題意分析:
N個客人,第i個在時間si到達,ei離開,點了ni份烤肉,每份需要ti的時間烤熟,廚師每分鐘最多烤M塊肉,客人需要在ei時間前拿到烤肉,問:廚師是否能滿足所有客人的需求?
解題思路:
si和ei的區間範圍灰常大= =,考慮將區間離散化。源點和客人i連一條ni*ti的邊,客人和自己規定時間範圍內的離散後區間連一條INF的邊,離散後的區間和匯點連一條區間長度(ei - si)*M的邊(因爲在ei前需要烤完,所以不需要+1),最後求解最大流是否等於所有顧客的需求之和即可。
個人感受:
阿西吧,你以爲你會了HDU 3572這題就沒問題啦?naive= =
具體代碼如下:
#include<algorithm>
#include<cctype>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iomanip>
#include<iostream>
#include<map>
#include<queue>
#include<set>
#include<sstream>
#include<stack>
#include<string>
#define lowbit(x) (x & (-x))
#define root 1, n, 1
#define lson l, m, rt << 1
#define rson m + 1, r, rt << 1 | 1
#define ll long long
#define pr(x) cout << #x << " = " << (x) << '\n';
using namespace std;
const int MAXN = 1010;//點數的最大值
const int MAXM = 4e5;//邊數的最大值
const int INF = 0x3f3f3f3f;
struct Edge{
int to,next,cap,flow;
}edge[MAXM];//注意是MAXM
int tol;
int head[MAXN];
int gap[MAXN],dep[MAXN],cur[MAXN];
void addedge(int u,int v,int w,int rw = 0)
{
edge[tol].to = v; edge[tol].cap = w; edge[tol].flow = 0;
edge[tol].next = head[u]; head[u] = tol++;
edge[tol].to = u; edge[tol].cap = rw; edge[tol].flow = 0;
edge[tol].next = head[v]; head[v] = tol++;
}
int Q[MAXN];
void BFS(int start,int end)
{
memset(dep,-1,sizeof(dep));
memset(gap,0,sizeof(gap));
gap[0] = 1;
int front = 0, rear = 0;
dep[end] = 0;
Q[rear++] = end;
while(front != rear)
{
int u = Q[front++];
for(int i = head[u]; i != -1; i = edge[i].next)
{
int v = edge[i].to;
if(dep[v] != -1)continue;
Q[rear++] = v;
dep[v] = dep[u] + 1;
gap[dep[v]]++;
}
}
}
int S[MAXN];
int sap(int start,int end,int N)
{
BFS(start,end);
memcpy(cur,head,sizeof(head));
int top = 0;
int u = start;
int ans = 0;
while(dep[start] < N)
{
if(u == end)
{
int Min = INF;
int inser;
for(int i = 0;i < top;i++)
if(Min > edge[S[i]].cap - edge[S[i]].flow)
{
Min = edge[S[i]].cap - edge[S[i]].flow;
inser = i;
}
for(int i = 0;i < top;i++)
{
edge[S[i]].flow += Min;
edge[S[i]^1].flow -= Min;
}
ans += Min;
top = inser;
u = edge[S[top]^1].to;
continue;
}
bool flag = false;
int v;
for(int i = cur[u]; i != -1; i = edge[i].next)
{
v = edge[i].to;
if(edge[i].cap - edge[i].flow && dep[v]+1 == dep[u])
{
flag = true;
cur[u] = i;
break;
}
}
if(flag)
{
S[top++] = cur[u];
u = v;
continue;
}
int Min = N;
for(int i = head[u]; i != -1; i = edge[i].next)
if(edge[i].cap - edge[i].flow && dep[edge[i].to] < Min)
{
Min = dep[edge[i].to];
cur[u] = i;
}
gap[dep[u]]--;
if(!gap[dep[u]]) return ans;
dep[u] = Min + 1;
gap[dep[u]]++;
if(u != start)u = edge[S[--top]^1].to;
}
return ans;
}
void init() {
tol = 0;
memset(head,-1,sizeof(head));
}
int s[MAXN], n[MAXN], e[MAXN], t[MAXN], tt[MAXN];
int main()
{
#ifdef LOCAL
freopen("C:\\Users\\apple\\Desktop\\in.txt", "r", stdin);
#endif
int N, M;
while (~scanf("%d%d", &N, &M)) {
init();
int src = 0, des = 0, sum = 0, cnt = 0;
for (int i = 1; i <= N; ++i) {
scanf("%d%d%d%d", &s[i], &n[i], &e[i], &t[i]);
addedge(src, i, n[i] * t[i]);
sum += n[i] * t[i];
tt[cnt++] = s[i];
tt[cnt++] = e[i];
}
sort(tt, tt + cnt);
cnt = unique(tt, tt + cnt) - tt;
des = cnt + N + 1;
for (int i = 1; i < cnt; ++i) {
addedge(i + N, des, (tt[i] - tt[i - 1]) * M);
for (int j = 1; j <= N; ++j) {
if (s[j] <= tt[i - 1] && tt[i] <= e[j])
addedge(j, N + i, INF);
}
}
if (sap(src, des, des + 1) == sum) printf("Yes\n");
else printf("No\n");
}
return 0;
}