feat: 添加P8816问题的动态规划解决方案

实现了一个动态规划算法来解决P8816问题，计算在给定约束条件下的最大长度。算法通过排序点和状态转移来优化计算效率。

src/9/25/P8816.cpp

@@ -0,0 +1,83 @@
+#include <algorithm>
+#include <cstdint>
+#include <iostream>
+#include <vector>
+
+using ll = int64_t;
+
+const int MAXN = 500 + 5;
+const int MAXK = 100 + 5;
+
+int n;
+int k;
+
+struct P {
+    ll x, y;
+    bool operator<(const P &other) const {
+        if (x != other.x)
+            return x < other.x;
+        return y < other.y;
+    }
+} p[MAXN];
+
+int dp[MAXN][MAXK];
+
+int main() {
+    std::ios_base::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    std::cin >> n >> k;
+    for (int i = 1; i <= n; i++) {
+        std::cin >> p[i].x >> p[i].y;
+    }
+
+    std::sort(p + 1, p + n + 1);
+
+    ll maxlen = 0;
+
+    for (int i = 1; i <= n; i++) {
+
+        dp[i][0] = 1;
+
+        for (int j = 1; j < i; j++) {
+
+            if (p[j].y <= p[i].y) {
+
+                ll dist = (p[i].x - p[j].x) + (p[i].y - p[j].y);
+
+                if (dist <= 0)
+                    continue;
+
+                ll cost = dist - 1;
+
+                for (int pk = 0; pk <= k; pk++) {
+
+                    if (dp[j][pk] > 0) {
+                        ll tot = pk + cost;
+                        if (tot <= k) {
+
+                            int nlen = dp[j][pk] + dist;
+
+                            dp[i][tot] = std::max(dp[i][tot], nlen);
+                        }
+                    }
+                }
+            }
+        }
+    }
+
+    maxlen = k + 1;
+
+    for (int i = 1; i <= n; i++) {
+        for (int j = 0; j <= k; j++) {
+            if (dp[i][j] > 0) {
+
+                maxlen = std::max(maxlen, (ll)dp[i][j] + (k - j));
+            }
+        }
+    }
+
+    std::cout << maxlen << "\n";
+
+    return 0;
+}