diff --git a/src/class41/Code01_BestSplitForAll.java b/src/class41/Code01_BestSplitForAll.java new file mode 100644 index 0000000..1f6578e --- /dev/null +++ b/src/class41/Code01_BestSplitForAll.java @@ -0,0 +1,71 @@ +package class41; + +public class Code01_BestSplitForAll { + + public static int bestSplit1(int[] arr) { + if (arr == null || arr.length < 2) { + return 0; + } + int N = arr.length; + int ans = 0; + for (int s = 0; s < N - 1; s++) { + int sumL = 0; + for (int L = 0; L <= s; L++) { + sumL += arr[L]; + } + int sumR = 0; + for (int R = s + 1; R < N; R++) { + sumR += arr[R]; + } + ans = Math.max(ans, Math.min(sumL, sumR)); + } + return ans; + } + + public static int bestSplit2(int[] arr) { + if (arr == null || arr.length < 2) { + return 0; + } + int N = arr.length; + int sumAll = 0; + for (int num : arr) { + sumAll += num; + } + int ans = 0; + int sumL = 0; + for (int s = 0; s < N - 1; s++) { + sumL += arr[s]; + int sumR = sumAll - sumL; + ans = Math.max(ans, Math.min(sumL, sumR)); + } + return ans; + } + + public static int[] randomArray(int len, int max) { + int[] ans = new int[len]; + for (int i = 0; i < len; i++) { + ans[i] = (int) (Math.random() * max); + } + return ans; + } + + public static void main(String[] args) { + int N = 20; + int max = 30; + int testTime = 1000000; + System.out.println("测试开始"); + for (int i = 0; i < testTime; i++) { + int len = (int) (Math.random() * N); + int[] arr = randomArray(len, max); + int ans1 = bestSplit1(arr); + int ans2 = bestSplit2(arr); + if (ans1 != ans2) { + System.out.println(ans1); + System.out.println(ans2); + System.out.println("Oops!"); + } + } + System.out.println("测试结束"); + } + +} \ No newline at end of file diff --git a/src/class41/Code01_NiuNiuSplitField.java b/src/class41/Code01_NiuNiuSplitField.java deleted file mode 100644 index d98b48e..0000000 --- a/src/class41/Code01_NiuNiuSplitField.java +++ /dev/null @@ -1,179 +0,0 @@ -package class41; - -import java.util.*; - -public class Code01_NiuNiuSplitField { - - // arr都是正数，0~i切的时候，怎么切最优，最优的结论生成一个数组返回 - public static int[] getAnswers(int[] arr) { - if (arr == null || arr.length < 1) { - return null; - } - // ans[i] 代表的含义： - // arr[0..i]切两块的各种方案中，哪一种方案能让左右两部份的累加和最小值，尽量大 - int[] ans = new int[arr.length]; - ans[0] = 0; - int best = 0;// 左 0..0 右 无 - for (int i = 1; i < arr.length; i++) { - while (best < i - 1 && getSplit(arr, best, i) < getSplit(arr, best + 1, i)) { - best++; - } - ans[i] = getSplit(arr, best, i); - } - return ans; - } - - public static int getSum(int[] arr, int i, int j) { - return 0; - } - - // arr[0..j] 如果我把切的这一刀定在m位置，左0..m，右m+1..j - public static int getSplit(int[] arr, int m, int j) { - return 0; - } - - public static int maxMinSumIn16(int[][] matrix) { - if (matrix == null || matrix.length < 4 || matrix[0].length < 4) { - return 0; - } - // help[i][j] 含义，左上角为(0,0) 右下角为(i,j)的子矩阵累加和是多少 - int[][] help = generateSumRecord(matrix); - // 通过help，得到任何子矩阵的累加和 - int col = matrix[0].length; - int res = Integer.MIN_VALUE; - // 3个for循环在暴力枚举纵向三刀 - for (int c1 = 0; c1 < col - 3; c1++) { - for (int c2 = c1 + 1; c2 < col - 2; c2++) { - for (int c3 = c2 + 1; c3 < col - 1; c3++) { - // c1 c2 c3 - res = Math.max(res, getBestDicision(help, c1, c2, c3)); - } - } - } - return res; - } - - // record[i][j] 左上角点0,0， 有效角点i、j , 该矩阵的累加和 - public static int[][] generateSumRecord(int[][] matrix) { - int row = matrix.length; - int col = matrix[0].length; - int[][] record = new int[row][col]; - record[0][0] = matrix[0][0]; - for (int i = 1; i < row; i++) { - record[i][0] = record[i - 1][0] + matrix[i][0]; - } - for (int j = 1; j < col; j++) { - record[0][j] = record[0][j - 1] + matrix[0][j]; - } - for (int i = 1; i < row; i++) { - for (int j = 1; j < col; j++) { - record[i][j] = record[i][j - 1] + record[i - 1][j] - record[i - 1][j - 1] + matrix[i][j]; - } - } - return record; - } - - // 忘掉原来的矩阵，只使用help - // 竖着三刀固定，c1，c2，c3 - // 所有横着切三刀的可能性中，那种切法能得到最好的结果，把结果返回 - public static int getBestDicision(int[][] help, int c1, int c2, int c3) { - // 0～i 切一刀，出来八块，最优指标，up[i] - int[] up = getUpSplitArray(help, c1, c2, c3); // 0行~i行 切一刀，分8块，min max - - // i ~ N-1 切一刀，出来八块，最优指标，down[i] - int[] down = getDownSplitArray(help, c1, c2, c3); // i~n-1 切一刀 - - int res = Integer.MIN_VALUE; - for (int mid = 1; mid < help.length - 2; mid++) { - res = Math.max(res, Math.min(up[mid], down[mid + 1])); - } - return res; - } - - public static int value(int[][] record, int c1, int c2, int c3, int prow, int crow) { - int value1 = area(record, prow, 0, crow, c1); - int value2 = area(record, prow, c1 + 1, crow, c2); - int value3 = area(record, prow, c2 + 1, crow, c3); - int value4 = area(record, prow, c3 + 1, crow, record[0].length - 1); - return Math.min(Math.min(value1, value2), Math.min(value3, value4)); - } - - public static int area(int[][] record, int i1, int j1, int i2, int j2) { - int all = record[i2][j2]; - int left = j1 > 0 ? record[i2][j1 - 1] : 0; - int up = i1 > 0 ? record[i1 - 1][j2] : 0; - int makeUp = (i1 > 0 && j1 > 0) ? record[i1 - 1][j1 - 1] : 0; - return all - left - up + makeUp; - } - - public static int[] getUpSplitArray(int[][] record, int c1, int c2, int c3) { - int size = record.length; - int[] up = new int[size]; - int split = 0; - up[1] = Math.min(value(record, c1, c2, c3, 0, 0), value(record, c1, c2, c3, 1, 1)); - for (int i = 2; i < size; i++) { - int minsMax = towSubMatrixMin(record, c1, c2, c3, 0, split, i); - while (split < i) { - if (split == i - 1) { - break; - } - int moved = towSubMatrixMin(record, c1, c2, c3, 0, split + 1, i); - if (moved < minsMax) { - break; - } else { - minsMax = moved; - split++; - } - } - up[i] = minsMax; - } - return up; - } - - public static int[] getDownSplitArray(int[][] record, int c1, int c2, int c3) { - int size = record.length; - int[] down = new int[size]; - int split = size - 1; - down[size - 2] = Math.min(value(record, c1, c2, c3, size - 2, size - 2), - value(record, c1, c2, c3, size - 1, size - 1)); - for (int i = size - 3; i >= 0; i--) { - int minsMax = towSubMatrixMin(record, c1, c2, c3, i, split - 1, size - 1); - while (split > i) { - if (split == i + 1) { - break; - } - int moved = towSubMatrixMin(record, c1, c2, c3, i, split - 2, size - 1); - if (moved < minsMax) { - break; - } else { - minsMax = moved; - split--; - } - } - down[i] = minsMax; - } - return down; - } - - public static int towSubMatrixMin(int[][] record, int c1, int c2, int c3, int i, int split, int j) { - return Math.min(value(record, c1, c2, c3, i, split), value(record, c1, c2, c3, split + 1, j)); - } - - public static void main(String[] args) { - Scanner in = new Scanner(System.in); - while (in.hasNext()) { - int n = in.nextInt(); - int m = in.nextInt(); - int[][] matrix = new int[n][m]; - for (int i = 0; i < n; i++) { - char[] chas = in.next().toCharArray(); - for (int j = 0; j < m; j++) { - matrix[i][j] = chas[j] - '0'; - } - } - System.out.println(maxMinSumIn16(matrix)); - } - in.close(); - } - -} \ No newline at end of file diff --git a/src/class41/Code02_BestSplitForEveryPosition.java b/src/class41/Code02_BestSplitForEveryPosition.java new file mode 100644 index 0000000..88d985e --- /dev/null +++ b/src/class41/Code02_BestSplitForEveryPosition.java @@ -0,0 +1,121 @@ +package class41; + +public class Code02_BestSplitForEveryPosition { + + public static int[] bestSplit1(int[] arr) { + if (arr == null || arr.length == 0) { + return new int[0]; + } + int