Create 1269-number-of-ways-to-stay-in-the-same-place-after-some-steps.java

Author: sujal-goswami

Diff for: java/1269-number-of-ways-to-stay-in-the-same-place-after-some-steps.java

@@ -0,0 +1,59 @@
+/*      Top-Down Approach
+-------------------------------------
+  Time Complexity: O(n*min(n,m))
+  Space Complexity: O(n*min(n,m))
+------------------------------------*/  
+class Solution {
+    Map<String, Integer> memo;
+    int MOD = (int)1e9+7;
+    public int numWays(int steps, int arrLen){
+        memo = new HashMap<>();
+        return dfs(0, steps, arrLen);
+    }
+    private int dfs(int i, int steps, int n){
+        String pos = i + "," + steps;
+        if(memo.containsKey(pos))
+            return memo.get(pos);
+        if(steps == 0 && i == 0)
+            return 1;
+        if(i < 0 || i > n-1 || steps == 0)
+            return 0;
+        
+        long left = dfs(i-1, steps-1, n);
+        long stay = dfs(i, steps-1, n);
+        long right = dfs(i+1, steps-1, n);
+        int res = (int)((left + stay + right)%MOD);
+        memo.put(pos, res);
+        return res;       
+    }
+}
+
+/*      Bottom-Up Approach
+------------------------------------
+  Time Complexity: O(n*min(n,m))
+  Space Complexity: O(n*min(n,m))
+-----------------------------------*/  
+class Solution {
+    public int numWays(int steps, int arrLen) {
+        int MOD = (int)1e9+7;
+        arrLen = Math.min(arrLen, steps);
+        int[][] dp = new int[steps + 1][arrLen];
+        
+        dp[0][0] = 1;
+
+        for (int step = 1; step <= steps; step++) {
+            for (int pos = 0; pos < arrLen; pos++) {
+                dp[step][pos] = dp[step - 1][pos];
+                
+                if (pos - 1 >= 0) {
+                    dp[step][pos] = (dp[step][pos] + dp[step - 1][pos - 1]) % MOD;
+                }
+                if (pos + 1 < arrLen) {
+                    dp[step][pos] = (dp[step][pos] + dp[step - 1][pos + 1]) % MOD;
+                }
+            }
+        }
+
+        return dp[steps][0];
+    }
+}