UVa 1451 - Average (斜率优化 + 单挑队列)
题意
输出平均值最大的子序列。
思路
斜率优化。
简单来说就是用队列维护一个下凸的集合。
半知半解中。。
一开始不小心把返回斜率的函数定义成
bool
，所以返回不出第三种状态了。被搞死TAT
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|1
const double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
const double eps = 1e-8;
const int MAXN = 1e5 + 10;
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;
int Q[MAXN], arr[MAXN];
char str[MAXN];
int Check(int x1, int x2, int x3, int x4)
{
return (arr[x2] - arr[x1-1]) * (x4-x3+1) - (arr[x4]-arr[x3-1])*(x2-x1+1);
}
int main()
{
//ROP;
int T;
scanf("%d", &T);
while (T--)
{
int len, L;
scanf("%d%d", &len, &L);
scanf("%s", str+1);
for (int i = 1; i <= len; i++) arr[i] = arr[i-1] + str[i] - '0';
int head = 0, tail = 0;
pii ans = MP(1, L);
for (int i = L; i <= len; i++)
{
int j = i-L;
while (head+1 < tail && Check(Q[tail-2], j, Q[tail-1], j) >= 0) tail--;
Q[tail++] = j+1;
while (head+1 < tail && Check(Q[head], i, Q[head+1], i) <= 0) head++;
int tmp = Check(Q[head], i, ans.X, ans.Y);
if (tmp > 0 || (tmp == 0 && i - Q[head] < ans.Y - ans.X))
ans.X = Q[head], ans.Y = i;
}
printf("%d %d\n", ans.X, ans.Y);
}
return 0;
}