N = arr.length; + int[] ans = new int[N]; + ans[0] = 0; + for (int range = 1; range < N; range++) { + for (int s = 0; s < range; s++) { + int sumL = 0; + for (int L = 0; L <= s; L++) { + sumL += arr[L]; + } + int sumR = 0; + for (int R = s + 1; R <= range; R++) { + sumR += arr[R]; + } + ans[range] = Math.max(ans[range], Math.min(sumL, sumR)); + } + } + return ans; + } + + public static int sum(int[] sum, int L, int R) { + return sum[R + 1] - sum[L]; + } + + public static int[] bestSplit2(int[] arr) { + if (arr == null || arr.length == 0) { + return new int[0]; + } + int N = arr.length; + int[] ans = new int[N]; + ans[0] = 0; + int[] sum = new int[N + 1]; + for (int i = 0; i < N; i++) { + sum[i + 1] = sum[i] + arr[i]; + } + for (int range = 1; range < N; range++) { + for (int s = 0; s < range; s++) { + int sumL = sum(sum, 0, s); + int sumR = sum(sum, s + 1, range); + ans[range] = Math.max(ans[range], Math.min(sumL, sumR)); + } + } + return ans; + } + + public static int[] bestSplit3(int[] arr) { + if (arr == null || arr.length == 0) { + return new int[0]; + } + int N = arr.length; + int[] ans = new int[N]; + ans[0] = 0; + int[] sum = new int[N + 1]; + for (int i = 0; i < N; i++) { + sum[i + 1] = sum[i] + arr[i]; + } + int best = 0; + for (int range = 1; range < N; range++) { + while (best + 1 < range) { + int before = Math.min(sum(sum, 0, best), sum(sum, best + 1, range)); + int after = Math.min(sum(sum, 0, best + 1), sum(sum, best + 2, range)); + // 注意，一定要是>=，只是>会出错 + // 课上会讲解 + if (after >= before) { + best++; + } else { + break; + } + } + ans[range] = Math.min(sum(sum, 0, best), sum(sum, best + 1, range)); + } + return ans; + } + + public static int[] randomArray(int len, int max) { + int[] ans = new int[len]; + for (int i = 0; i < len; i++) { + ans[i] = (int) (Math.random() * max); + } + return ans; + } + + public static boolean isSameArray(int[] arr1, int[] arr2) { + if (arr1.length != arr2.length) { + return false; + } + int N = arr1.length; + for (int i = 0; i < N; i++) { + if (arr1[i] != arr2[i]) { + return false; + } + } + return true; + } + + public static void main(String[] args) { + int N = 20; + int max = 30; + int testTime = 1000000; + System.out.println("测试开始"); + for (int i = 0; i < testTime; i++) { + int len = (int) (Math.random() * N); + int[] arr = randomArray(len, max); + int[] ans1 = bestSplit1(arr); + int[] ans2 = bestSplit2(arr); + int[] ans3 = bestSplit3(arr); + if (!isSameArray(ans1, ans2) || !isSameArray(ans1, ans3)) { + System.out.println("Oops!"); + } + } + System.out.println("测试结束"); + } + +} diff --git a/src/class41/Code02_StoneMerge.java b/src/class41/Code03_StoneMerge.java similarity index 98% rename from src/class41/Code02_StoneMerge.java rename to src/class41/Code03_StoneMerge.java index 2feaea0..dab3bf0 100644 --- a/src/class41/Code02_StoneMerge.java +++ b/src/class41/Code03_StoneMerge.java @@ -1,7 +1,7 @@ package class41; // 四边形不等式：合并石子问题 -public class Code02_StoneMerge { +public class Code03_StoneMerge { public static int[] sum(int[] arr) { int N = arr.length; diff --git a/src/class41/Code03_SplitArrayLargestSum.java b/src/class41/Code04_SplitArrayLargestSum.java similarity index 95% rename from src/class41/Code03_SplitArrayLargestSum.java rename to src/class41/Code04_SplitArrayLargestSum.java index c83922d..7015b1d 100644 --- a/src/class41/Code03_SplitArrayLargestSum.java +++ b/src/class41/Code04_SplitArrayLargestSum.java @@ -1,6 +1,8 @@ package class41; -public class Code03_SplitArrayLargestSum { +// leetcode原题 +// 测试链接：https://leetcode.com/problems/split-array-largest-sum/ +public class Code04_SplitArrayLargestSum { public static int splitArray1(int[] nums, int m) { return process(nums, 0, m);