SDUT 2886 - Weighted Median (思维)

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题意

找出一个数，满足题目的要求，复杂度为O(n)

思路

题目要求O(n)，在最坏情况下。感觉不太可能，用快排的思想均摊好像才是O(n)。

类似于快排找中位数。

用sort也能过。不过好像有点不合要求。

代码

#include <stack>#include <cstdio>#include <list>#include <cassert>#include <set>#include <iostream>#include <string>#include <vector>#include <queue>#include <functional>#include <cstring>#include <algorithm>#include <cctype>#include <string>#include <map>#include <cmath>using namespace std;#define LL long long#define ULL unsigned long long#define SZ(x) (int)x.size()#define Lowbit(x) ((x) & (-x))#define MP(a, b) make_pair(a, b)#define MS(arr, num) memset(arr, num, sizeof(arr))#define PB push_back#define X first#define Y second#define ROP freopen("input.txt", "r", stdin);#define MID(a, b) (a + ((b - a) >> 1))#define LC rt << 1, l, mid#define RC rt << 1|1, mid + 1, r#define LRT rt << 1#define RRT rt << 1|1const double PI = acos(-1.0);const int INF = 0x3f3f3f3f;const double eps = 1e-8;const int MAXN = 1e7 + 2;const int MOD = 1e9 + 7;const int dir[][2] = { {-1, 0}, {0, -1}, { 1, 0 }, { 0, 1 } };int cases = 0;typedef pair<int, int> pii;LL sum;struct NODE{    int first, second;}arr[MAXN];LL QuickSort(int l, int r, LL small, LL large){    int index = l, pivot = arr[l].X;    swap(arr[l], arr[r]);    for (int i = l; i < r; i++)        if (arr[i].X < pivot) swap(arr[index++], arr[i]);    swap(arr[index], arr[r]);    LL sm = 0, equ = 0, big = 0;    for (int i = l; i <= r; i++)    {        if (arr[i].X < pivot) sm += arr[i].Y;        else if (arr[i].X == pivot) equ += arr[i].Y;        else big += arr[i].Y;    }    if ((small+sm)*2 < sum && (large+big)*2 <= sum) return pivot;    if ((small+sm)*2 >= sum) return QuickSort(l, index-1, small, large+equ+big);    while (index < r && arr[index].X == arr[index+1].X) index++;    if ((large+big)*2 > sum) return QuickSort(index+1, r, small+equ+sm, large);}int main(){    //ROP;    int n;    while (~scanf("%d", &n))    {        sum = 0;        for (int i = 0; i < n; i++)            scanf("%d", &arr[i].X);        for (int i = 0; i < n; i++)        {            scanf("%d", &arr[i].Y);            sum += arr[i].Y;        }        printf("%lld\n", QuickSort(0, n-1, 0, 0));    }    return 0;}

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