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2019/2/17训练日记 树状数组 线段树模板

热度:19   发布时间:2023-11-23 06:42:57.0
//树状数组    :利用二进制性质,可在O(logn)对区间前缀进行查询和修改操作const int N=100050;
int c[N],ans[N];      //c[n]表示a[1~n]的和,a数组省略
int lowbit(int x)       //求2^k
{ return x & -x;
}
int getsum(int n)   //区间查询,求a[1~n]的和
{int res = 0;while(n>0){res+=c[n];n=n-lowbit(n);}return res;
}
int change(int x)  //单点更新,将a[x]的值加1
{while(x<=N){c[x]++;x+=lowbit(x);}
}
int main()
{int n;cin>>n;memset(c,0,sizeof(c));memset(ans,0,sizeof(ans));for(int i=0;i<n;i++){int x,y;cin>>x>>y;x++;ans[getsum(x)]++;change(x);}for(int i=0;i<n;i++)cout<<ans[i]<<endl;return 0;
}

 


//单点操作,区间更新using namespace std;  
#define INF 10000000  
#define lson l,mid,rt<<1      //左儿子  
#define rson mid+1,r,rt<<1|1  //右儿子  
const int maxn = 222222;  
struct Node{  int Max,Min;  //区间的最大值和最小值  int sum;      //区间的和  
}stree[maxn<<2];  
void up(int rt){  //更新该区间的最值与和  stree[rt].Max=max(stree[rt<<1].Max,stree[rt<<1|1].Max);  stree[rt].Min=min(stree[rt<<1].Min,stree[rt<<1|1].Min);  stree[rt].sum=stree[rt<<1].sum+stree[rt<<1|1].sum;  
}  
void build(int l,int r,int rt){  //在结点i上建立区间为[l,r]  if(l==r){                    //叶子结点  int num;  scanf("%d",&num);  stree[rt].Max=stree[rt].Min=stree[rt].sum=num;  return ;  }  int mid=(l+r)>>1;  build(lson); //建立左儿子  build(rson); //建立右儿子  up(rt);      //更新  
}  
int querymax(int a,int b,int l,int r,int rt){  //求区间[a,b]的最大值  if(a<=l&&r<=b){  //如果全包含,直接取区间最大值  return stree[rt].Max;  }  int mid = (r+l)>>1;  int ret = -INF;  if(a<=mid) ret=max(ret,querymax(a,b,lson));//如果左端点在中点的左边,找出左区间的最大值  if(mid<b) ret=max(ret,querymax(a,b,rson));//如果右端点在中点的右边,找出右区间(以及左区间)的最大值  return ret;  
}  
int querymin(int a,int b,int l,int r,int rt){  //求区间[a,b]的最小值  if(a<=l&&r<=b){  //如果全包含,直接取区间最小值  return stree[rt].Min;  }  int mid = (r+l)>>1;  int ret = INF;  if(a<=mid) ret=min(ret,querymin(a,b,lson));//如果左端点在中点的左边,找出左区间的最小值  if(mid<b) ret=min(ret,querymin(a,b,rson)); //如果右端点在中点的右边,找出右区间(以及左区间)的最小值  return ret;  
}  
int querysum(int a,int b,int l,int r,int rt){  //求区间[a,b]的和(a,b的值相同时为求单点的值)  if(a<=l&&r<=b){ //如果全包含,直接取区间的和  return stree[rt].sum;  }  int mid = (r+l)>>1;  int ret=0;  if(a<=mid) ret+=querysum(a,b,lson);  if(mid<b) ret+=querysum(a,b,rson);  return ret;  
}  
void uppoint(int a,int b,int l,int r,int rt){  //单点替换,把第a个数换成b  if(l==r){  stree[rt].Max=stree[rt].Min=stree[rt].sum=b;  return ;  }  int mid =(r+l)>>1;  if(a<=mid)uppoint(a,b,lson);  else uppoint(a,b,rson);  up(rt);  
}  
void upadd(int a,int b,int l,int r,int rt){  //单点增减,把第a个数增减b  if(l==r){  stree[rt].sum=stree[rt].sum+b;  stree[rt].Max=stree[rt].Max+b;  stree[rt].Min=stree[rt].Min+b;  return ;  }  int mid=(l+r)>>1;  if(a<=mid) upadd(a,b,lson);  else upadd(a,b,rson);  up(rt);  
}  
int main()  
