HDU 4417Super Mario 划分树 + 二分

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题目：http://acm.hdu.edu.cn/showproblem.php?pid=4417

题意：给定一个数组，下标从0开始，然后有一定数量的询问，问给定区间内小于等于给定值得个数

思路：二分枚举第k小值，小于等于给定值时就更新结果为k，二分完毕后输出结果即可

PS：话说当时正在宿舍看这道题，突闻系主任要点名，撒腿就跑，终于及时赶到。。。听所谓企业宣讲时想这道题，首先想到的枚举中位数，可不就是二分么。。。

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>using namespace std;const int N = 100010;struct node{    int l, r;}s[N*4];int n, m;int arr[N], arrs[N], cut[20][N], seg[20][N];void build(int d, int l, int r, int k){    s[k].l = l, s[k].r = r;    if(l == r) return;    int mid = (l + r) >> 1, cnt = mid - l + 1, lb = l, rb = mid + 1;    for(int i = l; i <= mid; i++)        if(arrs[i] < arrs[mid]) cnt--;    for(int i = l; i <= r; i++)    {        if(i == l) cut[d][i] = 0;        else cut[d][i] = cut[d][i-1];        if(seg[d][i] == arrs[mid])        {            if(cnt)                cnt--, cut[d][i]++, seg[d+1][lb++] = seg[d][i];            else seg[d+1][rb++] = seg[d][i];        }        else if(seg[d][i] < arrs[mid])            cut[d][i]++, seg[d+1][lb++] = seg[d][i];        else seg[d+1][rb++] = seg[d][i];    }    build(d + 1, l, mid, k << 1);    build(d + 1, mid + 1, r, k << 1|1);}int query(int d, int l, int r, int x, int k){    if(s[k].l == s[k].r) return seg[d][s[k].l];    int mid = (s[k].l + s[k].r) >> 1, ls, lss;    if(l == s[k].l) ls = 0, lss = cut[d][r];    else ls = cut[d][l-1], lss = cut[d][r] - ls;    if(x <= lss) return query(d + 1, s[k].l + ls, s[k].l + ls + lss - 1, x, k << 1);    else return query(d + 1, mid + 1 + l - s[k].l - ls, mid + 1 + r - s[k].l - ls - lss, x - lss, k << 1|1);}int main(){    int t, a, b, c, x = 0;    scanf("%d", &t);    while(t--)    {        scanf("%d%d", &n, &m);        for(int i = 1; i <= n; i++)        {            scanf("%d", arr + i);            seg[0][i] = arrs[i] = arr[i];        }        sort(arrs + 1, arrs + 1 + n);        build(0, 1, n, 1);        printf("Case %d:\n", ++x);        while(m--)        {            scanf("%d%d%d", &a, &b, &c);            a++, b++; /*给定的数组和区间都是下标0开始的，我按1开始，因此加1*/            int l = 1, r = b - a + 1, res = 0;            while(l <= r)            {                int mid = (l + r) >> 1;                int tmp = query(0, a, b, mid, 1);                if(tmp > c) r = mid - 1;                else l = mid + 1, res = mid;            }            printf("%d\n", res);        }    }    return 0;}

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