problem 9.1

Chapter9-Recursion&Dynamic Programming/9.1-HoppingSteps.js

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+/*
+Problem: A child is running up a staircase with n steps, and can hop either 1 step, 2 steps, or 3 steps at a time. Implement a method to count how many possible ways the child can run up the stairs.
+*/
+
+/** ex: 4 steps should return 7 ways:
+1,1,1,1; 2,2; 2,1,1; 1,2,1; 1,1,2; 1,3; 3,1
+**/
+
+function numberOfWays(steps) {
+  if (steps < 0) return 0;
+  else if (steps === 0) return 1;
+  //num of steps will equal num of steps to previous step plus one
+  else {
+    return numberOfWays(steps - 1) + numberOfWays(steps - 2) + numberOfWays(steps - 3);
+  }
+}