【POJ】2104 K-th Number

区间第K大数。
主席树可解。

/* 2104 */
#include <iostream>
#include <sstream>
#include <string>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <vector>
#include <deque>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstring>
#include <climits>
#include <cctype>
#include <cassert>
#include <functional>
#include <iterator>
#include <iomanip>
using namespace std;
//#pragma comment(linker,"/STACK:102400000,1024000")

#define sti                set<int>
#define stpii            set<pair<int, int> >
#define mpii            map<int,int>
#define vi                vector<int>
#define pii                pair<int,int>
#define vpii            vector<pair<int,int> >
#define rep(i, a, n)     for (int i=a;i<n;++i)
#define per(i, a, n)     for (int i=n-1;i>=a;--i)
#define clr                clear
#define pb                 push_back
#define mp                 make_pair
#define fir                first
#define sec                second
#define all(x)             (x).begin(),(x).end()
#define SZ(x)             ((int)(x).size())
// #define lson            l, mid, rt<<1
// #define rson            mid+1, r, rt<<1|1

const int maxn = 1e5+5;
const int maxm = maxn * 50;
int T[maxn];
int lson[maxm], rson[maxm], c[maxm];
int a[maxn], b[maxn];
int n, m;
int tot = 0;

int Build(int l, int r) {
    int rt = tot++;
    
    c[rt] = 0;
    if (l == r)
        return rt;
    
    int mid = (l + r) >> 1;
    
    lson[rt] = Build(l, mid);
    rson[rt] = Build(mid+1, r);
    
    return rt;
}

int Insert(int rt, int x, int delta) {
    int nrt = tot++, ret = nrt;
    int l = 0, r = m - 1, mid;
    
    c[nrt] = c[rt] + delta;
    while (l < r) {
        mid = (l + r) >> 1;
        if (x <= mid) {
            lson[nrt] = tot++;
            rson[nrt] = rson[rt];
            nrt = lson[nrt];
            rt = lson[rt];
            r = mid;
        } else {
            lson[nrt] = lson[rt];
            rson[nrt] = tot++;
            nrt = rson[nrt];
            rt = rson[rt];
            l = mid + 1;
        }
        c[nrt] = c[rt] + delta;
    }
    
    return ret;
}

int Query(int lrt, int rrt, int k) {
    int l = 0, r = m - 1, mid;
    int tmp;
    
    while (l < r) {
        mid = (l + r) >> 1;
        tmp = c[lson[rrt]] - c[lson[lrt]];
        if (tmp >= k) {
            lrt = lson[lrt];
            rrt = lson[rrt];
            r = mid;
        } else {
            k -= tmp;
            lrt = rson[lrt];
            rrt = rson[rrt];
            l = mid + 1;
        }
    }
    
    return l;
}

int main() {
    ios::sync_with_stdio(false);
    #ifndef ONLINE_JUDGE
        freopen("data.in", "r", stdin);
        freopen("data.out", "w", stdout);
    #endif
    
    int n, q;
    
    scanf("%d %d", &n, &q);
    rep(i, 0, n) {
        scanf("%d", &a[i]);
        b[i] = a[i];
    }
    sort(b, b+n);
    m = unique(b, b+n) - b;
    T[0] = Build(0, m-1);
    rep(i, 0, n) {
        int id = lower_bound(b, b+m, a[i]) - b;
        T[i+1] = Insert(T[i], id, 1);
    }
    
    int l, r, kth;
    int ans;
    
    while (q--) {
        scanf("%d %d %d", &l, &r, &kth);
        ans = b[Query(T[l-1], T[r], kth)];
        printf("%d
", ans);
    }
    
    #ifndef ONLINE_JUDGE
        printf("time = %d.
", (int)clock());
    #endif
    
    return 0;
}

划分树可解。

/* 2104 */
#include <iostream>
#include <sstream>
#include <string>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <vector>
#include <deque>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstring>
#include <climits>
#include <cctype>
#include <cassert>
#include <functional>
#include <iterator>
#include <iomanip>
using namespace std;
//#pragma comment(linker,"/STACK:102400000,1024000")

