(HasApple[a])            {                Modify(start[a], -1);                Modify(end[a], -1);                HasApple[a] = 0;            }            else            {                Modify(start[a], 1);                Modify(end[a], 1);                HasApple[a] = 1;            }        }        else        {            int t1 = QuerySum(end[a]);            int t2 = QuerySum(start[a]-1);            printf("%d\n", (t1-t2)/2);        }    }    return 0;}

Tree array _ poj tree Array