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package class_2023_07_1_week;
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import java.util.Arrays;
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// 小扣在探索丛林的过程中，无意间发现了传说中"落寞的黄金之都"
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// 而在这片建筑废墟的地带中，小扣使用探测仪监测到了存在某种带有「祝福」效果的力场
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// 经过不断的勘测记录，小扣将所有力场的分布都记录了下来
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// forceField[i] = [x,y,side]
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// 表示第 i 片力场将覆盖以坐标 (x,y) 为中心，边长为 side 的正方形区域。
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// 若任意一点的 力场强度 等于覆盖该点的力场数量
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// 请求出在这片地带中 力场强度 最强处的 力场强度
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// 注意：力场范围的边缘同样被力场覆盖。
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// 测试链接 : https://leetcode.cn/problems/xepqZ5/
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public class Code03_StrongestForceField {
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public static int fieldOfGreatestBlessing(int[][] fields) {
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int n = fields.length;
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// n : 矩形的个数，x 2*n个坐标
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long[] xs = new long[n << 1];
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long[] ys = new long[n << 1];
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for (int i = 0, k = 0, p = 0; i < n; i++) {
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long x = fields[i][0];
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long y = fields[i][1];
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long r = fields[i][2];
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xs[k++] = (x << 1) - r;
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xs[k++] = (x << 1) + r;
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ys[p++] = (y << 1) - r;
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ys[p++] = (y << 1) + r;
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}
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int sizex = sort(xs);
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int sizey = sort(ys);
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int[][] diff = new int[sizex + 2][sizey + 2];
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for (int i = 0, a, b, c, d; i < n; i++) {
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long x = fields[i][0];
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long y = fields[i][1];
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long r = fields[i][2];
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a = rank(xs, (x << 1) - r, sizex);
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b = rank(ys, (y << 1) - r, sizey);
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c = rank(xs, (x << 1) + r, sizex);
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d = rank(ys, (y << 1) + r, sizey);
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set(diff, a, b, c, d);
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}
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int ans = 0;
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for (int i = 1; i < diff.length; i++) {
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for (int j = 1; j < diff[0].length; j++) {
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diff[i][j] += diff[i - 1][j] + diff[i][j - 1] - diff[i - 1][j - 1];
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ans = Math.max(ans, diff[i][j]);
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}
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}
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return ans;
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}
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public static int sort(long[] nums) {
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Arrays.sort(nums);
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int size = 1;
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for (int i = 1; i < nums.length; i++) {
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if (nums[i] != nums[size - 1]) {
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nums[size++] = nums[i];
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}
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}
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return size;
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}
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public static int rank(long[] nums, long v, int size) {
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int l = 0;
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int r = size - 1;
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int m, ans = 0;
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while (l <= r) {
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m = (l + r) / 2;
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if (nums[m] >= v) {
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ans = m;
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r = m - 1;
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} else {
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l = m + 1;
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}
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}
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return ans + 1;
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}
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// 二维差分
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public static void set(int[][] diff, int a, int b, int c, int d) {
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diff[a][b] += 1;
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diff[c + 1][d + 1] += 1;
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diff[c + 1][b] -= 1;
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diff[a][d + 1] -= 1;
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}
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}
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