SOJ-3010（划分树求区间内的第k个数）

 

/******************************************************************************************************
 ** Copyright (C) 2011.06.12(8:000)-2013.07.01
 ** Author: famousDT <[email protected]>
 ** Edit date: 2011-06-12
******************************************************************************************************/
#include <stdio.h>
#include <stdlib.h>//abs,atof(string to float),atoi,atol,atoll
#include <math.h>//atan,acos,asin,atan2(a,b)(a/b atan),ceil,floor,cos,exp(x)(e^x),fabs,log(for E),log10
#include <algorithm>
using namespace std;

//typedef long long int ll;

#define PI acos(-1)
#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define MIN(a, b) ((a) < (b) ? (a) : (b))
#define MALLOC(n, type) ((type *)malloc((n) * sizeof(type)))
#define FABS(a) ((a) >= 0 ? (a) : (-(a)))

/* 分析：划分树 */

#define MAX_SIZE 100005

int sorted[MAX_SIZE];//已经排好序的数据
int toleft[25][MAX_SIZE];
int tree[25][MAX_SIZE];

void build_tree(int left, int right, int deep) 
{
    int i;
    if (left == right) return ;
    int mid = (left + right) >> 1;
    int same = mid - left + 1; //位于左子树的数据
    for (i = left; i <= right; ++i) {//计算放于左子树中与中位数相等的数字个数
        if (tree[deep][i] < sorted[mid]) {
            --same;
        }
    }
    int ls = left;
    int rs = mid + 1;
    for (i = left; i <= right; ++i) {
        int flag = 0;
        if ((tree[deep][i] < sorted[mid]) || (tree[deep][i] == sorted[mid] && same > 0)) {
            flag = 1;
            tree[deep + 1][ls++] = tree[deep][i];
            if (tree[deep][i] == sorted[mid])
                same--;
        } else {
            tree[deep + 1][rs++] = tree[deep][i];
        }
        toleft[deep][i] = toleft[deep][i - 1]+flag;
    }
    build_tree(left, mid, deep + 1);
    build_tree(mid + 1, right, deep + 1);
}

int query(int left, int right, int k, int L, int R, int deep)
{
    if (left == right)
        return tree[deep][left];
    int mid = (L + R) >> 1;
    int x = toleft[deep][left - 1] - toleft[deep][L - 1];//位于left左边的放于左子树中的数字个数
    int y = toleft[deep][right] - toleft[deep][L - 1];//到right为止位于左子树的个数
    int ry = right - L - y;//到right右边为止位于右子树的数字个数
    int cnt = y - x;//[left,right]区间内放到左子树中的个数
    int rx = left - L - x;//left左边放在右子树中的数字个数
    if (cnt >= k) {
        //printf("sss %d %d %d\n", xx++, x, y);
        return query(L + x, L + y - 1, k, L, mid, deep + 1);
    }
    else {
        //printf("qqq %d %d %d\n", xx++, x, y);
        return query(mid + rx + 1, mid + 1 + ry, k - cnt, mid + 1, R, deep + 1);
    }
}

int main()
{
    int m, n;
    int a, b, k;
    int i;
    while (scanf("%d%d", &m, &n) == 2) {
        for (i = 1; i <= m; ++i) {
            scanf("%d", &sorted[i]);
            tree[0][i] = sorted[i];
        }
        sort(sorted + 1, sorted + 1 + m);
        build_tree(1, m, 0);
        for (i = 0; i < n; ++i) {
            scanf("%d%d%d", &a, &b, &k);
            printf("%d\n", query(a, b, k, 1, m, 0));
        }
    }
    return 0;
}