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package class_2022_04_3_week;
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import java.util.Arrays;
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// 来自腾讯音乐
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// 原本数组中都是大于0、小于等于k的数字，是一个单调不减的数组
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// 其中可能有相等的数字，总体趋势是递增的
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// 但是其中有些位置的数被替换成了0，我们需要求出所有的把0替换的方案数量：
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// 1）填充的每一个数可以大于等于前一个数，小于等于后一个数
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// 2）填充的每一个数不能大于k
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public class Code03_ValidSortedArrayWays {
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// 动态规划
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public static long ways1(int[] nums, int k) {
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int n = nums.length;
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// dp[i][j] : 一共i个格子，随意填，但是不能降序，j种数可以选
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long[][] dp = new long[n + 1][k + 1];
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for (int i = 1; i <= n; i++) {
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dp[i][1] = 1;
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}
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for (int i = 1; i <= k; i++) {
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dp[1][i] = i;
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}
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for (int i = 2; i <= n; i++) {
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for (int j = 2; j <= k; j++) {
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dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
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}
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}
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long res = 1;
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for (int i = 0, j = 0; i < nums.length; i++) {
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if (nums[i] == 0) {
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j = i + 1;
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while (j < nums.length && nums[j] == 0) {
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j++;
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}
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int leftValue = i - 1 >= 0 ? nums[i - 1] : 1;
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int rightValue = j < nums.length ? nums[j] : k;
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res *= dp[j - i][rightValue - leftValue + 1];
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i = j;
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}
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}
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return res;
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}
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// 数学方法
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// a ~ b范围的数字随便选，可以选重复的数，一共选m个
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// 选出有序序列的方案数：C ( m, b - a + m )
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public static long ways2(int[] nums, int k) {
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long res = 1;
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for (int i = 0, j = 0; i < nums.length; i++) {
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if (nums[i] == 0) {
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j = i + 1;
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while (j < nums.length && nums[j] == 0) {
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j++;
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}
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int leftValue = i - 1 >= 0 ? nums[i - 1] : 1;
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int rightValue = j < nums.length ? nums[j] : k;
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int numbers = j - i;
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res *= c(rightValue - leftValue + numbers, numbers);
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i = j;
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}
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}
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return res;
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}
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// 从一共a个数里，选b个数，方法数是多少
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public static long c(int a, int b) {
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if (a == b) {
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return 1;
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}
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long x = 1;
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long y = 1;
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for (int i = b + 1, j = 1; i <= a; i++, j++) {
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x *= i;
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y *= j;
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long gcd = gcd(x, y);
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x /= gcd;
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y /= gcd;
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}
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return x / y;
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}
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public static long gcd(long m, long n) {
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return n == 0 ? m : gcd(n, m % n);
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}
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// 为了测试
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public static int[] randomArray(int n, int k) {
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int[] ans = new int[n];
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for (int i = 0; i < n; i++) {
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ans[i] = (int) (Math.random() * k) + 1;
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}
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Arrays.sort(ans);
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for (int i = 0; i < n; i++) {
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ans[i] = Math.random() < 0.5 ? 0 : ans[i];
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}
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return ans;
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}
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// 为了测试
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public static void main(String[] args) {
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int N = 20;
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int K = 30;
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int testTimes = 10000;
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System.out.println("测试开始");
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for (int i = 0; i < testTimes; i++) {
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int n = (int) (Math.random() * N) + 1;
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int k = (int) (Math.random() * K) + 1;
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int[] arr = randomArray(n, k);
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long ans1 = ways1(arr, k);
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long ans2 = ways2(arr, k);
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if (ans1 != ans2) {
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System.out.println("出错了");
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for (int num : arr) {
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System.out.print(num + " ");
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}
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System.out.println();
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System.out.println(ans1);
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System.out.println(ans2);
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}
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}
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System.out.println("测试结束");
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}
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}
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