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package 第03期.mca_10;
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import java.util.ArrayList;
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// 本题测试链接 : https://leetcode.com/problems/burst-balloons/
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public class Code03_BurstBalloons {
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public static int maxCoins(int[] nums) {
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int n = nums.length;
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// 3 5 2
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// 1 3 5 2 1
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int[] arr = new int[n + 2];
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arr[0] = 1;
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arr[n + 1] = 1;
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// 1 3 5 2 1
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for (int i = 0; i < n; i++) {
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arr[i + 1] = nums[i];
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}
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// 3 5 2 3
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// 1 3 5 2 1
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// 0 1 2 3 4
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return hit(arr, 1, n);
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}
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// arr[l...r]范围上，选择最优的打爆顺序，返回最大的得分!
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// 想要调用递归，必须满足如下条件 :
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// arr[l-1]的气球，一定没爆!
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// arr[r+1]的气球，一定没爆!
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public static int hit(int[] arr, int l, int r) {
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if (l == r) {
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// l...r 只有一个气球了!
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return arr[l - 1] * arr[l] * arr[r + 1];
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}
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// l < r 不只一个气球
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// 可能性1 : 最后打爆l位置的气球
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int p1 = hit(arr, l + 1, r) + arr[l - 1] * arr[l] * arr[r + 1];
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// 可能性2 : 最后打爆r位置的气球
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int p2 = hit(arr, l, r - 1) + arr[l - 1] * arr[r] * arr[r + 1];
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int ans = Math.max(p1, p2);
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for (int m = l + 1; m < r; m++) {
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// 尝试中间每一个气球，都最后打爆
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int left = hit(arr, l, m - 1);
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int right = hit(arr, m + 1, r);
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int mid = arr[l - 1] * arr[m] * arr[r + 1];
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int curAns = left + right + mid;
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ans = Math.max(ans, curAns);
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}
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return ans;
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}
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public static void main(String[] args) {
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int[] arr = { 3, 3, 4, 3, 3 };
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System.out.println(maxCoins(arr));
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ArrayList<ArrayList<Integer>> paths = maxCoins2(arr);
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for (ArrayList<Integer> path : paths) {
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for (int num : path) {
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System.out.print(num + " ");
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}
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System.out.println();
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}
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}
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public static ArrayList<ArrayList<Integer>> maxCoins2(int[] arr) {
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int N = arr.length;
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int[] help = new int[N + 2];
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help[0] = 1;
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help[N + 1] = 1;
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for (int i = 0; i < N; i++) {
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help[i + 1] = arr[i];
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}
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int[][] dp = new int[N + 2][N + 2];
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for (int i = 1; i <= N; i++) {
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dp[i][i] = help[i - 1] * help[i] * help[i + 1];
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}
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for (int L = N; L >= 1; L--) {
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for (int R = L + 1; R <= N; R++) {
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int ans = help[L - 1] * help[L] * help[R + 1] + dp[L + 1][R];
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ans = Math.max(ans, help[L - 1] * help[R] * help[R + 1] + dp[L][R - 1]);
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for (int i = L + 1; i < R; i++) {
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ans = Math.max(ans, help[L - 1] * help[i] * help[R + 1] + dp[L][i - 1] + dp[i + 1][R]);
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}
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dp[L][R] = ans;
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}
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}
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System.out.println("结果 : " + dp[1][N]);
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ArrayList<ArrayList<Integer>> ans = new ArrayList<>();
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ArrayList<Integer> path = new ArrayList<>();
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generatePath2(dp, help, 1, N, N, path, ans);
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return ans;
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}
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public static int pi;
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// 回溯！倒着填路径
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public static void generatePath1(int[][] dp, int[] arr, int l, int r, int[] path) {
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if (l == r) {
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path[pi--] = l;
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} else {
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if (dp[l + 1][r] + arr[l - 1] * arr[l] * arr[r + 1] == dp[l][r]) {
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path[pi--] = l;
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generatePath1(dp, arr, l + 1, r, path);
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} else if (dp[l][r - 1] + arr[l - 1] * arr[r] * arr[r + 1] == dp[l][r]) {
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path[pi--] = r;
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generatePath1(dp, arr, l, r - 1, path);
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} else {
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for (int m = l + 1; m < r; m++) {
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int left = dp[l][m - 1];
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int right = dp[m + 1][r];
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int mid = arr[l - 1] * arr[m] * arr[r + 1];
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if (left + right + mid == dp[l][r]) {
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path[pi--] = m;
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generatePath1(dp, arr, l, m - 1, path);
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generatePath1(dp, arr, m + 1, r, path);
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break;
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}
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}
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}
