#feat:leetcode p53题题解

src/leetcode/p53/Solution.java

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+package leetcode.p53;
+
+/**
+ * @ProjectName: LeetCode
+ * @FileName: Solution
+ * @Author: 杨逸
+ * @Data:2026/3/23 22:33
+ * @Description: https://leetcode.cn/problems/maximum-subarray/description/
+ * 53. 最大子数组和
+ */
+public class Solution {
+    public int maxSubArray(int[] nums) {
+        /**
+         * 动态规划解法
+         * 1.当i=0为数组末尾时,num[i]就是最大子数组和
+         * 2.当i>0为数组末尾时,max(dp[i-1],0) + nums[i]就是最大子数组和
+         * max(dp[i-1],0)表示当子数组长度为i-1时,如何子数组和大于0则i续上子数组,否则重新开始子数组
+         * 3.维护所有情况下最大的子数组和就是答案
+         */
+        int res = nums[0];
+        //空间优化
+        int pre = nums[0];
+        for (int i = 1; i < nums.length; i++) {
+            int current = Math.max(pre,0) + nums[i];
+            res = Math.max(res,current);
+            pre = current;
+        }
+        return res;
+    }
+
+    /**
+     * 动态规划解法
+     * @param nums
+     * @return int
+     * @description:
+     * @author: 杨逸
+     * @data:2026/03/23 23:08:52
+     * @since 1.0.0
+     */
+    private int dp(int[] nums){
+        /**
+         * 动态规划解法
+         * 1.当i=0为数组末尾时,num[i]就是最大子数组和
+         * 2.当i>0为数组末尾时,max(dp[i-1],0) + nums[i]就是最大子数组和
+         * max(dp[i-1],0)表示当子数组长度为i-1时,如何子数组和大于0则i续上子数组,否则重新开始子数组
+         * 3.维护所有情况下最大的子数组和就是答案
+         */
+        int res = nums[0];
+        int[] dp = new int[nums.length];
+        dp[0] = nums[0];
+        for (int i = 1; i < nums.length; i++) {
+            dp[i] = Math.max(dp[i-1],0) + nums[i];
+            res = Math.max(res,dp[i]);
+        }
+        return res;
+    }
+    /**
+     * 前缀和解法
+     * @param nums
+     * @return int
+     * @description:
+     * @author: 杨逸
+     * @data:2026/03/23 22:43:46
+     * @since 1.0.0
+     */
+    private int prefix(int[] nums){
+        /**
+         * 前缀和
+         * 维护前缀和最小值,当前前缀和 减去最小前缀和 即为当前最大子数组和
+         */
+        int min = 0;
+        int[] prefix = new int[nums.length];
+        prefix[0] = nums[0];
+        int res = prefix[0] - min;
+        min = Math.min(min,prefix[0]);
+        for (int i = 1; i < nums.length; i++) {
+            prefix[i] = prefix[i-1] + nums[i];
+            res = Math.max(res,prefix[i] - min);
+            min = Math.min(min,prefix[i]);
+        }
+        return res;
+    }
+}

src/leetcode/p53/SolutionTest.java

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+package leetcode.p53;
+
+import org.junit.Test;
+import org.junit.runner.RunWith;
+import org.junit.runners.Parameterized;
+
+import java.util.Arrays;
+import java.util.Collection;
+
+import static org.junit.Assert.assertEquals;
+
+/**
+ * @ProjectName: LeetCode
+ * @FileName: SolutionTest
+ * @Author: 杨逸
+ * @Data:2026/3/23 22:40
+ * @Description:
+ */
+@RunWith(Parameterized.class)
+public class SolutionTest {
+    public static final Solution solution = new Solution();
+    private int[] nums;
+    private int expected;
+
+    public SolutionTest(int[] nums, int expected) {
+        this.nums = nums;
+        this.expected = expected;
+    }
+    @Parameterized.Parameters
+    public static Collection<Object[]> data() {
+        return Arrays.asList(new Object[][]{
+                {new int[]{-2,1,-3,4,-1,2,1,-5,4},6},
+                {new int[]{1},1},
+                {new int[]{5,4,-1,7,8},23},
+        });
+    }
+
+    @Test
+    public void maxSubArray() {
+        assertEquals(expected,solution.maxSubArray(nums));
+    }
+}