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- 已经出现了三次的博弈论
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#include <iostream>
using namespace std;
int main() {
int t, n, k;
cin >> t;
while (t--) {
cin >> n >> k;
if (n % (k + 1))
cout << "First" << endl;
else
cout << "Second" << endl;
}
return 0;
}
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- BFS搜索, 存下来每个点的到达时间.
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#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include <iostream>
#include <algorithm>
#include <queue>
using namespace std;
int t, n, m;
struct Node{
int x, y, deep;
}st, ed, now, nxt;
const int MAX = 333;
queue <Node> que;
char mp[MAX][MAX];
bool used[MAX][MAX];
const int dir[4][2] = {1, 0, 0, 1, 0, -1, -1, 0};
int judge() {
while (que.size()) que.pop();
memset (used, 0, sizeof (used));
que.push(st);
used[st.x][st.y] = true;
while (que.size()) {
now = que.front(); que.pop();
if (now.x == ed.x && now.y == ed.y)
return now.deep;
for (int i = 0; i < 4; ++i) {
nxt.x = now.x + dir[i][0], nxt.y = now.y + dir[i][1];
nxt.deep = now.deep + 1;
if (nxt.x < 0 || nxt.y < 0 || nxt.x >= n || nxt.y >= m)
continue;
if (used[nxt.x][nxt.y])
continue;
if (mp[nxt.x][nxt.y] == '#')
continue;
used[nxt.x][nxt.y] = true, que.push(nxt);
}
}
return -1;
}
int main() {
cin >> t;
while (t--) {
cin >> n >> m;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
cin >> mp[i][j];
if (mp[i][j] == 'S')
st.x = i, st.y = j, st.deep = 0;
else if (mp[i][j] == 'T')
ed.x = i, ed.y = j;
}
}
cout << judge() << endl;
}
return 0;
}
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- DP / 记忆化搜索
原题是LeetCode 198 House Robber
转移方程: $dp[i] = max(dp[i - 2], dp[i - 3]) + a[i]$
- DP / 记忆化搜索
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#include <iostream>
#include <vector>
using namespace std;
class Solution {
public:
vector <int> ary;
vector <int> cnt;
int dfs(int now) {
if (cnt[now] != -1) return cnt[now];
cnt[now] = ary[now];
if (now + 2 < ary.size()) cnt[now] = max(cnt[now], dfs(now + 2) + ary[now]);
if (now + 3 < ary.size()) cnt[now] = max(cnt[now], dfs(now + 3) + ary[now]);
if (now + 1 < ary.size()) cnt[now] = max(cnt[now], dfs(now + 1));
return cnt[now];
}
int rob(vector<int>& nums) {
if (nums.size() == 0) return 0;
for (int i = 0; i < nums.size(); ++i)
ary.push_back(nums[i]), cnt.push_back(-1);
return dfs(0);
}
};
int main() {
int t, n, k;
cin >> t;
while (t--) {
cin >> n;
vector <int> nums;
for (int i = 0; i < n; ++i) {
int tmp;
cin >> tmp;
nums.push_back(tmp);
}
Solution S;
cout << S.rob(nums) << endl;
}
return 0;
}
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- 容斥原理
三个数各自的倍数
任意两个数字的积的倍数
三个数字积的倍数
做容斥
- 容斥原理
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#include <iostream>
using namespace std;
int a, b, c, n, t;
int main() {
cin >> t;
while (t--) {
cin >> a >> b >> c >> n;
cout << n / a + n / b + n / c
- n / (a * b) - n / (a * c) - n / (b * c)
+ n / (a * b * c) << endl;
}
return 0;
}