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algorithmzuoalgorithmzuo
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add class 02
1 parent c9ca690 commit aec9feb

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+448
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lines changed

‎src/class02/Code05_PreSum.java renamed to ‎src/class02/Code01_PreSum.java

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package class02;
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public class Code05_PreSum {
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public class Code01_PreSum {
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public static class RangeSum1 {
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‎src/class02/Code02_RandToRand.java

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package class02;
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public class Code02_RandToRand {
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// 此函数只能用，不能修改
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// 等概率返回1~5
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public static int f() {
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return (int) (Math.random() * 5) + 1;
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}
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// 等概率得到0和1
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public static int a() {
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int ans = 0;
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do {
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ans = f();
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} while (ans == 3);
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return ans < 3 ? 0 : 1;
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}
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// 等概率返回0~6
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public static int b() {
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int ans = 0;
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do {
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ans = (a() << 2) + (a() << 1) + a();
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} while (ans == 7);
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return ans;
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}
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// 等概率返回1~7
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public static int c() {
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return b() + 1;
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}
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// 这个结构是唯一的随机机制
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// 你只能初始化并使用，不可修改
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public static class RandomBox {
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private final int min;
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private final int max;
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// 初始化时请一定不要让mi==ma
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public RandomBox(int mi, int ma) {
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min = mi;
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max = ma;
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}
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// 13 ~ 17
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// 13 + [0,4]
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public int random() {
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return min + (int) (Math.random() * (max - min + 1));
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}
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public int min() {
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return min;
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}
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public int max() {
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return max;
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}
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}
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// 利用条件RandomBox，如何等概率返回0和1
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public static int rand01(RandomBox randomBox) {
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int min = randomBox.min();
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int max = randomBox.max();
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// min ~ max
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int size = max - min + 1;
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// size是不是奇数，odd 奇数
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boolean odd = (size & 1) != 0;
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int mid = size / 2;
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int ans = 0;
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do {
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ans = randomBox.random() - min;
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} while (odd && ans == mid);
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return ans < mid ? 0 : 1;
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}
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// 给你一个RandomBox，这是唯一能借助的随机机制
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// 等概率返回from~to范围上任何一个数
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// 要求from<=to
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public static int random(RandomBox randomBox, int from, int to) {
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if (from == to) {
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return from;
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}
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// 3 ~ 9
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// 0 ~ 6
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// 0 ~ range
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int range = to - from;
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int num = 1;
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// 求0～range需要几个2进制位
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while ((1 << num) - 1 < range) {
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num++;
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}
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// 我们一共需要num位
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// 最终的累加和，首先+0位上是1还是0，1位上是1还是0，2位上是1还是0...
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int ans = 0;
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do {
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ans = 0;
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for (int i = 0; i < num; i++) {
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ans |= (rand01(randomBox) << i);
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}
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} while (ans > range);
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return ans + from;
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}
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public static void main(String[] args) {
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int[] count = new int[8]; // 0 1 2 .. 7
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int testTime = 10000000;
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for (int i = 0; i < testTime; i++) {
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int ans = c();
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count[ans]++;
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}
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for (int i = 0; i < 8; i++) {
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System.out.println(i + " : " + count[i]);
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}
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// RandomBox randomBox = new RandomBox(3, 9);
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// int from = 17;
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// int to = 29;
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// int[] ans = new int[to + 1];
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// int testTime1 = 1000000;
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// for (int i = 0; i < testTime1; i++) {
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// ans[random(randomBox, from, to)]++;
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// }
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// for (int i = 0; i < ans.length; i++) {
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// System.out.println(ans[i]);
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// }
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// System.out.println("==========");
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}
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}

