poj2761 Feed the dogs

Posted 2020-08-11 MashiroSky

http://poj.org/problem?id=2761 (题目链接)

题意：求区间第K大。

Solution 
　　和poj2104一模一样。

主席树代码：

// poj2761
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<cmath>
#define LL long long
#define inf 2147483640
#define Pi acos(-1.0)
#define free(a) freopen(a".in","r",stdin),freopen(a".out","w",stdout);
using namespace std;

const int M=10000010;
int a[M],b[M],lson[M],rson[M],T[M],c[M];
int n,tot,q;

int build(int l,int r) {
    int k=++tot;
    c[k]=0;
    if (l==r) return k;
    int mid=(l+r)>>1;
    lson[k]=build(l,mid);
    rson[k]=build(mid+1,r);
    return k;
}
int update(int l,int r,int K,int x) {
    int k=++tot;
    c[k]=c[K]+1;
    if (l==r) return k;
    int mid=(l+r)>>1;
    if (x<=mid) {
        rson[k]=rson[K];
        lson[k]=update(l,mid,lson[K],x);
    }
    else {
        lson[k]=lson[K];
        rson[k]=update(mid+1,r,rson[K],x);
    }
    return k;
}
int query(int l,int r,int k,int K,int x) {
    if (l==r) return l;
    int mid=(l+r)>>1;
    if (c[lson[K]]-c[lson[k]]>=x)
        return query(l,mid,lson[k],lson[K],x);
    else return query(mid+1,r,rson[k],rson[K],x-c[lson[K]]+c[lson[k]]);
}
int main() {
    while (scanf("%d%d",&n,&q)!=EOF) {
        tot=0;
        for (int i=1;i<=n;i++) scanf("%d",&a[i]),b[i]=a[i];
        sort(b+1,b+1+n);
        int m=unique(b+1,b+1+n)-b-1;
        T[0]=build(1,m);
        for (int i=1;i<=n;i++) {
            int x=lower_bound(b+1,b+1+m,a[i])-b;
            T[i]=update(1,m,T[i-1],x);
        }
        while (q--) {
            int l,r,k;
            scanf("%d%d%d",&l,&r,&k);
            printf("%d\n",b[query(1,m,T[l-1],T[r],k)]);
        }
    }
    return 0;
}

分块+莫队代码：

// poj2761
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<cmath>
#define LL long long
#define inf 2147483640
#define Pi acos(-1.0)
#define free(a) freopen(a".in","r",stdin),freopen(a".out","w",stdout);
using namespace std;

const int maxn=100010;
struct ask {int l,r,k,id;}t[maxn];
struct data {int w,id;}a[maxn];
int pos[maxn],cnts[maxn],b[maxn],p[maxn],ma[maxn],ans[maxn],n,m,s,q,block;


bool wcmp(data a,data b) {
    return a.w<b.w;
}
bool poscmp(ask a,ask b) {
    return pos[a.l]==pos[b.l] ? a.r<b.r : pos[a.l]<pos[b.l];
}
void build() {
    block=(int)sqrt((float)m);
    for (int i=1;i<=m;i++) pos[i]=(i-1)/block+1;
    s=m%block ? m/block+1 : m/block;
    for (int i=1;i<=s;i++) cnts[i]=0;
}
void update(int x,int val) {
    cnts[pos[x]]+=val;
    b[x]+=val;
}
int query(int k) {
    int tot=0;
    for (int i=1;i<=s;i++) {
        tot+=cnts[i];
        if (tot>=k) {
            tot-=cnts[i];
            for (int j=(i-1)*block+1;j<=min(i*block,m);j++) {
                if (tot+b[j]>=k) return ma[j];
                else tot+=b[j];
            }
        }
    }
}
int main() {
    scanf("%d%d",&n,&q);
    for (int i=1;i<=n;i++) scanf("%d",&a[i].w),a[i].id=i;
    for (int i=1;i<=q;i++) scanf("%d%d%d",&t[i].l,&t[i].r,&t[i].k),t[i].id=i;
    sort(a+1,a+1+n,wcmp);
    m=0;
    ma[p[a[1].id]=++m]=a[1].w;
    for (int i=2;i<=n;i++) {
        if (a[i].w!=a[i-1].w) m++;
        ma[p[a[i].id]=m]=a[i].w;
    }
    block=(int)sqrt((float)n);
    for (int i=1;i<=n;i++) pos[i]=(i-1)/block+1;
    sort(t+1,t+1+q,poscmp);
    build();
    for (int l=1,r=0,i=1;i<=q;i++) {
        for (;r<t[i].r;r++) update(p[r+1],1);
        for (;r>t[i].r;r--) update(p[r],-1);
        for (;l<t[i].l;l++) update(p[l],-1);
        for (;l>t[i].l;l--) update(p[l-1],1);
        ans[t[i].id]=query(t[i].k);
    }
    for (int i=1;i<=q;i++) printf("%d\n",ans[i]);
    return 0;
}