Description#
You are given an array of integers stones where stones[i] is the weight of the ith stone.
We are playing a game with the stones. On each turn, we choose any two stones and smash them together. Suppose the stones have weights x and y with x <= y. The result of this smash is:
- If
x == y, both stones are destroyed, and - If
x != y, the stone of weight x is destroyed, and the stone of weight y has new weight y - x.
At the end of the game, there is at most one stone left.
Return the smallest possible weight of the left stone. If there are no stones left, return 0.
Example 1:
Input: stones = [2,7,4,1,8,1]
Output: 1
Explanation:
We can combine 2 and 4 to get 2, so the array converts to [2,7,1,8,1] then,
we can combine 7 and 8 to get 1, so the array converts to [2,1,1,1] then,
we can combine 2 and 1 to get 1, so the array converts to [1,1,1] then,
we can combine 1 and 1 to get 0, so the array converts to [1], then that's the optimal value.
Example 2:
Input: stones = [31,26,33,21,40]
Output: 5
Constraints:
1 <= stones.length <= 301 <= stones[i] <= 100
Solutions#
Solution 1#
1
2
3
4
5
6
7
8
9
10
11
12
13
| class Solution:
def lastStoneWeightII(self, stones: List[int]) -> int:
s = sum(stones)
m, n = len(stones), s >> 1
dp = [[0] * (n + 1) for _ in range(m + 1)]
for i in range(1, m + 1):
for j in range(n + 1):
dp[i][j] = dp[i - 1][j]
if stones[i - 1] <= j:
dp[i][j] = max(
dp[i][j], dp[i - 1][j - stones[i - 1]] + stones[i - 1]
)
return s - 2 * dp[-1][-1]
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
| class Solution {
public int lastStoneWeightII(int[] stones) {
int s = 0;
for (int v : stones) {
s += v;
}
int m = stones.length;
int n = s >> 1;
int[][] dp = new int[m + 1][n + 1];
for (int i = 1; i <= m; ++i) {
for (int j = 0; j <= n; ++j) {
dp[i][j] = dp[i - 1][j];
if (stones[i - 1] <= j) {
dp[i][j] = Math.max(dp[i][j], dp[i - 1][j - stones[i - 1]] + stones[i - 1]);
}
}
}
return s - dp[m][n] * 2;
}
}
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
| class Solution {
public:
int lastStoneWeightII(vector<int>& stones) {
int s = accumulate(stones.begin(), stones.end(), 0);
int m = stones.size(), n = s >> 1;
vector<vector<int>> dp(m + 1, vector<int>(n + 1));
for (int i = 1; i <= m; ++i) {
for (int j = 0; j <= n; ++j) {
dp[i][j] = dp[i - 1][j];
if (stones[i - 1] <= j) dp[i][j] = max(dp[i][j], dp[i - 1][j - stones[i - 1]] + stones[i - 1]);
}
}
return s - dp[m][n] * 2;
}
};
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
| func lastStoneWeightII(stones []int) int {
s := 0
for _, v := range stones {
s += v
}
m, n := len(stones), s>>1
dp := make([][]int, m+1)
for i := range dp {
dp[i] = make([]int, n+1)
}
for i := 1; i <= m; i++ {
for j := 0; j <= n; j++ {
dp[i][j] = dp[i-1][j]
if stones[i-1] <= j {
dp[i][j] = max(dp[i][j], dp[i-1][j-stones[i-1]]+stones[i-1])
}
}
}
return s - dp[m][n]*2
}
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
| impl Solution {
#[allow(dead_code)]
pub fn last_stone_weight_ii(stones: Vec<i32>) -> i32 {
let n = stones.len();
let mut sum = 0;
for e in &stones {
sum += *e;
}
let m = (sum / 2) as usize;
let mut dp: Vec<Vec<i32>> = vec![vec![0; m + 1]; n + 1];
// Begin the actual dp process
for i in 1..=n {
for j in 1..=m {
dp[i][j] = if stones[i - 1] > (j as i32) {
dp[i - 1][j]
} else {
std::cmp::max(
dp[i - 1][j],
dp[i - 1][j - (stones[i - 1] as usize)] + stones[i - 1]
)
};
}
}
sum - 2 * dp[n][m]
}
}
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
| /**
* @param {number[]} stones
* @return {number}
*/
var lastStoneWeightII = function (stones) {
let s = 0;
for (let v of stones) {
s += v;
}
const n = s >> 1;
let dp = new Array(n + 1).fill(0);
for (let v of stones) {
for (let j = n; j >= v; --j) {
dp[j] = Math.max(dp[j], dp[j - v] + v);
}
}
return s - dp[n] * 2;
};
|
Solution 2#
1
2
3
4
5
6
7
8
9
| class Solution:
def lastStoneWeightII(self, stones: List[int]) -> int:
s = sum(stones)
m, n = len(stones), s >> 1
dp = [0] * (n + 1)
for v in stones:
for j in range(n, v - 1, -1):
dp[j] = max(dp[j], dp[j - v] + v)
return s - dp[-1] * 2
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
| class Solution {
public int lastStoneWeightII(int[] stones) {
int s = 0;
for (int v : stones) {
s += v;
}
int m = stones.length;
int n = s >> 1;
int[] dp = new int[n + 1];
for (int v : stones) {
for (int j = n; j >= v; --j) {
dp[j] = Math.max(dp[j], dp[j - v] + v);
}
}
return s - dp[n] * 2;
}
}
|
1
2
3
4
5
6
7
8
9
10
11
12
| class Solution {
public:
int lastStoneWeightII(vector<int>& stones) {
int s = accumulate(stones.begin(), stones.end(), 0);
int n = s >> 1;
vector<int> dp(n + 1);
for (int& v : stones)
for (int j = n; j >= v; --j)
dp[j] = max(dp[j], dp[j - v] + v);
return s - dp[n] * 2;
}
};
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
| func lastStoneWeightII(stones []int) int {
s := 0
for _, v := range stones {
s += v
}
n := s >> 1
dp := make([]int, n+1)
for _, v := range stones {
for j := n; j >= v; j-- {
dp[j] = max(dp[j], dp[j-v]+v)
}
}
return s - dp[n]*2
}
|
