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DP-Algo

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e2hang
2025-09-15 22:16:09 +08:00
parent eea1a643fb
commit e9519e8558
19 changed files with 513 additions and 0 deletions
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31
Algorithm/DP-DynamicProgramming/Linear-DP/AT_dp_f LCS.cpp Normal file
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#include <iostream>
#include <string>
#include <vector>
using namespace std;
int main(){
string a, b;
cin >> a >> b;
int a_size = a.size(), b_size = b.size();
vector<vector<pair<int, string>>> dp(a.size() + 1, vector<pair<int, string>>(b_size + 1, {0, ""}));
for(int i = 1; i <= a_size; i++){
for(int j = 1; j <= b_size; j++){
if(a[i - 1] == b[j - 1]) {
dp[i][j].first = dp[i - 1][j - 1].first + 1;
string tmp = dp[i - 1][j - 1].second;
tmp.push_back(a[i - 1]);
dp[i][j].second = tmp;
}
else{
dp[i][j].first = max(dp[i - 1][j].first, dp[i][j - 1].first);
if(dp[i - 1][j].first > dp[i][j - 1].first){
dp[i][j].second = dp[i - 1][j].second;
}
else dp[i][j].second = dp[i][j - 1].second;
}
}
}
//cout << dp[a_size][b_size].first << " " << dp[a_size][b_size].second << endl;
cout << dp[a_size][b_size].second << endl;
return 0;
}

28
Algorithm/DP-DynamicProgramming/Linear-DP/B3637 最长上升子序列.cpp Normal file
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#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
struct cmp{
bool operator()(const pair<int, int>& a, const pair<int, int>& b){
if(a.first != b.first) return a.first > b.first;
return a.second < b.second;
}
};
int main(){
int n;
cin >> n;
vector<int> a(n);
for(int i = 0; i < n; i++){
cin >> a[i];
}
//dp[i]-><3E><><EFBFBD><EFBFBD>ǰi<C7B0><69><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EEB3A4><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> pair(<28><><EFBFBD><EFBFBD>, <20><><EFBFBD><EFBFBD>ֵ)
vector<int> dp(n, 1);
for(int i = 0; i < n; i++){
for(int j = 0; j < i; j++){
if(a[i] > a[j]) dp[i] = max(dp[i], dp[j] + 1);
}
}
int m = *max_element(dp.begin(), dp.end());
cout << m << endl;
return 0;
}

38
Algorithm/DP-DynamicProgramming/Linear-DP/Interval-DP/UVa10003CuttingSticks.cpp Normal file
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#include <iostream>
#include <vector>
using namespace std;
int main(){
int len, n;
cin >> len >> n;
vector<int> a(n + 2);
vector<vector<int>> dp(n + 2, vector<int>(n + 2, 0));
//<2F><><EFBFBD><EFBFBD>dp[i][j]Ϊ<>и<EFBFBD>ľ<EFBFBD><C4BE>[i, j]<5D><> 0|---1|-----2|----3|--4| <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ķ<EFBFBD><C4B7><EFBFBD> a[0] = 0 a[1] = x,,, a[n + 1] = len
a[0] = 0; a[n + 1] = len;
for(int i = 1; i <= n; i++){
cin >> a[i];
}
//a[i]<5D>Ƿֵ<C7B7>
/*<2A><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
for(int i = 0; i <= n + 1; i++){
for(int j = i; j <= n + 1 ;j++){
dp[i][j] = 114514;
for(int k = i + 1; k < j; k++){
dp[i][j] = min(dp[i][j], dp[i][k] + dp[k][j] + a[j] - a[i]);
}
if(dp[i][j] == 114514) dp[i][j] = 0;
}
} */
// <20><><EFBFBD><EFBFBD> DP<44><50><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ȵ<EFBFBD><C8B5><EFBFBD>
for(int l = 2; l <= n + 1; l++){ // <20><><EFBFBD>䳤<EFBFBD><E4B3A4><EFBFBD><EFBFBD><EFBFBD><EFBFBD>2
for(int i = 0; i + l <= n + 1; i++){
int j = i + l;
dp[i][j] = INT_MAX;
for(int k = i + 1; k < j; k++){
dp[i][j] = min(dp[i][j], dp[i][k] + dp[k][j] + a[j] - a[i]);
}
if(dp[i][j] == INT_MAX) dp[i][j] = 0;
}
}
cout << dp[0][n + 1] << endl;
return 0;
}

