Given an array of non-negative integers, you are initially positioned at the first index of the array.

Each element in the array represents your maximum jump length at that position.

Your goal is to reach the last index in the minimum number of jumps.

For example:

Given array A = [2,3,1,1,4]

The minimum number of jumps to reach the last index is 2. (Jump 1 step from index 0 to 1, then 3 steps to the last index.)

Have you met this question in a real interview?

 

Solution 1 (not the best solution):

We use an array to record the max reachable range of n steps into a list called stepMaxLen. We then go through every node i:

1. Find out the min steps to reach this step from the list stepMaxLen, i.e., minStep.

2. Check whether the max reachable length at i, i.e., A[i]+i, is larger than stepMaxLen[minStep+1], if yes, then update the stepMaxLen[minStep+1].

3. During update stepMaxLen, once at some step n, we reach the end (len-1), we then return n.

 

1 public class Solution { 2     public int jump(int[] A) { 3         if (A.length==0 || A.length==1) return 0; 4         int len = A.length; 5  6         int[] stepMaxLen = new int[len+1]; 7         Arrays.fill(stepMaxLen, 0); 8         stepMaxLen[1] = A[0]; 9         if (stepMaxLen[1]>=len-1) return 1;10         for (int i=1;i
      
       stepMaxLen[minStep+1]){21                 stepMaxLen[minStep+1] = i+A[i];22                 if (i+A[i]>=len-1) return minStep+1;23             }24         }25             26        27         return -1;     28         29     }30 }
      

Solution 2 (better solution):

In solution 1, we actually do need to use loop to find out the minStep to reach node i. We only need to maintain the maxReachLen of current number of steps, i.e., the last node that can be reached by using current number of steps, and the max reachable length at current node. Once we reach a node that is beyong the maxReachLen of current step, it means that now the node can only be reached by using one more step, we then update the current number of steps and the maxReachLen of current step.

NOTE: the principle of solution 1 and solution 2 is actually the same.

NOTE_UPDATE: This is BFS solution. The idea here is maxStepReach define the boundary of current level (i.e., the node can be reached by X steps). Whenever, i exceeds the boundary, it enters next level. We keep recording maxReach, the maximum reachable nodes. Just when i == maxStepReach+1, the maxReach at that time is the boundary of the newly entered level.

1 public class Solution { 2     public int jump(int[] A) { 3         if (A.length==0 || A.length==1) return 0; 4         int len = A.length; 5          6         int step = 1; 7         int maxStepReach = A[0]; 8         int maxReach = A[0]; 9         if (maxStepReach>=len-1) return step;10         for (int i=1;i
      
       maxStepReach){14                 step++;15                 maxStepReach = maxReach;16                 if (maxStepReach>=len-1) return step;17             }18             19             if (maxReach