dp uva1626 括号序列

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题目链接

状态转移

d(i,j)表示子串S[i~j]至少需要加几个括号

递推写法快

#include <bits/stdc++.h>using namespace std;const int maxn = 100+5;char S[maxn];int n,d[maxn][maxn];bool match(char a, char b){return (a=='(' && b==')') || (a=='[' && b==']');}void dp(){for(int i=0; i<n; i++){d[i+1][i] = 0;d[i][i] = 1;}for(int i=n-2; i>=0; i--)for(int j=i+1; j<n; j++){d[i][j] = n;if(match(S[i],S[j])) d[i][j] = min(d[i][j],d[i+1][j-1]);for(int k=i; k<j; k++){d[i][j] = min(d[i][j],d[i][k]+d[k+1][j]);}}}void print(int i,int j){if(i>j) return ;if(i==j){if(S[i]=='(' || S[i]==')') printf("()");else printf("[]");return;}int ans = d[i][j];if(match(S[i],S[j]) && ans==d[i+1][j-1]) {printf("%c",S[i]); print(i+1,j-1); printf("%c",S[j]);return ;}for(int k=i; k<j; k++){if(ans == d[i][k]+d[k+1][j]){print(i,k); print(k+1,j);return;}} }void readline(char* S){fgets(S,maxn,stdin);}int main(){int T;readline(S);sscanf(S,"%d",&T);readline(S);while(T--){readline(S);n = strlen(S)-1;memset(d,-1,sizeof(d));dp();print(0,n-1);printf("\n");if(T) printf("\n");readline(S);}}

记忆化搜索慢

#include <bits/stdc++.h>using namespace std;const int maxn = 100+5;char S[maxn];int n,d[maxn][maxn];bool match(char a, char b){return (a=='(' && b==')') || (a=='[' && b==']');}int dp(int i,int j){if(i > j) return 0;if(i==j) return 1;if(d[i][j]>=0) return d[i][j];d[i][j] = n;if(match(S[i],S[j])) d[i][j] = min(d[i][j],dp(i+1,j-1));for(int k=i; k<j; k++)d[i][j] = min(d[i][j],dp(i,k)+dp(k+1,j));return d[i][j];}void print(int i,int j){if(i > j) return;if(i==j){if(S[i]=='(' || S[i]==')') printf("()");else printf("[]");return; }int ans = dp(i,j);if(match(S[i],S[j]) && ans==dp(i+1,j-1)){printf("%c",S[i]);print(i+1,j-1);printf("%c",S[j]);return;}for(int k=i; k<j; k++)if(ans == dp(i,k)+dp(k+1,j)){print(i,k);print(k+1,j);return;}}void readline(char* S) {  fgets(S, maxn, stdin);}int main() {  int T;  readline(S);  sscanf(S, "%d", &T);  readline(S);  while(T--) {    readline(S);    n = strlen(S) - 1;    memset(d, -1, sizeof(d));    print(0, n-1);    printf("\n");    if(T) printf("\n");    readline(S);  }  return 0;}

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