all done but copied solution for grid paths: dfs with prune. very tedious

2024-06-02 14:22:00 +02:00
parent 5f6b389ee3
commit cf617f6dfa
6 changed files with 226 additions and 1 deletions
--- a/Set/Grid_Paths.cpp
+++ b/Set/Grid_Paths.cpp
@@ -0,0 +1,86 @@
+#include <iostream>
+using namespace std;
+
+const int DIR_LEN = 4;
+int dr[DIR_LEN] = {-1, 0, 1, 0};
+int dc[DIR_LEN] = {0, 1, 0, -1};
+const int PATH_LEN = 48;  // length of all possible paths
+int p[PATH_LEN];
+const int GRID_SIZE = 9;
+// added border to all four sides so a 7x7 becomes a 9x9
+bool onPath[GRID_SIZE][GRID_SIZE];
+
+int tryPath(int pathIdx, int curR, int curC) {
+    // Optimization 3
+    if ((onPath[curR][curC - 1] && onPath[curR][curC + 1]) &&
+        (!onPath[curR - 1][curC] && !onPath[curR + 1][curC]))
+        return 0;
+    if ((onPath[curR - 1][curC] && onPath[curR + 1][curC]) &&
+        (!onPath[curR][curC - 1] && !onPath[curR][curC + 1]))
+        return 0;
+
+    if (curR == 7 && curC == 1) {  // reached endpoint before visiting all
+        if (pathIdx == PATH_LEN) return 1;
+        return 0;
+    }
+
+    if (pathIdx == PATH_LEN) return 0;
+
+    int ret = 0;
+    onPath[curR][curC] = true;
+
+    // turn already determined:
+    if (p[pathIdx] < 4) {
+        int nxtR = curR + dr[p[pathIdx]];
+        int nxtC = curC + dc[p[pathIdx]];
+        if (!onPath[nxtR][nxtC]) ret += tryPath(pathIdx + 1, nxtR, nxtC);
+    }
+        // see Java solution for optimization 4 implementation
+    else {  // iterate through all four possible turns
+        for (int i = 0; i < DIR_LEN; i++) {
+            int nxtR = curR + dr[i];
+            int nxtC = curC + dc[i];
+            if (onPath[nxtR][nxtC]) continue;
+            ret += tryPath(pathIdx + 1, nxtR, nxtC);
+        }
+    }
+    // reset and return
+    onPath[curR][curC] = false;
+    return ret;
+}
+
+int main() {
+    string line;
+    getline(cin, line);
+
+    // convert path to ints
+    for (int i = 0; i < PATH_LEN; i++) {
+        char cur = line[i];
+
+        if (cur == 'U') p[i] = 0;
+        else if (cur == 'R') p[i] = 1;
+        else if (cur == 'D') p[i] = 2;
+        else if (cur == 'L') p[i] = 3;
+        else p[i] = 4;  // cur == '?'
+    }
+
+    // set borders of grid
+    for (int i = 0; i < GRID_SIZE; i++) {
+        onPath[0][i] = true;
+        onPath[8][i] = true;
+        onPath[i][0] = true;
+        onPath[i][8] = true;
+    }
+    // initialize the inside of the grid to be completely empty
+    for (int i = 1; i <= 7; i++) {
+        for (int j = 1; j <= 7; j++) { onPath[i][j] = false; }
+    }
+
+    int startIdx = 0;
+    int startR = 1;
+    int startC = 1;  // always start path at (1, 1)
+    int ans = tryPath(startIdx, startR, startC);
+    cout << ans << endl;
+}
+
+//https://usaco.guide/problems/cses-1625-grid-paths/solution