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Formatted question description: https://leetcode.ca/all/740.html

# 740. Delete and Earn (Medium)

Given an array nums of integers, you can perform operations on the array.

In each operation, you pick any nums[i] and delete it to earn nums[i] points. After, you must delete every element equal to nums[i] - 1 or nums[i] + 1.

You start with 0 points. Return the maximum number of points you can earn by applying such operations.

Example 1:

Input: nums = [3, 4, 2]
Output: 6
Explanation:
Delete 4 to earn 4 points, consequently 3 is also deleted.
Then, delete 2 to earn 2 points. 6 total points are earned.


Example 2:

Input: nums = [2, 2, 3, 3, 3, 4]
Output: 9
Explanation:
Delete 3 to earn 3 points, deleting both 2's and the 4.
Then, delete 3 again to earn 3 points, and 3 again to earn 3 points.
9 total points are earned.


Note:

• The length of nums is at most 20000.
• Each element nums[i] is an integer in the range [1, 10000].

Related Topics:
Dynamic Programming

Similar Questions:

## Solution 1. DP

Firstly, to avoid duplicate, store the data in a map from the number to its count.

Let dp[i] be the max point you can get at point i.

If num != prevNum + 1, we can freely pick num, then dp[i] = dp[i-1] + num * count.

Otherwise, if we don’t pick num, dp[i] = dp[i-1].

Otherwise, we pick num, dp[i] = dp[i-2] + num * count.

So in sum:

dp[i] = num == prevNum ? max(dp[i-1], dp[i-2] + num * count) : (dp[i-1] + num * count)

// OJ: https://leetcode.com/problems/delete-and-earn/
// Time: O(NlogN)
// Space: O(N)
class Solution {
public:
int deleteAndEarn(vector<int>& nums) {
map<int, int> m;
for (int n : nums) m[n]++;
int prev = 0, prev2 = 0, num = INT_MIN;
for (auto &p : m) {
int cur = p.first == num + 1 ? max(prev, prev2 + p.first * p.second) : (prev + p.first * p.second);
prev2 = prev;
prev = cur;
num = p.first;
}
return prev;
}
};

• class Solution {
public int deleteAndEarn(int[] nums) {
if (nums == null || nums.length == 0)
return 0;
if (nums.length == 1)
return nums[0];
int max = 0;
for (int num : nums)
max = Math.max(max, num);
int[] counts = new int[max + 1];
for (int num : nums)
counts[num]++;
int[] dp = new int[max + 1];
dp[1] = counts[1];
dp[2] = Math.max(dp[1], 2 * counts[2]);
for (int i = 3; i <= max; i++)
dp[i] = Math.max(dp[i - 1], dp[i - 2] + i * counts[i]);
return dp[max];
}
}

############

public class Solution {
public int deleteAndEarn(int[] nums) {
if (nums.length == 0) {
return 0;
}

int[] sums = new int[10010];
int[] select = new int[10010];
int[] nonSelect = new int[10010];

int maxV = 0;
for (int x : nums) {
sums[x] += x;
maxV = Math.max(maxV, x);
}

for (int i = 1; i <= maxV; i++) {
select[i] = nonSelect[i - 1] + sums[i];
nonSelect[i] = Math.max(select[i - 1], nonSelect[i - 1]);
}
return Math.max(select[maxV], nonSelect[maxV]);
}
}


• // OJ: https://leetcode.com/problems/delete-and-earn/
// Time: O(NlogN)
// Space: O(N)
class Solution {
public:
int deleteAndEarn(vector<int>& A) {
map<int, int> m;
for (int n : A) m[n]++;
int prev = 0, prev2 = 0, num = INT_MIN;
for (auto &[n, cnt] : m) {
int cur = n == num + 1 ? max(prev, prev2 + n * cnt) : (prev + n * cnt);
prev2 = prev;
prev = cur;
num = n;
}
return prev;
}
};

• class Solution:
def deleteAndEarn(self, nums: List[int]) -> int:
mx = -inf
for num in nums:
mx = max(mx, num)
total = [0] * (mx + 1)
for num in nums:
total[num] += num
first = total[0]
second = max(total[0], total[1])
for i in range(2, mx + 1):
cur = max(first + total[i], second)
first = second
second = cur
return second


• func deleteAndEarn(nums []int) int {

max := func(x, y int) int {
if x > y {
return x
}
return y
}

mx := math.MinInt32
for _, num := range nums {
mx = max(mx, num)
}
total := make([]int, mx+1)
for _, num := range nums {
total[num] += num
}
first := total[0]
second := max(total[0], total[1])
for i := 2; i <= mx; i++ {
cur := max(first+total[i], second)
first = second
second = cur
}
return second
}