54
Algorithm/DP-DynamicProgramming/Linear-DP/Interval-DP/UVa11584划分回文串.cpp Normal file
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#include <bits/stdc++.h>
using namespace std;
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
int T;
if(!(cin >> T)) return 0;
while(T--){
string s;
cin >> s;
int n = s.size();
if(n == 0){
cout << 0 << "\n";
continue;
}
// isPal[i][j] whether s[i..j] is palindrome
vector<vector<char>> isPal(n, vector<char>(n, 0));
// center expand to fill isPal (or use DP)
for(int center = 0; center < n; ++center){
// odd length
int l = center, r = center;
while(l >= 0 && r < n && s[l] == s[r]){
isPal[l][r] = 1;
--l; ++r;
}
// even length
l = center; r = center + 1;
while(l >= 0 && r < n && s[l] == s[r]){
isPal[l][r] = 1;
--l; ++r;
}
}
// dp[i] = min cuts for s[0..i]
const int INF = 1e9;
vector<int> dp(n, INF);
for(int i = 0; i < n; ++i){
if(isPal[0][i]){
dp[i] = 0;
} else {
for(int j = 0; j < i; ++j){
if(isPal[j+1][i]){
dp[i] = min(dp[i], dp[j] + 1);
}
}
}
}
cout << dp[n-1] << "\n";
}
return 0;
}

31
Algorithm/DP-DynamicProgramming/Linear-DP/Interval-DP/UVa1626括号序列.cpp Normal file
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#include <iostream>
#include <string>
#include <vector>
using namespace std;
const int INF = 1e9;
bool match(char a, char b){
return (a == '(' && b == ')') || (a == '[' && b == ']');
}
int main(){
string s;
cin >> s;
int n = s.size();
vector<vector<int>> dp(s.size() + 2, vector<int>(s.size() + 2, 1));
for(int l = 2; l <= n; l++){
for(int i = 0; i < n - l + 1; i++){
int j = i + l - 1;
dp[i][j] = INF;
for(int k = i; k < j; k++){
dp[i][j] = min(dp[i][j], dp[i][k] + dp[k + 1][j]);
}
if(match(s[i], s[j])) {
if (i + 1 <= j - 1)
dp[i][j] = min(dp[i][j], dp[i+1][j-1]);
else
dp[i][j] = 0; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD>ֱ<EFBFBD><D6B1>ƥ<EFBFBD><C6A5>
}
}
}
cout << dp[0][n - 1] << endl;
return 0;
}

22
Algorithm/DP-DynamicProgramming/Linear-DP/Knapsack-DP/P1616 疯狂的采药.cpp Normal file
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#include <iostream>
#include <utility>
#include <vector>
using namespace std;
typedef long long ll;
int main(){
ll t, m;
cin >> t >> m;
vector<pair<ll, ll>> arr(m);
vector<ll> dp(t + 1, 0);
for (int i = 0; i < m; i++) {
cin >> arr[i].first >> arr[i].second;
}
//״̬-> dp[i] = max(dp[i - time[i]] + value[i])
for(int i = 1; i < t + 1; i++){
for(int j = 0; j < m; j++){
if(i - arr[j].first >= 0) dp[i] = max(dp[i], dp[i - arr[j].first] + arr[j].second);
}
}
cout << dp[t] << endl;
return 0;
}

40
Algorithm/DP-DynamicProgramming/Linear-DP/Knapsack-DP/P2758 编辑距离.cpp Normal file
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//1<><31>״̬<D7B4>Լ<EFBFBD>״̬ת<CCAC><D7AA> -> <20><><EFBFBD><EFBFBD>
//2<><32><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ľ<EFBFBD> -> ȫ<><C8AB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ľ<EFBFBD>
//3<><33><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>п<EFBFBD><D0BF>ܲ<EFBFBD><DCB2><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD>Ž<EFBFBD><C5BD><EFBFBD>
//4<><34><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD>ֵ<EFBFBD><D6B5><EFBFBD>
#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
using namespace std;
int minEditDistance(const string& a, const string& b) {
int m = a.size(), n = b.size();
// dp[i][j]<5D><>ʾA[0:i]<5D><>B[0:j]<5D><><EFBFBD><EFBFBD>С<EFBFBD><D0A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));
// <20><>ʼ<EFBFBD><CABC><EFBFBD>߽<EFBFBD>
for (int i = 0; i <= m; ++i) dp[i][0] = i; // ɾ<><C9BE>i<EFBFBD><69><EFBFBD>ַ<EFBFBD>
for (int j = 0; j <= n; ++j) dp[0][j] = j; // <20><><EFBFBD><EFBFBD>j<EFBFBD><6A><EFBFBD>ַ<EFBFBD>
// ״̬ת<CCAC><D7AA>
for (int i = 1; i <= m; ++i) {
for (int j = 1; j <= n; ++j) {
if (a[i-1] == b[j-1]) {
dp[i][j] = dp[i-1][j-1]; // ƥ<>䣬<EFBFBD><E4A3AC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
} else {
dp[i][j] = min({dp[i-1][j-1], dp[i-1][j], dp[i][j-1]}) + 1; // <20>滻<EFBFBD><E6BBBB>ɾ<EFBFBD><C9BE><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
}
}
}
return dp[m][n];
}
int main() {
string a, b;
getline(cin, a); // <20><><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD>A
getline(cin, b); // <20><><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD>B
cout << minEditDistance(a, b) << endl; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
return 0;
}

