Implement climbing-stairs

name: climbing-stairs
url: https://leetcode.com/problems/climbing-stairs
difficulty: 1

time: 100.0 ms
time-rank: -1 %
time-complexity: O(N)

space: 5.8 MB
space-rank: 100.0 %
space-complexity: O(1)

Fixes #298

Signed-off-by: Christopher Friedt <[email protected]>

Author: cfriedt

climbing-stairs-test.cpp

@@ -0,0 +1,19 @@
+/*
+ * Copyright (c) 2021, Christopher Friedt
+ *
+ * SPDX-License-Identifier: MIT
+ */
+
+#include <gtest/gtest.h>
+
+#include "climbing-stairs.cpp"
+
+using namespace std;
+
+TEST(ClimbingStairs, 1) { EXPECT_EQ(1, Solution().climbStairs(1)); }
+
+TEST(ClimbingStairs, 2) { EXPECT_EQ(2, Solution().climbStairs(2)); }
+
+TEST(ClimbingStairs, 3) { EXPECT_EQ(3, Solution().climbStairs(3)); }
+
+TEST(ClimbingStairs, 4) { EXPECT_EQ(5, Solution().climbStairs(4)); }

climbing-stairs.cpp

@@ -0,0 +1,46 @@
+/*
+ * Copyright (c) 2021, Christopher Friedt
+ *
+ * SPDX-License-Identifier: MIT
+ */
+
+// clang-format off
+// name: climbing-stairs
+// url: https://leetcode.com/problems/climbing-stairs
+// difficulty: 1
+// clang-format on
+
+#include <vector>
+
+using namespace std;
+
+class Solution {
+public:
+  int climbStairs(int n) {
+    // observations
+    // * at any step i, the previous step is either going to have been (i - 1)
+    // or (i - 2)
+    // * simple table shows the recurrance relationship NW(i) = NW(i - 1) + NW(i
+    // - 2)
+    // * technically there are overlapping subproblems, which makes this 1d dp,
+    //   so it could be solved using a 1-d vector, but it's fairly obvious that
+    //   there only needs to be a memory of size 2, which produces a solution
+    // * O(N) time and O(1) space
+    //
+    //  i  NW(i)  NW(i-1)  NW(i-2)
+    // ---------------------------
+    //  1  1       1        0
+    //  2  2       1        1
+    //  3  3       2        1
+    //  4  5       3        2
+    int prev_prev = 0;
+    int prev = 1;
+    int result = 0;
+
+    for (int i = 1; i <= n; prev_prev = prev, prev = result, ++i) {
+      result = prev + prev_prev;
+    }
+
+    return result;
+  }
+};