一天一道算法题——优先队列

题目【[SHOI2002]滑雪】：https://www.luogu.com.cn/problem/P1434

解法可以用记忆化搜索，也可以DP。

这里我选了DP，使用了优先队列存储每个高度，从而实现从低到高的递推。

 1 #include<iostream>
 2 #include<algorithm>
 3 #include<queue>
 4 using namespace std;
 5 
 6 struct node {
 7     int i, j, num;
 8 } a;
 9 struct cmp1 {
10     bool operator()(node x, node y) {
11         return x.num > y.num;
12     }
13 };
14 int maxn, r, c, f[110][110], g[110][110];
15 int main() {
16     priority_queue<node,vector<node>,cmp1> q;
17     cin >> r >> c;
18     for (int i = 1; i <= r; i++) {
19         for (int j = 1; j <= c; j++) {
20             cin >> g[i][j];
21             f[i][j] = 1;
22             a.i = i, a.j = j, a.num = g[i][j];
23             q.push(a);
24         }
25     }
26     int i, j;
27     while (q.size()) {
28         a = q.top(); q.pop();
29         i = a.i, j = a.j;
30         if (g[i - 1][j] < a.num)f[i][j] = max(f[i][j], f[i - 1][j] + 1);
31         if (g[i + 1][j] < a.num)f[i][j] = max(f[i][j], f[i + 1][j] + 1);
32         if (g[i][j+1] < a.num)f[i][j] = max(f[i][j], f[i][j+1] + 1);
33         if (g[i][j-1] < a.num)f[i][j] = max(f[i][j], f[i ][j-1] + 1);
34         maxn = max(maxn, f[i][j]);
35     }
36     cout << maxn;
37     return 0;
38 }