DFS A - Joysticks
嫌麻烦直接DFS暴搜吧，有坑点是当前电量<=1就不能再掉电，直接结束。
#include <bits/stdc++.h>
typedef long long ll;
const int N = 1e5 + 5;
int ans = 0;
void DFS(int a, int b, int step) {
if (a <= 0 || b <= 0) {
ans = std::max (ans, step); return ;
}
if (a < b && b - 2 >= 0) {
DFS (a + 1, b - 2, step + 1);
} else if (a >= b && a - 2 >= 0) {
DFS (a - 2, b + 1, step + 1);
}
}
int main() {
int a, b; std::cin >> a >> b;
ans = 0;
DFS (a, b, 0);
std::cout << ans << '
';
return 0;
}
构造 + 贪心 B - Beautiful Paintings
每次取出不重复的递增序列，直到集合为空
#include <bits/stdc++.h>
typedef long long ll;
const int N = 1e5 + 5;
std::vector<int> vec;
int main() {
int n; std::cin >> n;
for (int x, i=0; i<n; ++i) {
std::cin >> x; vec.push_back (x);
}
std::sort (vec.begin (), vec.end ());
int ans = 0;
while (vec.size () > 0) {
std::vector<int> tmp;
int pre = 0, num = 0;
for (auto x: vec) {
if (x > pre) {
num++; pre = x;
} else {
tmp.push_back (x);
}
}
ans += num - 1; vec = tmp;
}
std::cout << ans << '
';
return 0;
}
数学 + 容斥 C - Watchmen
化简公式得到找到pair (i, j) xi == xj || yi == yj。找两次再容斥一下。map做更好。
#include <bits/stdc++.h>
typedef long long ll;
const int N = 2e5 + 5;
const int INF = 1e9 + 7;
std::pair<int, int> point[N];
ll calc(int n) {
return 1ll * n * (n - 1) / 2;
}
bool cmpx(std::pair<int, int> a, std::pair<int, int> b) {
return a.first < b.first;
}
bool cmpy(std::pair<int, int> a, std::pair<int, int> b) {
return a.second < b.second;
}
int main() {
int n; scanf ("%d", &n);
for (int x, y, i=0; i<n; ++i) {
scanf ("%d%d", &x, &y);
point[i] = std::make_pair (x, y);
}
std::sort (point, point+n, cmpx);
ll ans = 0;
int x = INF, y = INF, num = 1;
for (int i=0; i<n; ++i) {
if (x == point[i].first) {
num++;
} else {
x = point[i].first;
if (num > 1) {
ans += calc (num);
}
num = 1;
}
}
if (num > 1) {
ans += calc (num);
}
std::sort (point, point+n, cmpy);
x = INF; y = INF; num = 1;
for (int i=0; i<n; ++i) {
if (y == point[i].second) {
num++;
} else {
y = point[i].second;
if (num > 1) {
ans += calc (num);
}
num = 1;
}
}
if (num > 1) {
ans += calc (num);
}
std::sort (point, point+n);
x = INF; y = INF; num = 1;
for (int i=0; i<n; ++i) {
if (x == point[i].first && y == point[i].second) {
num++;
} else {
x = point[i].first, y = point[i].second;
if (num > 1) {
ans -= calc (num);
}
num = 1;
}
}
if (num > 1) {
ans -= calc (num);
}
printf ("%I64d
", ans);
return 0;
}
two points D - Image Preview
题意：浏览图片，浏览，滑动以及反转需要时间，问在T时间内最多浏览多少图片。
分析：定义两个指针from，to，可行的方案是n+1->from,from->n+1,n+1->to或者n+1->to,to->n+1,n+1->from,还有from->to。前两个重复滑动的可以选择距离小的，第三个只要定义to=n+1就对了。其实可以用二分做的。
#include <bits/stdc++.h>
typedef long long ll;
const int N = 5e5 + 5;
char str[2*N];
ll tim[2*N];
int n, a, b, T;
ll get_time(int from, int to) {
ll ret = tim[from] - tim[to-1];
int move = from - to + std::min (from-(n+1), (n+1)-to);
return ret + 1ll * a * move;
}
int main() {
scanf ("%d%d%d%d", &n, &a, &b, &T);
scanf ("%s", str + 1);
for (int i=1; i<=n; ++i) {
tim[i] = (str[i] == 'w' ? (b+1) : 1);
}
for (int i=n+1; i<=2*n; ++i) {
tim[i] = tim[i-n];
}
for (int i=1; i<=2*n; ++i) {
tim[i] += tim[i-1];
}
int ans = 0;
int from = n + 1;
for (int to=2; to<=n+1; ++to) {
while (from < to+n-1 && get_time (from+1, to) <= T) from++;
if (get_time (from, to) <= T) ans = std::max (ans, from - to + 1);
}
printf ("%d
", ans);
return 0;
}
图论 + 并查集 E - Table Compression
题意：给一个矩阵，求新的矩阵，使得原矩阵的同行，同列的大小关系不变，且使得新矩阵的最大值最小。即离散化
分析：找好顺序，一个一个从小到大填充就行了。因为有相同数字的存在，使用并查集使得将相同的数字赋值离散化后相同的数字。因为有行和列共同影响一个数字，所以建立一个大数到小数的图，类似树形DP，选择当前行或列的最大值+1为离散化后的数字
#include <bits/stdc++.h>
const int N = 1e6 + 5;
std::pair<int, std::pair<int, int> > A[N];
int val[N], ans[N];
int mr[N], mc[N];
int rt[N];
std::vector<int> edge[N];
std::vector<int> num[N];
int Find(int x) {
return rt[x] == x ? x : rt[x] = Find (rt[x]);
}
int main() {
int n, m; scanf ("%d%d", &n, &m);
int tot = n * m;
for (int i=0; i<n; ++i) {
for (int j=0; j<m; ++j) {
scanf ("%d", &val[i*m+j]);
A[i*m+j].first = val[i*m+j];
A[i*m+j].second = std::make_pair (i, j);
rt[i*m+j] = i * m + j;
}
}
std::fill (mr, mr+n, -1);
std::fill (mc, mc+m, -1);
std::sort (A, A+tot);
for (int i=0; i<tot; ++i) {
int r = A[i].second.first, c = A[i].second.second;
int pos = r * m + c;
if (mr[r] != -1) {
if (val[mr[r]] == A[i].first) {
rt[pos] = Find (mr[r]);
} else {
edge[pos].push_back (mr[r]);
}
}
if (mc[c] != -1) {
if (val[mc[c]] == A[i].first) {
rt[Find (pos)] = Find (mc[c]);
} else {
edge[pos].push_back (mc[c]);
}
}
mr[r] = mc[c] = pos;
}
for (int i=0; i<tot; ++i) {
num[Find (i)].push_back (i);
}
for (int i=0; i<tot; ++i) {
int r = A[i].second.first, c = A[i].second.second;
int id = r * m + c;
if (Find (id) == id) {
int _max = 0;
for (auto u: num[id]) {
for (auto v: edge[u]) {
_max = std::max (_max, ans[v]);
}
}
for (auto u: num[id]) {
ans[u] = _max + 1;
}
}
}
for (int i=0; i<n; ++i) {
for (int j=0; j<m; ++j) {
printf ("%d ", ans[i*m+j]);
}
puts ("");
}
return 0;
}