数字三角形

// 从上到下
#include <iostream>
#include <algorithm>
using namespace std;
const int N = 510, INF = 1e9;
int n;
int a[N][N];
int f[N][N];int main()
{scanf("%d", &n);for (int i = 1; i <= n; i ++ )for (int j = 1; j <= i; j ++ )scanf("%d", &a[i][j]);for (int i = 0; i <= n; i ++ )for (int j = 0; j <= i + 1; j ++ )f[i][j] = -INF;f[1][1] = a[1][1];for (int i = 2; i <= n; i ++ )for (int j = 1; j <= i; j ++ )f[i][j] = max(f[i - 1][j - 1] + a[i][j], f[i - 1][j] + a[i][j]);int res = -INF;for (int i = 1; i <= n; i ++ ) res = max(res, f[n][i]);printf("%d\n", res);return 0;
}// 从下到上
#include<iostream>
using namespace std;
const int N = 510;
int n, a[N][N];int main(){cin>>n;for(int i = 1; i <= n; i++){for(int j = 1; j <= i; j++){cin>>a[i][j];}}for(int i = n - 1; i > 0; i--){for(int j = 1; j <= i; j++){a[i][j] += max(a[i + 1][j], a[i + 1][j + 1]);}}cout<<a[1][1];return 0;
}

最长上升子序列

#include<iostream>
using namespace std;
const int N = 1e3 + 10;
int a[N], f[N];
int n, res;int main(){cin>>n;for(int i = 1; i <= n; i++) cin>>a[i];for(int i = 1; i <= n; i++){ f[i] = 1;for(int j = 1; j < i; j++){if(a[i] > a[j]) f[i] = max(f[i], f[j] + 1);}if(f[i] > res) res = f[i];}cout<<res;return 0;
}// 求这个序列
#include<iostream>
using namespace std;
const int N = 1e3 + 10;
int a[N], f[N];
int g[N], b[N];
int n;int main(){cin>>n;for(int i = 1; i <= n; i++) cin>>a[i];int k = 1;for(int i = 1; i <= n; i++){ f[i] = 1;for(int j = 1; j < i; j++){if(a[i] > a[j]){if(f[i] < f[j] + 1){f[i] = f[j] + 1;g[i] = j;}}}if(f[i] > f[k]) k = i;}cout<<f[k]<<endl;int cnt1 = f[k], cnt2 = f[k];for(int i = 0, len = f[k]; i < len; i++){b[cnt1--] = a[k];k = g[k];}//for(int i = 1; i <= cnt2; i++) cout<<b[i]<<" ";return 0;
}

最长上升子序列 II

#include<iostream>
using namespace std;
const int N = 1e5 + 10;
int a[N], b[N];
int n;int main(){scanf("%d", &n);for(int i = 1; i <= n; i++) scanf("%d", &a[i]);int len = 0;for(int i = 1; i <= n; i++){int l = 0, r = len + 1;while(l + 1 < r){int mid = (l + r) / 2;if(b[mid] < a[i]) l = mid;else r = mid;}len = max(len, r);// b[l] 是小于 a[i] 的最后一个数b[r] = a[i];}printf("%d", len);return 0;
}

最长公共子序列

#include<iostream>
using namespace std;
const int N = 1e3 + 10;
int f[N][N];
int n, m;
string a, b;int main(){cin>>n>>m>>a>>b;int res = 0;for(int i = 1; i <= n; i++){for(int j = 1; j <= m; j++){if(a[i - 1] == b[j - 1]) f[i][j] = f[i - 1][j - 1] + 1;else{f[i][j] = max(f[i - 1][j], f[i][j - 1]);}res = max(res, f[i][j]);}}cout<<res;return 0;
}

最短编辑距离

#include<iostream>
using namespace std;
const int N = 1e3 + 10;
int f[N][N];
int n, m;
string a, b;int main(){cin>>n>>a>>m>>b;for(int i = 0; i <= n; i++) f[i][0] = i;for(int j = 0; j <= m; j++) f[0][j] = j;for(int i = 1; i <= n; i++){for(int j = 1; j <= m; j++){if(a[i - 1] == b[j - 1]) f[i][j] = f[i - 1][j - 1];else{f[i][j] = min(f[i - 1][j - 1], min(f[i - 1][j], f[i][j - 1])) + 1;}}}cout<<f[n][m];return 0;
}

编辑距离

#include<iostream>
using namespace std;
const int N = 1e3 + 10;
int f[15][15];
int n, m;
string s[N];int main(){cin>>n>>m;for(int i = 0; i < n; i++) cin>>s[i];string a;int x;while(m--){cin>>a>>x;int cnt = 0;for(int k = 0; k < n; k++){int x1 = a.size(), x2 = s[k].size();for(int i = 0; i <= x1; i++) f[i][0] = i;for(int j = 0; j <= x2; j++) f[0][j] = j;for(int i = 1; i <= x1; i++){for(int j = 1; j <= x2; j++){if(a[i - 1] == s[k][j - 1]) f[i][j] = f[i - 1][j - 1];else{f[i][j] = min(f[i - 1][j - 1], min(f[i - 1][j], f[i][j - 1])) + 1;}}}if(f[x1][x2] <= x) cnt++;}cout<<cnt<<endl;}return 0;
}