diff --git a/problems/0416.分割等和子集.md b/problems/0416.分割等和子集.md index 45b8b416..9da1f8d5 100644 --- a/problems/0416.分割等和子集.md +++ b/problems/0416.分割等和子集.md @@ -210,6 +210,45 @@ class Solution { } ``` +二维数组版本(易于理解): +```Java +class Solution { + public boolean canPartition(int[] nums) { + int sum = 0; + for (int i = 0; i < nums.length; i++) { + sum += nums[i]; + } + + if (sum % 2 == 1) + return false; + int target = sum / 2; + + //dp[i][j]代表可装物品为0-i,背包容量为j的情况下,背包内容量的最大价值 + int[][] dp = new int[nums.length][target + 1]; + + //初始化,dp[0][j]的最大价值nums[0](if j > weight[i]) + //dp[i][0]均为0,不用初始化 + for (int j = nums[0]; j <= target; j++) { + dp[0][j] = nums[0]; + } + + //遍历物品,遍历背包 + //递推公式: + for (int i = 1; i < nums.length; i++) { + for (int j = 0; j <= target; j++) { + //背包容量可以容纳nums[i] + if (j >= nums[i]) { + dp[i][j] = Math.max(dp[i - 1][j], dp[i - 1][j - nums[i]] + nums[i]); + } else { + dp[i][j] = dp[i - 1][j]; + } + } + } + + return dp[nums.length - 1][target] == target; + } +} +``` Python: ```python class Solution: diff --git a/problems/1049.最后一块石头的重量II.md b/problems/1049.最后一块石头的重量II.md index d64e7e56..7b67b1ac 100644 --- a/problems/1049.最后一块石头的重量II.md +++ b/problems/1049.最后一块石头的重量II.md @@ -153,6 +153,8 @@ public: Java: + +一维数组版本 ```Java class Solution { public int lastStoneWeightII(int[] stones) { @@ -173,6 +175,41 @@ class Solution { return sum - 2 * dp[target]; } } +``` +二维数组版本(便于理解) +```Java +class Solution { + public int lastStoneWeightII(int[] stones) { + int sum = 0; + for (int s : stones) { + sum += s; + } + + int target = sum / 2; + //初始化,dp[i][j]为可以放0-i物品,背包容量为j的情况下背包中的最大价值 + int[][] dp = new int[stones.length][target + 1]; + //dp[i][0]默认初始化为0 + //dp[0][j]取决于stones[0] + for (int j = stones[0]; j <= target; j++) { + dp[0][j] = stones[0]; + } + + for (int i = 1; i < stones.length; i++) { + for (int j = 1; j <= target; j++) {//注意是等于 + if (j >= stones[i]) { + //不放:dp[i - 1][j] 放:dp[i - 1][j - stones[i]] + stones[i] + dp[i][j] = Math.max(dp[i - 1][j], dp[i - 1][j - stones[i]] + stones[i]); + } else { + dp[i][j] = dp[i - 1][j]; + } + } + } + + System.out.println(dp[stones.length - 1][target]); + return (sum - dp[stones.length - 1][target]) - dp[stones.length - 1][target]; + } +} + ``` Python: