线段树专题

按照习惯，这里只是对我这几天所写的线段树题目的总结

hdu 1166 排兵布阵
点增减

#include<cstdio>

#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1

const int maxn=55555;
int sum[maxn<<2];
void push(int rt)
{
  sum[rt]=sum[rt<<1]+sum[rt<<1|1];
}

void build(int l,int r,int rt)
{
  if(l==r)
  {
    scanf("%d",&sum[rt]);
    return ;
  }
  int m=(l+r)>>1;
  build(lson);
  build(rson);
  push(rt);
}

void update(int p,int add,int l,int r,int rt)
{
  if(l==r)
  {
    sum[rt]+=add;
    return;
  }
  int m=(l+r)>>1;
  if(p<=m)update(p,add,lson);
  else update(p,add,rson);
  push(rt);
}

int query(int L,int R,int l,int r,int rt)
{
  if(L<=l&&r<=R)return sum[rt];
  int m=(l+r)>>1;
  int ret=0;
  if(L<=m)ret+=query(L,R,lson);
  if(R>m)ret+=query(L,R,rson);
  return ret;
}

int main()
{
  int t,n;
  scanf("%d",&t);
  for(int i=1;i<=t;i++)
  {
    printf("Case %d:\n",i);
    scanf("%d",&n);
    build(1,n,1);
    char op[10];
    while(scanf("%s",op))
    {
      if(op[0]=='E')break;
      int a,b;
      scanf("%d%d",&a,&b);
      if(op[0]=='Q')printf("%d\n",query(a,b,1,n,1));
      else
        if(op[0]=='S')update(a,-b,1,n,1);
          else update(a,b,1,n,1);
    }
  }
  return 0;
}

hdu 1754
点替换

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int N = 200010;
int max(int a,int b){return a > b ? a : b;}

int maxn[N * 4];
int n,m,a,b;

void build(int o,int l,int r)
{
    if(l == r){ scanf("%d",&maxn[o]);return;}
    int mid = (l + r) >> 1;
    build(o << 1,l,mid);
    build(o << 1 | 1,mid + 1,r);
    maxn[o] = max(maxn[o << 1],maxn[o << 1 | 1]);
}

int query(int o,int l,int r)
{
    int mid =(l + r) >> 1;
    if(a <= l && b >= r) return maxn[o];
    int ans = -1;
    if(a <= mid) ans = max(ans,query(o << 1,l,mid));
    if(b > mid) ans = max(ans,query(o << 1 | 1,mid+1,r));
    return ans;
}

void update(int o,int l,int r)
{
    if(l == r){ maxn[o] = b; return; }
    int mid = (l + r) >> 1;
    if(a <= mid) update(o << 1,l,mid); else update(o << 1 | 1,mid+1,r);
    maxn[o] = max(maxn[o << 1],maxn[o << 1 | 1]);
}

int main()
{
    char c[2];
    while(scanf("%d%d",&n,&m)!=EOF && n && m)
    {
    build(1,1,n);
    for(int i = 1;i <= m; i++)
    {
        scanf("%s",c);
        if(c[0] == 'Q')
        {
            scanf("%d%d",&a,&b);
            printf("%d\n",query(1,1,n));
        }
        else
        {
            scanf("%d%d",&a,&b);
            update(1,1,n);
        }
    }
    }
    return 0;
}

hdu 1698
段替换

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

#define fill(a,x) memset(a,x,sizeof(a))
#define lson o << 1
#define rson o << 1 | 1
const int N = 100010;

int setv[N << 2],sum[N << 2];
int n,m,ll,rr,v;

void build(int o,int l,int r)
{
    if(l == r){sum[o] = 1;return;}
    int mid = (l+r)/2;
    build(lson,l,mid);
    build(rson,mid+1,r);
    sum[o] = sum[lson] + sum[rson];
}

void pushdown(int o,int l,int r)
{
    if(setv[o] > 0)
    {
        setv[lson] = setv[rson] = setv[o];
        int mid = (l+r) >> 1;
        sum[lson] = setv[o] * (mid-l+1);
        sum[rson] = setv[o] * (r-mid);
        setv[o] = 0;
    }
    return;
}

void update(int o,int l,int r)
{
    if(ll <= l && rr >= r) {setv[o] = v;sum[o] = v * (r-l+1);}
    else
    {
        pushdown(o,l,r);
        int mid = (l+r) >> 1;
        if(ll <= mid) update(lson,l,mid);
        if(rr > mid) update(rson,mid+1,r);
        sum[o] = sum[lson] + sum[rson];
    }
}

int main()
{
    int t;
    scanf("%d",&t);
    for(int kase = 1;kase <= t;kase ++)
    {
        scanf("%d%d",&n,&m);
        build(1,1,n);
        fill(setv,0);
        for(int i = 1;i <= m; i++)
        {
            scanf("%d%d%d",&ll,&rr,&v);
            update(1,1,n);
        }
        printf("Case %d: The total value of the hook is %d.\n",kase,sum[1]);
    }
    return 0;
}

bzoj 1798
较难，区间乘与加的混合，注意使用分配率

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

#define rep(i,x,y) for(int i=x;i<=y;i++)
#define dep(i,x,y) for(int i=x;i>=y;i--)
#define fill(a,x) memset(a,x,sizeof(a))
typedef long long LL;
const int N = 100010;

struct node{
    LL add,mul,sum;
}seq[N * 4];

