Jump Game II (DP Approach)

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Find minimum number of jumps to reach the last index.

Example 1
Input: nums=[2,3,1,1,4] → Output: 2
Example 2
Input: nums=[2,3,0,1,4] → Output: 2

Solution Approach

DP: dp[i] = minimum jumps to reach index i.

  • dp[0]=0, rest Integer.MAX_VALUE
  • For each i: for each reachable j from i: dp[j]=min(dp[j],dp[i]+1)
  • Return dp[n-1]
Java
public int jump(int[] nums) {
    int n = nums.length;
    int[] dp = new int[n];
    Arrays.fill(dp, Integer.MAX_VALUE);
    dp[0] = 0;
    for (int i = 0; i < n; i++) {
        if (dp[i] == Integer.MAX_VALUE) continue;
        for (int j = 1; j <= nums[i] && i + j < n; j++)
            dp[i + j] = Math.min(dp[i + j], dp[i] + 1);
    }
    return dp[n - 1];
}
  • Time Complexity: O(n^2)
  • Space Complexity: O(n)