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package class_2023_04_4_week;
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// 来自微众银行
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// 给出两个长度均为n的数组
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// A = { a1, a2, ... ,an }
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// B = { b1, b2, ... ,bn }。
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// 你需要求出其有多少个区间[L,R]满足:
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// 数组A中下标在[L,R]中的元素之和在[La,Ra]之中
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// 数组B中下标在[L,R]中的元素之和在[Lb,Rb]之中
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// 输入
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// 第一行有一个正整数N(1<=N<=100000)，代表两个数组的长度。
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// 第二行有N个非负整数，范围在0到1000000000之间，代表数组中的元素。
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// 第三行有N个非负整数，范围在0到1000000000之间，代表数组中的元素。
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// 第四行有4个整数La,Ra,Lb,Rb，范围在0到10^18之间，代表题目描述中的参数。
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// 输出
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// 输出一个整数，代表所求的答案。
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public class Code05_ValidRangeBetweenTwoArrays {
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// 暴力方法
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// 为了测试
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public static int nums1(int[] A, int[] B, int la, int ra, int lb, int rb) {
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int n = A.length;
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int ans = 0;
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for (int l = 0; l < n; l++) {
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for (int r = l; r < n; r++) {
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int sumA = 0;
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int sumB = 0;
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for (int i = l; i <= r; i++) {
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sumA += A[i];
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sumB += B[i];
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}
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if (sumA >= la && sumA <= ra && sumB >= lb && sumB <= rb) {
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ans++;
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}
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}
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}
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return ans;
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}
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// 正式方法
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// 时间复杂度O(N)
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public static int nums2(int[] A, int[] B, int la, int ra, int lb, int rb) {
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int n = A.length;
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int ans = 0;
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int rightA1 = 0, sumA1 = 0, rightA2 = 0, sumA2 = 0, rightB1 = 0, sumB1 = 0, rightB2 = 0, sumB2 = 0;
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for (int l = 0; l < n; l++) {
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while (rightA1 < n && sumA1 + A[rightA1] < la) {
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sumA1 += A[rightA1++];
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}
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while (rightA2 < n && sumA2 + A[rightA2] <= ra) {
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sumA2 += A[rightA2++];
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}
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while (rightB1 < n && sumB1 + B[rightB1] < lb) {
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sumB1 += B[rightB1++];
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}
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while (rightB2 < n && sumB2 + B[rightB2] <= rb) {
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sumB2 += B[rightB2++];
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}
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int left = Math.max(rightA1, rightB1);
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int right = Math.min(rightA2, rightB2);
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if (left < right) {
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ans += right - left;
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}
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if (rightA1 == l) {
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rightA1++;
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} else {
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sumA1 -= A[l];
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}
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sumA2 -= A[l];
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if (rightB1 == l) {
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rightB1++;
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} else {
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sumB1 -= B[l];
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}
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sumB2 -= B[l];
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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 int[] randomArray(int n, int v) {
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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() * v);
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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 = 50;
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int V = 100;
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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);
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int[] A = randomArray(n, V);
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int[] B = randomArray(n, V);
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int a = (int) (Math.random() * V);
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int b = (int) (Math.random() * V);
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int c = (int) (Math.random() * V);
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int d = (int) (Math.random() * V);
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int la = Math.min(a, b);
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int ra = Math.max(a, b);
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int lb = Math.min(c, d);
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int rb = Math.max(c, d);
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int ans1 = nums1(A, B, la, ra, lb, rb);
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int ans2 = nums2(A, B, la, ra, lb, rb);
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if (ans1 != ans2) {
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System.out.println("出错了!");
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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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