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e2hang
2025-09-21 12:21:50 +08:00
parent 24522486f1
commit 3bde00039c
25 changed files with 842 additions and 0 deletions
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22
Algorithm/DP-DynamicProgramming/Linear-DP/P1115 最大子段和.cpp Normal file
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#include <iostream>
#include <utility>
#include <vector>
#include <climits>
#include <algorithm>
using namespace std;
const int INF = INT_MAX >> 1;
int main() {
int n;
cin >> n;
vector<int> a(n);
vector<int> dp(n + 1, -INF);
for (int i = 0; i < n; i++) {
cin >> a[i];
}
dp[0] = 0;
for (int i = 1; i < n + 1; i++) {
dp[i] = max(dp[i - 1] + a[i - 1], a[i - 1]);
}
cout << *max_element(dp.begin() + 1, dp.end()) << endl;
return 0;
}

31
Algorithm/DP-DynamicProgramming/Linear-DP/P12143 [蓝桥杯 2025 省 A] 好串的数目.cpp Normal file
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#include <iostream>
#include <vector>
#include <string>
using namespace std;
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
string s;
cin >> s;
int n = s.size();
vector<int> dp(n, 1);
//dp[i]: <20><>i<EFBFBD><69>β<EFBFBD><CEB2><EFBFBD><EFBFBD><EEB3A4><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD>
//<2F><><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ӵ<EFBFBD><D3B4><EFBFBD>Ȼ<EFBFBD><C8BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD>
//Ԥ<><D4A4><EFBFBD><EFBFBD>
for(int i = 1; i < n; i++){
if(s[i] == s[i - 1] + 1 || s[i] == s[i - 1]){
dp[i] = dp[i - 1] + 1;
}
}
//<2F><><EFBFBD><EFBFBD>Ҫ<EFBFBD>ݳ⣬<DDB3><E2A3AC>ô<EFBFBD>ֶ<EFBFBD><D6B6><EFBFBD><EFBFBD><EFBFBD>
int sum = 0;
for(int i = 0; i < n; i++){
//<2F>Լ<EFBFBD><D4BC><EFBFBD>
sum += (dp[i] - 1) * dp[i] / 2;
//ǰ<><C7B0>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
sum += dp[i] * (i - dp[i]);
}
cout << sum << endl;
return 0;
}

36
Algorithm/DP-DynamicProgramming/Linear-DP/P2285 [HNOI2004] 打鼹鼠.cpp Normal file
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#include <iostream>
#include <tuple>
#include <cmath>
#include <vector>
#include <algorithm>
using namespace std;
//tuple(t, x, y)
int dist(const tuple<int, int, int>& i, const tuple<int, int, int>& j){
return ( abs(get<1>(i) - get<1>(j)) + abs(get<2>(i) - get<2>(j)) );
}
int time(const tuple<int, int, int>& i, const tuple<int, int, int>& j){
return abs( get<0>(i) - get<0>(j) );
}
int main(){
int n, m;
cin >> n >> m;
//n * n, m <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
vector<tuple<int, int, int>> ham(m);
vector<int> dp(m, 1);
for(int i = 0; i < m; i++){
int t, x, y;
cin >> t >> x >> y;
ham[i] = make_tuple(t, x, y);
}
//dp[m] = max (<28><><EFBFBD>ߵ<EFBFBD><DFB5><EFBFBD>(t2 - t1 > dist)dp[x] + 1)
for(int i = 1; i < m; i++){
for(int j = 0; j < i; j++){
//<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ߵ<EFBFBD><DFB5>͸<EFBFBD><CDB8><EFBFBD>
if(dist(ham[i], ham[j]) <= time(ham[i], ham[j])){
dp[i] = max(dp[i], dp[j] + 1);
}
}
}
cout << *max_element(dp.begin(), dp.end()) << endl;
return 0;
}

0
Algorithm/DP-DynamicProgramming/Linear-DP/转化成一维O(n)是极好的 Normal file
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42
Algorithm/DP-DynamicProgramming/P1807 最长路.cpp Normal file
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#include <iostream>
#include <vector>
using namespace std;
const int NEG_INF = -1e9;
int main() {
int v, e;
cin >> v >> e;
vector<vector<int>> dp(v, vector<int>(v, NEG_INF));
for (int i = 0; i < v; i++) dp[i][i] = 0; // <20>Ի<EFBFBD>=0
for (int i = 0; i < e; i++) {
int a, b, w;
cin >> a >> b >> w;
dp[a - 1][b - 1] = max(dp[a - 1][b - 1], w); // <20><><EFBFBD>ܶ<EFBFBD><DCB6><EFBFBD><EFBFBD>ߣ<EFBFBD>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD>
}
for (int k = 0; k < v; k++) {
for (int i = 0; i < v; i++) {
if (dp[i][k] <= NEG_INF / 2) continue;
for (int j = 0; j < v; j++) {
if (dp[k][j] <= NEG_INF / 2) continue;
dp[i][j] = max(dp[i][j], dp[i][k] + dp[k][j]);
}
}
}
int mx = -1;
for (int i = 0; i < v; i++) {
for (int j = 0; j < v; j++) {
if (dp[i][j] > NEG_INF / 2) {
mx = max(mx, dp[i][j]);
}
}
}
mx == -1 ? cout << mx << endl;
return 0;
}

61
Algorithm/DP-DynamicProgramming/P3916 图的遍历.cpp Normal file
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#include <iostream>
#include <vector>
using namespace std;
int main(){
//dpֻ<70><D6BB>O(n3)<29><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>bfs<66><73><EFBFBD><EFBFBD>dfs
int v, e;
cin >> v >> e;
//vector<vector<int>> adj(v, vector<int>());
vector<vector<bool>> dp(v, vector<bool>(v, false));
for(int i = 0; i < e; i++){
int a, b;
cin >> a >> b;
//adj[a - 1].push_back(b - 1);
//adj[b - 1].push_back(a - 1);
dp[a - 1][b - 1] = true;
}
//<2F><><EFBFBD><EFBFBD>dp[i][j] : <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ƿ<EFBFBD><C7B7><EFBFBD>ͨ<EFBFBD><CDA8><EFBFBD><EFBFBD>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD>k<EFBFBD>ķ<EFBFBD>ʽ<EFBFBD><CABD><EFBFBD><EFBFBD>
for (int i = 0; i < v; i++) dp[i][i] = true; // <20>Լ<EFBFBD><D4BC><EFBFBD><EFBFBD>Լ<EFBFBD><D4BC><EFBFBD>ͨ
for(int k = 0; k < v; k++){
for(int i = 0; i < v; i++){
for(int j = 0; j < v; j++){
if(dp[i][j]) continue;
dp[i][j] = dp[i][j] || (dp[i][k] & dp[k][j]);
}
}
}
//bfs
for(int i = 0; i < v; i++) {
vector<bool> visited(v, false);
queue<int> q;
q.push(i);
visited[i] = true;
int mx = i;
while (!q.empty()) {
int curr = q.front();
q.pop();
for (int next : adj[curr]) {
if (!visited[next]) {
visited[next] = true;
q.push(next);
mx = max(mx, next);
}
}
}
cout << mx + 1 << " ";
}
for(int i = 0; i < v; i++){
int mx = -1;
for(int j = 0; j < v; j++){
if(dp[i][j] && mx < j) mx = j;
}
cout << mx + 1 << " ";
}
cout << endl;
return 0;
}