LL ll,rr,Add,Mul,mod,n,m;

void build(int o,int l,int r)
{
    seq[o].mul = 1;seq[o].add = 0;
    if(l == r){ cin >> seq[o].sum; return; }
    int mid = (l + r) / 2;
    build(o*2, l, mid);
    build(o*2+1, mid+1, r);
    seq[o].sum = (seq[o*2].sum + seq[o*2+1].sum) % mod;
    return;
}

inline void refresh(int o,int l,int r)
{
    int lc = o*2,rc = o*2+1,mid = (l+r)/2;
    seq[lc].sum = (seq[lc].sum * seq[o].mul + seq[o].add * (mid-l+1)) % mod;
    seq[lc].mul = (seq[lc].mul * seq[o].mul) % mod;
    seq[lc].add = (seq[lc].add * seq[o].mul + seq[o].add) % mod;
    seq[rc].sum = (seq[rc].sum * seq[o].mul + seq[o].add * (r - mid)) % mod;
    seq[rc].mul = (seq[rc].mul * seq[o].mul) % mod;
    seq[rc].add = (seq[rc].add * seq[o].mul + seq[o].add) % mod;
    seq[o].mul = 1;seq[o].add = 0;
    return;
}   

void update(int o,int l,int r)
{
    if(rr < l || ll > r) return;
    if(ll <= l && rr >= r)
    {
        seq[o].sum = (seq[o].sum * Mul + (r - l +1) * Add) % mod;
        seq[o].add = (seq[o].add * Mul + Add) % mod;
        seq[o].mul = seq[o].mul * Mul % mod;
        return;
    }
    int mid = (l+r)/2;
    refresh(o,l,r);
    update(o*2,l,mid);
    update(o*2+1,mid+1,r);
    seq[o].sum = (seq[o*2].sum + seq[o*2+1].sum) % mod;
}

LL query(int o,int l,int r)
{
    if (rr < l || r < ll) return 0;
    if (ll <= l && r <= rr) return seq[o].sum;
    int mid = (l+r)/2;
    refresh(o,l,r);
    LL res = (query(o*2,l,mid) + query(o*2+1,mid+1,r)) % mod;
    seq[o].sum = (seq[o*2].sum + seq[o*2+1].sum) % mod;
    return res;
}

int main()
{
    scanf("%lld%lld",&n,&mod);
    build(1,1,n);

    scanf("%lld",&m);
    LL x;
    rep(i,1,m)
    {
        scanf("%lld%lld%lld",&x,&ll,&rr);
        if(x == 1){scanf("%lld",&Mul); Add = 0;update(1,1,n);}
        else
        if(x == 2){scanf("%lld",&Add); Mul = 1;update(1,1,n);}
        else printf("%lld\n",query(1,1,n));
    }
    return 0;
}

poj 3468
段增减

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

#define lson o << 1
#define rson o << 1 | 1
typedef long long LL;
const int N = 100010;

LL add[N << 2],sum[N << 2],v;
int n,m,ll,rr;

void build(int o,int l,int r)
{
    add[o] = 0;
    if(l == r){scanf("%lld",&sum[o]);return;}
    int mid = (l+r)>>1;
    build(lson,l,mid);
    build(rson,mid+1,r);
    sum[o] = sum[rson] + sum[lson];
}

void pushdown(int o,int l,int r)
{
    if(add[o])
    {
        int mid = (l+r)>>1;
        add[lson] += add[o];
        add[rson] += add[o]; 
        sum[lson] += add[o] * (mid-l+1);
        sum[rson] += add[o] * (r-mid);
        add[o] = 0;
    }
}

void update(int o,int l,int r)
{
    if(ll <= l && rr >= r)
    {
        add[o] += v;
        sum[o] += v * (r-l+1);
        return;
    }
    pushdown(o,l,r);
    int mid = (l+r)>>1;
    if(ll <= mid)update(lson,l,mid);
    if(rr > mid) update(rson,mid+1,r);
    sum[o] = sum[lson] + sum[rson];
}

LL query(int o,int l,int r)
{
    if(ll <= l && rr >= r) return sum[o];
    int mid = (l+r) >> 1;
    pushdown(o,l,r);
    LL ans = 0;
    if(ll <= mid) ans += query(lson,l,mid);
    if(rr > mid) ans += query(rson,mid+1,r);
    return ans;
}

int main()
{
    char c[2];
    scanf("%d%d",&n,&m);
    build(1,1,n);
    for(int i = 1;i <= m; i++)
    {
        scanf("%s",c);
        scanf("%d%d",&ll,&rr);
        if(c[0] == 'C')
        {
            scanf("%lld",&v);
            update(1,1,n);
        }
        else printf("%lld\n",query(1,1,n));
    }
    return 0;
}