‎src/class02/Code03_EqualProbabilityRandom.java

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package class02;
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public class Code03_EqualProbabilityRandom {
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// 内部内容不可见
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public static int f() {
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return Math.random() < 0.8 ? 0 : 1;
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}
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// 等概率返回0和1
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public static int g() {
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int first = 0;
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do {
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first = f(); // 0 1
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} while (first == f());
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return first;
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}
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// 这个结构是唯一的随机机制
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// 你只能初始化并使用，不可修改
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public static class RandomBox {
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private final double p;
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// 初始化时请一定满足：0 < zeroP < 1
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public RandomBox(double zeroP) {
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p = zeroP;
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}
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public int random() {
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return Math.random() < p ? 0 : 1;
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}
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}
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// 底层依赖一个以p概率返回0，以1-p概率返回1的随机函数rand01p
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// 如何加工出等概率返回0和1的函数
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public static int rand01(RandomBox randomBox) {
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int num;
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do {
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num = randomBox.random();
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} while (num == randomBox.random());
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return num;
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}
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public static void main(String[] args) {
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int[] count = new int[2];// 0 1
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for (int i = 0; i < 1000000; i++) {
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int ans = g();
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count[ans]++;
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}
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System.out.println(count[0] + " , " + count[1]);
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// double zeroP = 0.88;
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// RandomBox randomBox = new RandomBox(zeroP);
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//
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// int testTime = 10000000;
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// int count = 0;
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// for (int i = 0; i < testTime; i++) {
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// if (rand01(randomBox) == 0) {
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// count++;
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// }
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// }
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// System.out.println((double) count / (double) testTime);
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}
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}

‎src/class02/Code04_BSExist.java

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package class02;
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import java.util.Arrays;
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public class Code04_BSExist {
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public static boolean exist(int[] sortedArr, int num) {
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if (sortedArr == null || sortedArr.length == 0) {
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return false;
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}
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int L = 0;
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int R = sortedArr.length - 1;
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int mid = 0;
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// L..R
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while (L < R) { // L..R 至少两个数的时候
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mid = L + ((R - L) >> 1);
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if (sortedArr[mid] == num) {
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return true;
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} else if (sortedArr[mid] > num) {
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R = mid - 1;
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} else {
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L = mid + 1;
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}
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}
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return sortedArr[L] == num;
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}
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// for test
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public static boolean test(int[] sortedArr, int num) {
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for(int cur : sortedArr) {
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if(cur == num) {
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return true;
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}
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}
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return false;
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}
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// for test
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public static int[] generateRandomArray(int maxSize, int maxValue) {
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int[] arr = new int[(int) ((maxSize + 1) * Math.random())];
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for (int i = 0; i < arr.length; i++) {
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arr[i] = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());
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}
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return arr;
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}
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public static void main(String[] args) {
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int testTime = 500000;
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int maxSize = 10;
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int maxValue = 100;
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boolean succeed = true;
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for (int i = 0; i < testTime; i++) {
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int[] arr = generateRandomArray(maxSize, maxValue);
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Arrays.sort(arr);
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int value = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());
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if (test(arr, value) != exist(arr, value)) {
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succeed = false;
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break;
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}
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}
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System.out.println(succeed ? "Nice!" : "Fucking fucked!");
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}
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}

‎src/class02/Code05_BSNearLeft.java

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package class02;
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import java.util.Arrays;
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public class Code05_BSNearLeft {
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// 在arr上，找满足>=value的最左位置
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public static int nearestIndex(int[] arr, int value) {
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int L = 0;
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int R = arr.length - 1;
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int index = -1; // 记录最左的对号
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while (L <= R) { // 至少一个数的时候
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int mid = L + ((R - L) >> 1);
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if (arr[mid] >= value) {
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index = mid;
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R = mid - 1;
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} else {
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L = mid + 1;
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}
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}
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return index;
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}
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// for test
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public static int test(int[] arr, int value) {
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for (int i = 0; i < arr.length; i++) {
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if (arr[i] >= value) {
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return i;
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}
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}
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return -1;
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}
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// for test
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public static int[] generateRandomArray(int maxSize, int maxValue) {
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int[] arr = new int[(int) ((maxSize + 1) * Math.random())];
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for (int i = 0; i < arr.length; i++) {
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arr[i] = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());
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}
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return arr;
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}
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// for test
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public static void printArray(int[] arr) {
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if (arr == null) {
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return;
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}
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for (int i = 0; i < arr.length; i++) {
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System.out.print(arr[i] + " ");
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}
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System.out.println();
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}
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public static void main(String[] args) {
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int testTime = 500000;
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int maxSize = 10;
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int maxValue = 100;
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boolean succeed = true;
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for (int i = 0; i < testTime; i++) {
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int[] arr = generateRandomArray(maxSize, maxValue);
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Arrays.sort(arr);
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int value = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());
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if (test(arr, value) != nearestIndex(arr, value)) {
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printArray(arr);
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System.out.println(value);
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System.out.println(test(arr, value));
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System.out.println(nearestIndex(arr, value));
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succeed = false;
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break;
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}
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}
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System.out.println(succeed ? "Nice!" : "Fucking fucked!");
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}
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}

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