树状数组:
1.树状数组可以做什么?
一句话,树状数组有其特定的作用,其用途较窄,它能做的线段树都能做!
2.树状数组是什么?
tree[1] = a1
tree[2] = tree[1] + a2;
tree[3] = a3;
tree[4] = tree[3] + tree[2] + a4 = a1 + a2 + a3 + a4;
tree[5] = a5;
tree[6] = tree[5] + a6 = a5 + a6;e
…
3. 求区间查询和单点更新
lowbit : 用于取出最低位的1
int lowbit(int x){
return x & (-x);
}
单点更新
void update(int x,int val){
while(x<=n){
c[x] += val;
x += lowbit(x);
}
}
区间查询(前缀和)
int getSum(int x){
int ans = 0;
while(x){
ans += c[x];
x -= lowbit(x);
}
return ans;
}
#include <iostream>
#include <cstdio>
#include <cstring>
// 树状数组
using namespace std;
// 原数组 树状数组
int a[100010],c[100010];
int n,m;
int lowbit(int x){
return x & (-x);
}
// 求前缀和
int getSum(int x){
int ans = 0;
while(x){
ans += c[x];
x -= lowbit(x);
}
return ans;
}
void update(int x,int val){
while(x<=n){
c[x] += val;
x += lowbit(x);
}
}
int main()
{
while(scanf("%d",&n)!=EOF){
memset(a,0,sizeof a);
memset(c,0,sizeof c);
for(int i=1;i<=n;i++){
scanf("%d",&a[i]);
update(i,a[i]);
}
int ans = getSum(n);
cout << ans << endl;
}
return 0;
}
4. 求逆序对
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
using namespace std;
typedef pair<int,int> PII;
const int N = 100100;
int n;
int tree[N],b[N]; // b[n]存储离散化且排序后原始 pos
PII a[N]; // 输入 a[i].fi 存储值,a[i].se 存储 pos
// 取出二进制下第一个1及以后的数
int lowbit(int x){
return x & (-x);
}
// 更新点
void update(int x,int val){
while(x<=n){
tree[x] += val;
x += lowbit(x);
}
}
// 前缀和
int getSum(int x){
int ans = 0;
while(x){
ans += tree[x];
x -= lowbit(x);
}
return ans;
}
int main()
{
memset(tree,0,sizeof tree);
scanf("%d",&n);
for(int i=1;i<=n;i++){
scanf("%d",&a[i].first);
a[i].second = i;
}
sort(a+1,a+n+1);
int pos = 1;
for(int i=1;i<=n;i++){
if(a[i].first!=a[i-1].first && i!=1) pos++;
b[a[i].second] = pos;
}
// 求逆序对数量.
int sum = 0;
for(int i=1;i<=n;i++){
update(b[i],1);
sum += (i - getSum(b[i]));
}
cout << sum << endl;
return 0;
}
求逆序对(贪心+树状数组)
Array Optimization by Deque