Poj2104 K-th Number

最新推荐文章于 2021-10-09 14:23:30 发布

原创最新推荐文章于 2021-10-09 14:23:30 发布 · 314 阅读

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本文提供了一种解决 POJ 2104 问题的有效方法，通过离散化和线段树实现区间修改和查询操作，讨论了使用指针和结构体在时间和空间效率上的差异。

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原题网址：http://poj.org/problem?id=2104

//#include<bits/stdc++.h>
#include<cstdio>
#include<iostream>
#include<algorithm>
const int N = 1e5 + 10;
template <typename T> void read (T &x){
    x = 0; int f = 1;
    char c = getchar();
    while (c < '0' || c > '9') {if (c == '-') f *= -1; c = getchar();}
    while (c >= '0' && c <= '9') {x = x * 10 + c - '0'; c = getchar();}
    x *= f;
}
int n,m,a[N],b[N],c[N],root[N],lc[20*N],rc[20*N],sum[20*N],s;
int tra(int x){
    int l = 1, r = n;
    while (l < r){
        int mid = (l + r + 1) >> 1;
        if (b[mid] <= x)
            l = mid;
        else
            r = mid - 1;
    }
    return c[l];
}
int detra(int x){
    int l = 1, r = n;
    while (l < r){
        int mid = (l + r + 1) >> 1;
        if (c[mid] <= x)
            l = mid;
        else
            r = mid - 1;
    }
    return b[l];
}
void init(int i,int l, int r){
    sum[i] = 0;
    if (l == r) return;
    lc[i] = ++s; init(lc[i],l,(l+r)/2);
    rc[i] = ++s; init(rc[i],(l+r)/2+1,r);
}
void add(int i, int last, int l, int r, int c){
    sum[i] = sum[last] + 1;
    if (l == r) return;
    if (c <= (l+r)/2){
        rc[i] = rc[last];
        lc[i] = ++s;
        add(lc[i],lc[last],l,(l+r)/2,c);
    }else{
        lc[i] = lc[last];
        rc[i] = ++s;
        add(rc[i],rc[last],(l+r)/2+1,r,c);
    }
}
int qry(int i, int last, int l, int r, int k){
    if (l == r) return l;
    if (sum[lc[i]] - sum[lc[last]] >= k)
        return qry(lc[i],lc[last],l,(l+r)/2,k);
    else
        return qry(rc[i],rc[last],(l+r)/2+1,r,k - (sum[lc[i]] - sum[lc[last]]));
}
int main(){
    //printf("%.6f\n",sizeof(root)*3.0/1024/1024);
    //freopen("tree.in","r",stdin);
    //freopen("tree.out","w",stdout);
    int T;
    T = 1;//read(T);
    while (T--){
        read(n);read(m);
        init(root[0] = s = 0,1,n);
        for (int i=1; i<=n; i++)
            read(a[i]),
            b[i] = a[i];
        std::sort(b+1,b+n+1);
        c[1] = 1;
        for (int i=2; i<=n; i++)
            c[i] = c[i - 1] + (b[i] > b[i - 1]);
        for (int i=1; i<=n; i++)
            add(root[i] = ++s,root[i - 1],1,n,tra(a[i]));
        int l,r,k;
        while (m--){
            read(l);read(r);read(k);
            printf("%d\n",detra(qry(root[r],root[l - 1],1,n,k/*r-l+2-k*/)));
        }
    }
    //fprintf(stderr,"Elapsed time:%.3f secs.\n",(double)clock()/CLOCKS_PER_SEC);
    return 0;
}

吐槽一开始用指针写被Poj卡时间，被Hdu卡空间，Hdu题面还写错mdzz。
以下被卡版本：

//#include<bits/stdc++.h>
#include<cstdio>
#include<iostream>
#include<algorithm>
const int N = 1e5 + 10;
template <typename T> void read (T &x){
    x = 0; int f = 1;
    char c = getchar();
    while (c < '0' || c > '9') {if (c == '-') f *= -1; c = getchar();}
    while (c >= '0' && c <= '9') {x = x * 10 + c - '0'; c = getchar();}
    x *= f;
}
int n,m,a[N],b[N],c[N];
int tra(int x){
    int l = 1, r = n;
    while (l < r){
        int mid = (l + r + 1) >> 1;
        if (b[mid] <= x)
            l = mid;
        else
            r = mid - 1;
    }
    return c[l];
}
int detra(int x){
    int l = 1, r = n;
    while (l < r){
        int mid = (l + r + 1) >> 1;
        if (c[mid] <= x)
            l = mid;
        else
            r = mid - 1;
    }
    return b[l];
}
struct node{
    int l,r,sum;
    node *lc,*rc;
    void init(int _l, int _r){
        l=_l;r=_r;sum=0;
        if (l == r) return;
        lc=new(node), lc->init(l,(l+r)/2);
        rc=new(node), rc->init((l+r)/2+1,r);
    }
    void add(node *last, int c){
        sum++;
        if (l == r) return;
        if (c <= lc->r){
            lc=new(node);
            last=last->lc;
            *lc = *last;
            lc->add(last,c);
        }else{
            rc=new(node);
            last=last->rc;
            *rc = *last;
            rc->add(last,c);
        }
    }
    int qry(node *last, int k){
        if (l == r) return l;
        if (lc->sum - last->lc->sum >= k)
            return lc->qry(last->lc,k);
        else
            return rc->qry(last->rc,k-(lc->sum - last->lc->sum));
    }
};
node root[N];
int main(){
    freopen("tree.in","r",stdin);
    freopen("tree.out","w",stdout);
    //read(n);read(m);
    scanf("%d%d",&n,&m);
    root[0].init(1,n);
    for (int i=1; i<=n; i++)
        scanf("%d",&a[i]),
        //read(a[i]),
        b[i] = a[i];
    std::sort(b+1,b+n+1);
    c[1] = 1;
    for (int i=2; i<=n; i++)
        c[i] = c[i - 1] + (b[i] > b[i - 1]);
    for (int i=1; i<=n; i++)
        root[i] = root[i - 1],
        root[i].add(&root[i - 1],tra(a[i]));
    int l,r,k;
    while (m--){
        //read(l);read(r);read(k);
        scanf("%d%d%d",&l,&r,&k);
        printf("%d\n",detra(root[r].qry(&root[l - 1],k)));
    }
    //fprintf(stderr,"Elapsed time:%.3f secs.\n",(double)clock()/CLOCKS_PER_SEC);
    return 0;
}