{  //freopen("F:\\11.txt","r",stdin);  int n,q;  while(~scanf("%d%d",&n,&q)){  build(1,n,1);//build(l,r,rt);  while(q--){  char op[10];  int a,b;  scanf("%s%d%d",op,&a,&b);  if(op[0]=='X'){//求区间[a,b]的最大值  printf("%d\n",querymax(a,b,1,n,1));//querymax(int a,int b,int l,int r,int rt);  }  else if(op[0]=='N'){//求区间[a,b]的最小值  printf("%d\n",querymin(a,b,1,n,1));//querymin(int a,int b,int l,int r,int rt);  }  else if(op[0]=='U'){//单点替换,把第a个数换成b  uppoint(a,b,1,n,1);//uppoint(int a,int b,int l,int r,int rt);  }  else if(op[0]=='S'){//求区间[a,b]的和(a,b的值相同时为求单点的值)  printf("%d\n",querysum(a,b,1,n,1));//querysum(int a,int b,int l,int r,int rt);  }  else if(op[0]=='A'){//单点增加,把第a个数增加b  upadd(a,b,1,n,1);  }  else if(op[0]=='E'){//单点减少,把第a个数减少b  upadd(a,-b,1,n,1);  }  }  }  return 0;  
}  
//区间更换,区间查询#define max(a,b) (a>b)?a:b
#define min(a,b) (a>b)?b:a
#define lson l , m , rt << 1
#define rson m + 1 , r , rt << 1 | 1
const int maxn = 100100;
const int INF=0x7fffffff;
using namespace std;
int lazy[maxn<<2];
int MAX[maxn<<2];
int MIN[maxn<<2];
int SUM[maxn<<2];
void PushUp(int rt) { //由左孩子、右孩子向上更新父节点SUM[rt] = SUM[rt<<1] + SUM[rt<<1|1];MAX[rt] = max(MAX[rt<<1],MAX[rt<<1|1]);MIN[rt] = min(MIN[rt<<1],MIN[rt<<1|1]);
}
void PushDown(int rt,int m) { //向下更新if (lazy[rt]) { //懒惰标记lazy[rt<<1] = lazy[rt<<1|1] = lazy[rt];SUM[rt<<1] = (m - (m >> 1)) * lazy[rt];SUM[rt<<1|1] = ((m >> 1)) * lazy[rt];MAX[rt<<1]=MAX[rt<<1|1]=lazy[rt];MIN[rt<<1]=MIN[rt<<1|1]=lazy[rt];lazy[rt] = 0;}
}
//所有的l,r,rt  带入1,n,1
void build(int l,int r,int rt) { //初始化建树lazy[rt] = 0;if (l== r) {SUM[rt]=MAX[rt]=MIN[rt]=0;  //初始化为0的建树/*scanf("%d",&SUM[rt]);  //边读入边建树的方法MAX[rt]=MIN[rt]=SUM[rt];*/return ;}int m = (l + r) >> 1;build(lson);build(rson);PushUp(rt);
}
void update(int L,int R,int v,int l,int r,int rt) { //将L~R区间的值置为v//if(L>l||R>r) return;if (L <= l && r <= R) {lazy[rt] = v;SUM[rt] = v * (r - l + 1);MIN[rt] = v;MAX[rt] = v;//printf("%d %d %d %d %d\n", rt, sum[rt], c, l, r);return ;}PushDown(rt , r - l + 1);int m = (l + r) >> 1;if (L <= m) update(L , R , v , lson);if (R > m) update(L , R , v , rson);PushUp(rt);
}
int querySUM(int L,int R,int l,int r,int rt) {  //求区间L~R的和if (L <= l && r <= R) {//printf("%d\n", sum[rt]);return SUM[rt];}PushDown(rt , r - l + 1);int m = (l + r) >> 1;int ret = 0;if (L <= m) ret += querySUM(L , R , lson);if (m < R) ret += querySUM(L , R , rson);return ret;
}
int queryMIN(int L,int R,int l,int r,int rt) {  //求区间L~R的最小值if (L <= l && r <= R) {//printf("%d\n", sum[rt]);return MIN[rt];}PushDown(rt , r - l + 1);int m = (l + r) >> 1;int ret = INF;if (L <= m) ret = min(ret, queryMIN(L , R , lson));if (m < R) ret = min(ret,queryMIN(L , R , rson));return ret;
}
int queryMAX(int L,int R,int l,int r,int rt) {  //求区间L~R的最大值if (L <= l && r <= R) {//printf("%d\n", sum[rt]);return MAX[rt];}PushDown(rt , r - l + 1);int m = (l + r) >> 1;int ret = -INF;if (L <= m) ret = max(ret, queryMAX(L , R , lson));if (m < R) ret = max(ret,queryMAX(L , R , rson));return ret;
}
