#include "robots.h"
#include <bits/stdc++.h>
#define x first
#define y second
#define all(v) v.begin(), v.end()
#define chkmin(a, b) a = min(a, b)
#define chkmax(a, b) a = max(a, b)
using namespace std;
typedef long long ll;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef pair<int, int> pii;
typedef vector<pii> vii;
const int MAX_T = 1e4 + 5;
const int MAX_A = 1000 + 5;
const int MAX_B = 1000 + 5;
const int infinity = 1e9;
int a, b, t;
int x[MAX_A], y[MAX_B], w[MAX_T], s[MAX_T];
const int MAX_N = 2e4;
int c[MAX_N][MAX_N];
queue<int> q;
int e[MAX_N], label[MAX_N];
vi graph[MAX_N];
int ind[MAX_N];
int source, sink;
void Push(int a, int b) {
int x = min(e[a], c[a][b]);
e[a] -= x, c[a][b] -= x;
if (!e[b] && b != sink) {
q.push(b);
}
e[b] += x, c[b][a] += x;
}
void Relabel(int a) {
label[a] = infinity;
for (int neighbor : graph[a]) {
if (c[a][neighbor]) {
chkmin(label[a], label[neighbor] + 1);
}
}
}
void Discharge(int a) {
while (e[a]) {
if (ind[a] == graph[a].size()) {
Relabel(a);
ind[a] = 0;
}
int b = graph[a][ind[a]];
if (c[a][b] && label[b] == label[a] - 1) Push(a, b);
ind[a]++;
}
}
int n;
bool MaxFlow() {
fill(e, e + n, 0);
e[source] = infinity;
for (int neighbor : graph[source]) {
Push(source, neighbor);
}
fill(label, label + n, 0);
fill(ind, ind + n, 0);
label[source] = n;
while (!q.empty()) {
int node = q.front();
q.pop();
Discharge(node);
}
return e[sink] == t;
}
bool Match(int time) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
c[i][j] = 0;
}
}
for (int i = 0; i < t; i++) {
for (int neighbor : graph[i]) {
if (neighbor != source) {
c[i][neighbor] = 1;
}
}
c[source][i] = 1;
}
for (int i = t; i < t + a + b; i++) {
c[i][sink] = time;
}
return MaxFlow();
}
vii robots;
int putaway(int A, int B, int T, int X[], int Y[], int W[], int S[]) {
a = A, b = B, t = T;
for (int i = 0; i < a; i++) x[i] = X[i];
for (int i = 0; i < b; i++) y[i] = Y[i];
for (int i = 0; i < t; i++) w[i] = W[i], s[i] = S[i];
for (int i = 0; i < a; i++) {
robots.push_back({i, 0});
}
for (int j = 0; j < b; j++) {
robots.push_back({j, 1});
}
n = t + a + b + 2;
for (int i = 0; i < t; i++) {
for (int j = 0; j < a + b; j++) {
if (robots[j].y && s[i] < y[robots[j].x] || !robots[j].y && w[i] < x[robots[j].x]) {
graph[i].push_back(j + t);
graph[j + t].push_back(i);
}
}
}
source = t + a + b;
sink = t + a + b + 1;
for (int i = 0; i < t; i++) {
graph[source].push_back(i);
graph[i].push_back(source);
}
for (int i = t; i < t + a + b; i++) {
graph[sink].push_back(i);
graph[i].push_back(sink);
}
int begin = 0, end = t + 1, mid;
while (begin < end) {
mid = (begin + end) >> 1;
if (Match(mid)) {
end = mid;
} else begin = mid + 1;
}
if (end == t + 1) return -1;
return end;
}
/*
3 0 6
6 2 9
4 6
8 5
7 9
1 8
5 1
8 7
*/