26
Algorithm/DP-DynamicProgramming/Linear-DP/Knapsack-DP/P2842 纸币问题 1.cpp Normal file
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#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
int main() {
int n, w;
cin >> n >> w;
vector<int> a(n);
for (int i = 0; i < n; i++) cin >> a[i];
vector<int> dp(w + 1, 1e9);
dp[0] = 0;
for (int j = 0; j < n; j++) {
for (int i = a[j]; i <= w; i++) {
dp[i] = min(dp[i], dp[i - a[j]] + 1);
}
}
if (dp[w] == 1e9) cout << -1 << endl; // <20>޽<EFBFBD>
else cout << dp[w] << endl;
return 0;
}

35
Algorithm/DP-DynamicProgramming/Linear-DP/P1164 小A点菜.cpp Normal file
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#include <iostream>
#include <vector>
#include <unordered_map>
using namespace std;
int main(){
int n, m;
cin >> n >> m;
vector<int> arr(n);
vector<int> dp(m + 1, 0);
unordered_map<int, int> mp;
for(int i = 0; i < n; i++){
cin >> arr[i];
mp[i]++;
}
dp[0] = 1;
//dp[i] += dp[i - arr[j]]
/* 0/1<><31><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>j<EFBFBD><6A><EFBFBD><EFBFBD><EFBFBD>㣬<EFBFBD><E3A3AC><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>d[i]
for(int i = 1; i <= m; i++){
for(int j = 0; j < n; j++){
if(i - arr[j] >= 0) {
dp[i] += dp[i - arr[j]];
}
}
}*/
//<2F><><EFBFBD>ظ<EFBFBD><D8B8><EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD><D4AA>
for(int j = 0; j < n; j++){
for(int i = m; i >= arr[j]; i--){
dp[i] += dp[i - arr[j]];
}
}
cout << dp[m] << endl;
return 0;
}

33
Algorithm/DP-DynamicProgramming/Linear-DP/P1216 [IOI 1994 USACO1.5] 数字三角形 Number Triangles.cpp Normal file
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#include <iostream>
#include <vector>
using namespace std;
int main(){
int n;
cin >> n;
vector<vector<int>> arr(n);
vector<vector<int>> dp(n);
int tmp;
for(int i = 0; i < n; i++){
for(int j = 0; j < i + 1; j++){
cin >> tmp;
arr[i].push_back(tmp);
dp[i].push_back(-1);
}
}
dp[0][0] = arr[0][0];
for(int i = 1; i < n; i++){
for(int j = 0; j < i + 1; j++){
if(j == 0) dp[i][j] = dp[i - 1][j] + arr[i][j];
else if(j == i) dp[i][j] = dp[i - 1][j - 1] + arr[i][j];
else{
dp[i][j] = max(dp[i - 1][j - 1] + arr[i][j], dp[i - 1][j] + arr[i][j]);
}
}
}
int max = -2;
for(int i = 0; i < n; i++){
if(dp[n - 1][i] > max) max = dp[n - 1][i];
}
cout << max << endl;
return 0;
}

28
Algorithm/DP-DynamicProgramming/Linear-DP/P1439.cpp Normal file
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#include <iostream>
#include <vector>
using namespace std;
int main(){
int n;
cin >> n;
vector<int> a(n), b(n);
for(int i = 0; i < n; i++){
cin >> a[i];
}
for(int i = 0; i < n; i++){
cin >> b[i];
}
int a_size = a.size(), b_size = b.size();
vector<vector<int>> dp(a.size() + 1, vector<int>(b_size + 1, 0));
for(int i = 1; i <= a_size; i++){
for(int j = 1; j <= b_size; j++){
if(a[i - 1] == b[j - 1]) {
dp[i][j] = dp[i - 1][j - 1] + 1;
}
else{
dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
}
}
}
cout << dp[a_size][b_size] << endl;
return 0;
}

7
Algorithm/DP-DynamicProgramming/Linear-DP/P1802 5 倍经验日.cpp Normal file
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#include <iostream>
#include <vector>
using namespace std;
int main(){
return 0;
}

29
Algorithm/DP-DynamicProgramming/Linear-DP/UVA1347 旅行 Tour.cpp Normal file
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#include <iostream>
#include <cmath>
#include <vector>
using namespace std;
double dist(const pair<int, int>& x, const pair<int, int>& y){
double r = sqrt( (y.first - x.first) * (y.first - x.first) + (y.second - x.second) * (y.second - x.second) );
return r;
}
int main(){
int n;
cin >> n;
vector<pair<int, int>> m(n);
for(int i = 0; i < n; i++){
cin >> m[i].first >> m[i].second;
}
vector<vector<int>> dp(n, vector<int>(n, 0));
int k = 0;
//dp[0][0] = 0;
int i = 0, j = 0;
while(dp[n - 1][n - 1] == 0){
k = max(i, j) + 1;
dp[i][k] = min(d[i][k], d[i][j] + dist(m[k], m[j]));
dp[k][j] = min(d[k][j], d[i][j] + dist(m[k], m[i]));
i++;j++;
}
return 0;
}