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algorithmbasic2020
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左程云 5 years ago
parent 1aeb05cedd
commit ff7cd7b9a4
5 changed files with 196 additions and 181 deletions
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71
src/class41/Code01_BestSplitForAll.java
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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");
}
}

179
src/class41/Code01_NiuNiuSplitField.java
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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();
}
}

121
src/class41/Code02_BestSplitForEveryPosition.java
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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");
}
}

2
src/class41/Code02_StoneMerge.java → src/class41/Code03_StoneMerge.java
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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;

4
src/class41/Code03_SplitArrayLargestSum.java → src/class41/Code04_SplitArrayLargestSum.java
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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);
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