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