[USACO14DEC]Cow Jog G【最長反鏈性質】

題目鏈接

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  求的是跑了T分鐘之後的情況，要求是每個跑道都沒有被超越現象，問最少的跑道需求數量。

  很明顯的就是求一個反鏈的偏序問題，我們倒過來看，求最長不降序列，於是就可以用樹狀數組來進行查詢了。

#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <bitset>
#include <unordered_map>
#include <unordered_set>
#define lowbit(x) ( x&(-x) )
#define pi 3.141592653589793
#define e 2.718281828459045
#define INF 0x3f3f3f3f
#define HalF (l + r)>>1
#define lsn rt<<1
#define rsn rt<<1|1
#define Lson lsn, l, mid
#define Rson rsn, mid+1, r
#define QL Lson, ql, qr
#define QR Rson, ql, qr
#define myself rt, l, r
using namespace std;
typedef unsigned long long ull;
typedef unsigned int uit;
typedef long long ll;
const int maxN = 1e5 + 7;
int N;
ll T, Lsan[maxN];
int trie[maxN] = {0};
void update(int x, int val) { while(x <= N) { trie[x] = max(trie[x], val); x += lowbit(x); } }
int query(int x) { int ans = 0; while(x) { ans = max(trie[x], ans); x -= lowbit(x); } return ans; }
struct node
{
    ll a[2];
    node(int _a=0, int _b=0):a{_a, _b} {}
} t[maxN];
int main()
{
    scanf("%d%lld", &N, &T);
    ll vi;
    for(int i=1; i<=N; i++)
    {
        scanf("%lld%lld", &t[i].a[0], &vi);
        t[i].a[1] = t[i].a[0] + vi * T;
        Lsan[i] = t[i].a[1];
    }
    sort(Lsan + 1, Lsan + N + 1);
    int _UP = (int)(unique(Lsan + 1, Lsan + N + 1) - Lsan - 1);
    for(int i=1; i<=N; i++) t[i].a[1] = lower_bound(Lsan + 1, Lsan + _UP + 1, t[i].a[1]) - Lsan;
    int ans = 1;
    for(int i=N, tmp; i>=1; i--)
    {
        tmp = 1 + query((int)t[i].a[1]);
        ans = max(ans, tmp);
        update(t[i].a[1], tmp);
    }
    printf("%d\n", ans);
    return 0;
}