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[编程题]游历魔法王国

https://www.nowcoder.com/questionTerminal/f58859adc39f4edc9cd8e40ba4160339

给定一棵树，可以走L步，最多能访问多少个节点

思路：分类讨论，首先贪心走最长链，如果还有多余的步数，可以知道如果从最底端返回上面再访问节点的话，这样不是最优，应该是在最长链的某个点就走进去然后再回来，如果多了k步，那么最多可以访问k / 2个节点，因为一去一回需要2步，相当于回到这个节点

#include <bits/stdc++.h>
#define IOS ios::sync_with_stdio(false)
using namespace std;
#define inf (0x3f3f3f3f)
typedef long long int LL;
const int maxn = 50 + 2;
char str[maxn], sub[maxn];
int dp[maxn][maxn];
int calc(char str[], char sub[], int lenstr) {
memset(dp, -1, sizeof dp);
dp[0][0] = 0;
for (int i = 1; i <= lenstr; ++i) {
for (int j = 1; j <= lenstr; ++j) {
if (str[i] == sub[j]) {
dp[i][j] = dp[i - 1][j - 1] + 1;
}
dp[i][j] = max(dp[i][j], dp[i - 1][j]);
dp[i][j] = max(dp[i][j], dp[i][j - 1]);
}
}
return dp[lenstr][lenstr];
}
int lenstr;
int ans;
char op[2222];

bool check() {
int lef = 0;
for (int i = 1; i <= lenstr; ++i) {
if (sub[i] == '(') lef++;
else lef--;
if (lef < 0) return false;
}
return lef == 0;
}

void did(int from, int to) {
strcpy(sub + 1, str + 1);
if (from > to) {
char ch = sub[from];
for (int i = from; i >= to; --i) {
sub[i] = sub[i - 1];
}
sub[to] = ch;
} else {
char ch = sub[from];
for (int i = from + 1; i <= to; ++i) {
sub[i - 1] = sub[i];
}
sub[to] = ch;
}
}
map<string, bool> mp;
void work() {
scanf("%s", str + 1);
lenstr = strlen(str + 1);
strcpy(sub + 1, str + 1);
for (int i = 1; i <= lenstr; ++i) {
for (int j = 1; j <= lenstr; ++j) {
if (i == j) continue;
did(i, j);
if (check() && mp.find(sub + 1) == mp.end() && calc(str, sub, lenstr) == lenstr - 1) {
mp[sub + 1] = true;
ans++;
}
}
}
printf("%d\n", ans);
}

int main() {
#ifdef local
freopen("data.txt", "r", stdin);
//    freopen("data.txt", "w", stdout);
#endif
op['('] = ')';
op[')'] = '(';
work();
return 0;
}

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