✅ 状态压缩动态规划

state-compress-dp/main.cpp

@@ -0,0 +1,64 @@
+#include <iostream>
+#include <vector>
+
+using namespace std;
+
+int m, n;
+int obstacle[101];
+int dp[101][1025];
+
+const int MOD_FACTOR = 100000007;
+
+vector<int> state;
+
+void init_state() {
+    state.push_back(0);
+    for (int i = 0; i < (1 << n); i++) {
+        if (!(i & i << 1)) {
+            state.push_back(i);
+        }
+    }
+}
+
+void calculate() {
+    for (int j = 1; j < state.size(); j++) {
+        if (!(state[j] & obstacle[1])) { // Check overlap
+            dp[1][j] = 1;
+        }
+    }
+    for (int i = 2; i <= m; i++) {
+        for (int j = 1; j < state.size(); j++) {
+            if (!(state[j] & obstacle[i])) { // Check obstacle overlap
+                for (int k = 1; k < state.size(); k++) {
+                    if (!(state[j] & state[k])) { // Check overlap
+                        dp[i][j] = (dp[i][j] + dp[i - 1][k]) % MOD_FACTOR;
+                    }
+                }
+            }
+        }
+    }
+
+}
+
+int main() {
+    cin >> m >> n;
+    for (int i = 1; i <= m; i++) {
+        obstacle[i] = 0;
+        int num;
+        for (int j = 1; j <= n; j++) {
+            cin >> num;
+            if (num == 0) {
+                obstacle[i] += (1 << (n - j));
+            }
+        }
+    }
+
+    init_state();
+    calculate();
+    int ans = 0;
+    for (int j = 1; j < state.size(); j++) {
+        ans = (ans + dp[m][j]) % MOD_FACTOR;
+    }
+    cout << ans - 1 << endl;
+    return 0;
+}