#define sti                set<int>
#define stpii            set<pair<int, int> >
#define mpii            map<int,int>
#define vi                vector<int>
#define pii                pair<int,int>
#define vpii            vector<pair<int,int> >
#define rep(i, a, n)     for (int i=a;i<n;++i)
#define per(i, a, n)     for (int i=n-1;i>=a;--i)
#define clr                clear
#define pb                 push_back
#define mp                 make_pair
#define fir                first
#define sec                second
#define all(x)             (x).begin(),(x).end()
#define SZ(x)             ((int)(x).size())
// #define lson            l, mid, rt<<1
// #define rson            mid+1, r, rt<<1|1
#define LL                __int64

const int maxn = 1e5+5;
int order[maxn];
int val[18][maxn];
int toLeft[18][maxn];

void Build(int l, int r, int dep) {
    if (l == r)
        return ;
    
    int mid = (l + r) >> 1;
    int same = mid - l + 1;
    
    rep(i, l, r+1) {
        if (val[dep][i] < order[mid])
            --same;
    }
    
    int lpos = l, rpos = mid + 1;
    rep(i, l, r+1) {
        if (val[dep][i] < order[mid]) {
            val[dep+1][lpos++] = val[dep][i];
        } else if (val[dep][i]==order[mid] && same>0) {
            val[dep+1][lpos++] = val[dep][i];
            --same;
        } else {
            val[dep+1][rpos++] = val[dep][i];
        }
        toLeft[dep][i] = toLeft[dep][l-1] + lpos - l;        
    }
    
    Build(l, mid, dep+1);
    Build(mid+1, r, dep+1);
}

int Query(int l, int r, int k, int L, int R, int dep) {
    if (l == r)
        return val[dep][l];
    
    int mid = (L + R) >> 1;
    int tmp = toLeft[dep][r] - toLeft[dep][l-1];
    
    if (tmp >= k) {
        int ll = L + toLeft[dep][l-1] - toLeft[dep][L-1];
        int rr = ll + tmp - 1;
        
        return Query(ll, rr, k, L, mid, dep+1);
    } else {
        k-= tmp;
        
        int rr = r + toLeft[dep][R] - toLeft[dep][r];
        int ll = rr - (r-l+1-tmp) + 1;
        
        return Query(ll, rr, k, mid+1, R, dep+1);
    }
}

int main() {
    ios::sync_with_stdio(false);
    #ifndef ONLINE_JUDGE
        freopen("data.in", "r", stdin);
        freopen("data.out", "w", stdout);
    #endif
    
    int n, q;
    int l, r, kth;
    int ans;
    
    scanf("%d %d", &n, &q);
    rep(i, 1, n+1) {
        scanf("%d", &val[0][i]);
        order[i] = val[0][i];
    }
    sort(order+1, order+1+n);
    Build(1, n, 0);
    while (q--) {
        scanf("%d %d %d", &l, &r, &kth);
        ans = Query(l, r, kth, 1, n, 0);
        printf("%d
", ans);
    }
    
    #ifndef ONLINE_JUDGE
        printf("time = %d.
", (int)clock());
    #endif
    
    return 0;
}

数据发生器。

from copy import deepcopy
from random import randint, shuffle
import shutil
import string


def GenDataIn():
    with open("data.in", "w") as fout:
        t = 1
        bound = 10**3
        # fout.write("%d
" % (t))
        for tt in xrange(t):
            n = randint(100, 200)
            q = randint(100, 200)
            fout.write("%d %d
" % (n, q))
            L = []
            for i in xrange(n):
                x = randint(1, bound)
                L.append(x)
            fout.write(" ".join(map(str, L)) + "
")
            for i in xrange(q):
                l = randint(1, n)
                r = randint(l, n)
                k = randint(1, r-l+1)
                fout.write("%d %d %d
" % (l, r, k))
                
            
                
def MovDataIn():
    desFileName = "F:eclipse_prjworkspacehdojdata.in"
    shutil.copyfile("data.in", desFileName)

    
if __name__ == "__main__":
    GenDataIn()
    MovDataIn()