Codeforces Round #343 (Div. 2) D. Babaei and Birthday Cake（dp、BIT）

题意:

给定N≤105个蛋糕,编号为1∼N,每个都有体积Vi
任意一个蛋糕都可以放在桌子上,对于蛋糕对(i,j),i可以放在j上,当且仅当i>j且Vi≥Vj
求能摆放的蛋糕的最大体积和

分析:

LIS模型的经典水题了
f[i]表示第i个蛋糕在最上面的最大体积和
f[i]=max{f[j]}+Vi,j<i且Vj<Vi
考虑用BIT优化一下这个转移,离散化一下,记录当前体积蛋糕在最上面的最大体积和,然后就可以O(logn)转移了
ans=max{f[i]},时间复杂度为O(nlogn)

代码:

////  Created by TaoSama on 2016-02-23//  Copyright (c) 2016 TaoSama. All rights reserved.//#pragma comment(linker, "/STACK:1024000000,1024000000")#include <algorithm>#include <cctype>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <iomanip>#include <iostream>#include <map>#include <queue>#include <string>#include <set>#include <vector>using namespace std;#define pr(x) cout << #x << " = " << x << "  "#define prln(x) cout << #x << " = " << x << endlconst int N = 1e5 + 10, INF = 0x3f3f3f3f, MOD = 1e9 + 7;typedef long long LL;int n;LL v[N];struct BIT {    int n; LL b[N];    void init(int _n) {        n = _n;        memset(b, 0, sizeof b);    }    void add(int i, LL v) {        for(; i <= n; i += i & - i) b[i] = max(b[i], v);    }    LL sum(int i) {        LL ret = 0;        for(; i; i -= i & -i) ret = max(ret, b[i]);        return ret;    }} bit;int main() {#ifdef LOCAL    freopen("C:\\Users\\TaoSama\\Desktop\\in.txt", "r", stdin);//  freopen("C:\\Users\\TaoSama\\Desktop\\out.txt","w",stdout);#endif    ios_base::sync_with_stdio(0);    while(scanf("%d", &n) == 1) {        vector<LL> xs;        for(int i = 1; i <= n; ++i) {            int r, h; scanf("%d%d", &r, &h);            v[i] = 1LL * r * r * h;            xs.push_back(v[i]);        }        sort(xs.begin(), xs.end());        xs.resize(unique(xs.begin(), xs.end()) - xs.begin());        LL ans = 0;        bit.init(xs.size());        for(int i = 1; i <= n; ++i) {            int idx = lower_bound(xs.begin(), xs.end(), v[i]) - xs.begin() + 1;            LL cur = bit.sum(idx - 1) + v[i];            ans = max(ans, cur);            bit.add(idx, cur);        }        printf("%.12f\n", ans * acos(-1));    }    return 0;}