int main() {int  n , m;char str[5];while(scanf("%d%d",&n,&m)) {build(1 , n , 1);while (m--) {scanf("%s",str);int a , b , c;if(str[0]=='T') {scanf("%d%d%d",&a,&b,&c);update(a , b , c , 1 , n , 1);} else if(str[0]=='Q') {scanf("%d%d",&a,&b);cout<<querySUM(a,b,1,n,1)<<endl;} else if(str[0]=='A') {scanf("%d%d",&a,&b);cout<<queryMAX(a,b,1,n,1)<<endl;} else if(str[0]=='I') {scanf("%d%d",&a,&b);cout<<queryMIN(a,b,1,n,1)<<endl;}}}return 0;
}
//区间增加,区间查询#define max(a,b) (a>b)?a:b
#define min(a,b) (a>b)?b:a
#define lson l , m , rt << 1
#define rson m + 1 , r , rt << 1 | 1
const int maxn = 100100;
const int INF=0x7fffffff;
using namespace std;
int lazy[maxn<<2];
int SUM[maxn<<2],MAX[maxn<<2],MIN[maxn<<2];
void putup(int rt) {SUM[rt] = SUM[rt<<1] + SUM[rt<<1|1];MAX[rt] =max(MAX[rt<<1],MAX[rt<<1|1]) ;MIN[rt] =min(MIN[rt<<1],MIN[rt<<1|1]);
}
void putdown(int rt,int m) {if (lazy[rt]) {lazy[rt<<1] += lazy[rt];lazy[rt<<1|1] += lazy[rt];SUM[rt<<1] += lazy[rt] * (m - (m >> 1));SUM[rt<<1|1] += lazy[rt] * (m >> 1);MAX[rt<<1]+=lazy[rt];MAX[rt<<1|1] +=lazy[rt];MIN[rt<<1]+=lazy[rt];MIN[rt<<1|1]+=lazy[rt];lazy[rt] = 0;}
}
//以下的 l,r,rt 都带入 1,n,1
void build(int l,int r,int rt) {  //初始化建树lazy[rt] = 0;if (l == r) {//初始化树为0的写法SUM[rt]=MAX[rt]=MIN[rt]=0;/*  //边读入边建树的写法scanf("%d",&SUM[rt]);MAX[rt]=MIN[rt]=SUM[rt];*/return ;}int m = (l + r) >> 1;build(lson);build(rson);putup(rt);
}
void update(int L,int R,int v,int l,int r,int rt) {  //将区间L~R的值增加vif (L <= l && r <= R) {lazy[rt] += v;SUM[rt] += v * (r - l + 1);MAX[rt]+=v;MIN[rt]+=v;return ;}putdown(rt , r - l + 1);int m = (l + r) >> 1;if (L <= m) update(L , R , v , lson);if (m < R) update(L , R , v , rson);putup(rt);
}
int querySUM(int L,int R,int l,int r,int rt) {  //求区间L~R的和if (L <= l && r <= R) {return SUM[rt];}putdown(rt , r - l + 1);int m = (l + r) >> 1;int ret = 0;if (L <= m) ret += querySUM(L , R , lson);if (m < R) ret += querySUM(L , R , rson);return ret;
}
int queryMAX(int L,int R,int l,int r,int rt) {  //求区间L~R的最大值if (L <= l && r <= R) {return MAX[rt];}putdown(rt , r - l + 1);int m = (l + r) >> 1;int ret = -INF;if (L <= m) ret =max(ret,queryMAX(L , R , lson)) ;if (m < R) ret =max(ret,queryMAX(L , R , rson)) ;return ret;
}
int queryMIN(int L,int R,int l,int r,int rt) {  //求区间L~R的最小值if (L <= l && r <= R) {return MIN[rt];}putdown(rt , r - l + 1);int m = (l + r) >> 1;int ret = INF;if (L <= m) ret = min(ret,queryMIN(L , R , lson));if (m < R) ret = min(ret,queryMIN(L , R , rson));return ret;
}
int main() {int n , m;int a , b , c;char str[5];scanf("%d%d",&n,&m);build(1 , n , 1);while (m--) {scanf("%s",str);if (str[0] == 'S') {scanf("%d%d",&a,&b);printf("%d\n",querySUM(a , b , 1 , n , 1));} else if(str[0]=='C') {scanf("%d%d%d",&a,&b,&c);update(a , b , c , 1 , n , 1);} else if(str[0]=='A') {scanf("%d%d",&a,&b);printf("%d\n",queryMAX(a , b , 1 , n , 1));} else if(str[0]=='I') {scanf("%d%d",&a,&b);printf("%d\n",queryMIN(a , b , 1 , n , 1));}}return 0;
}