added day3 q1 solution

Author: MANISH-BEESA

Problems/Mathematics/Day-03/Solution1.cpp

@@ -0,0 +1,86 @@
+
+/*
+TC -O(N)
+SC -O(1)
+
+*/
+
+
+#include <bits/stdc++.h>
+using namespace std;
+
+string s;
+bool visited[7][7];
+int ans;
+
+bool inside(int x, int y) {
+    return x >= 0 && x < 7 && y >= 0 && y < 7;
+}
+
+void dfs(int x, int y, int step) {
+    if (x == 6 && y == 0) {
+        if (step == 48) ans++;
+        return;
+    }
+
+    if (step == 48) return;
+
+    if ((!inside(x-1,y) || visited[x-1][y]) &&
+        (!inside(x+1,y) || visited[x+1][y])) {
+        if (inside(x,y-1) && !visited[x][y-1] &&
+            inside(x,y+1) && !visited[x][y+1])
+            return;
+    }
+
+    if ((!inside(x,y-1) || visited[x][y-1]) &&
+        (!inside(x,y+1) || visited[x][y+1])) {
+        if (inside(x-1,y) && !visited[x-1][y] &&
+            inside(x+1,y) && !visited[x+1][y])
+            return;
+    }
+
+    char c = s[step];
+
+    if (c == '?' || c == 'U') {
+        int nx = x - 1, ny = y;
+        if (inside(nx, ny) && !visited[nx][ny]) {
+            visited[nx][ny] = true;
+            dfs(nx, ny, step + 1);
+            visited[nx][ny] = false;
+        }
+    }
+
+    if (c == '?' || c == 'D') {
+        int nx = x + 1, ny = y;
+        if (inside(nx, ny) && !visited[nx][ny]) {
+            visited[nx][ny] = true;
+            dfs(nx, ny, step + 1);
+            visited[nx][ny] = false;
+        }
+    }
+
+    if (c == '?' || c == 'L') {
+        int nx = x, ny = y - 1;
+        if (inside(nx, ny) && !visited[nx][ny]) {
+            visited[nx][ny] = true;
+            dfs(nx, ny, step + 1);
+            visited[nx][ny] = false;
+        }
+    }
+
+    if (c == '?' || c == 'R') {
+        int nx = x, ny = y + 1;
+        if (inside(nx, ny) && !visited[nx][ny]) {
+            visited[nx][ny] = true;
+            dfs(nx, ny, step + 1);
+            visited[nx][ny] = false;
+        }
+    }
+}
+
+int main() {
+    cin >> s;
+    visited[0][0] = true;
+    dfs(0, 0, 0);
+    cout << ans;
+}