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}
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}
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// 回溯！倒着填路径
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public static void generatePath2(int[][] dp, int[] arr, int l, int r, int n, ArrayList<Integer> path,
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ArrayList<ArrayList<Integer>> ans) {
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if (l == r) {
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path.add(l);
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if (path.size() == n) {
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addPath(ans, path);
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}
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} else {
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if (dp[l + 1][r] + arr[l - 1] * arr[l] * arr[r + 1] == dp[l][r]) {
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ArrayList<Integer> p = new ArrayList<>(path);
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p.add(l);
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generatePath2(dp, arr, l + 1, r, n, p, ans);
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}
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if (dp[l][r - 1] + arr[l - 1] * arr[r] * arr[r + 1] == dp[l][r]) {
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ArrayList<Integer> p = new ArrayList<>(path);
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p.add(r);
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generatePath2(dp, arr, l, r - 1, n, p, ans);
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}
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for (int m = l + 1; m < r; m++) {
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int left = dp[l][m - 1];
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int right = dp[m + 1][r];
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int mid = arr[l - 1] * arr[m] * arr[r + 1];
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if (left + right + mid == dp[l][r]) {
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// 可以先左、后右
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ArrayList<Integer> p1 = new ArrayList<>(path);
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p1.add(m);
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generatePath2(dp, arr, l, m - 1, n, p1, ans);
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generatePath2(dp, arr, m + 1, r, n, p1, ans);
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// 也可以先右、后左
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ArrayList<Integer> p2 = new ArrayList<>(path);
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p2.add(m);
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generatePath2(dp, arr, m + 1, r, n, p2, ans);
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generatePath2(dp, arr, l, m - 1, n, p2, ans);
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}
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}
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}
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}
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public static void addPath(ArrayList<ArrayList<Integer>> ans, ArrayList<Integer> path) {
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ArrayList<Integer> curPath = new ArrayList<>();
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for (int i = path.size() - 1; i >= 0; i--) {
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curPath.add(path.get(i) - 1);
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}
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ans.add(curPath);
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}
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//
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// public static int maxCoins0(int[] arr) {
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// // [3,2,1,3]
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// // [1,3,2,1,3,1]
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// int N = arr.length;
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// int[] help = new int[N + 2];
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// for (int i = 0; i < N; i++) {
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// help[i + 1] = arr[i];
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// }
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// help[0] = 1;
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// help[N + 1] = 1;
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// return func(help, 1, N);
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// }
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//
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// // L-1位置，和R+1位置，永远不越界，并且，[L-1] 和 [R+1] 一定没爆呢！
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// // 返回，arr[L...R]打爆所有气球，最大得分是什么
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// public static int func(int[] arr, int L, int R) {
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// if (L == R) {
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// return arr[L - 1] * arr[L] * arr[R + 1];
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// }
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// // 尝试每一种情况，最后打爆的气球，是什么位置
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// // L...R
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// // L位置的气球，最后打爆
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// int max = func(arr, L + 1, R) + arr[L - 1] * arr[L] * arr[R + 1];
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// // R位置的气球，最后打爆
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// max = Math.max(max, func(arr, L, R - 1) + arr[L - 1] * arr[R] * arr[R + 1]);
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// // 尝试所有L...R，中间的位置，(L,R)
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// for (int i = L + 1; i < R; i++) {
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// // i位置的气球，最后打爆
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// int left = func(arr, L, i - 1);
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// int right = func(arr, i + 1, R);
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// int last = arr[L - 1] * arr[i] * arr[R + 1];
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// int cur = left + right + last;
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// max = Math.max(max, cur);
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// }
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// return max;
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// }
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//
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// public static int maxCoins1(int[] arr) {
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// if (arr == null || arr.length == 0) {
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// return 0;
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// }
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// if (arr.length == 1) {
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// return arr[0];
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// }
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// int N = arr.length;
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// int[] help = new int[N + 2];
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// help[0] = 1;
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// help[N + 1] = 1;
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// for (int i = 0; i < N; i++) {
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// help[i + 1] = arr[i];
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// }
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// return process(help, 1, N);
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// }
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//
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// // 打爆arr[L..R]范围上的所有气球，返回最大的分数
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// // 假设arr[L-1]和arr[R+1]一定没有被打爆
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// public static int process(int[] arr, int L, int R) {
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// if (L == R) {// 如果arr[L..R]范围上只有一个气球，直接打爆即可
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// return arr[L - 1] * arr[L] * arr[R + 1];
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// }
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// // 最后打爆arr[L]的方案，和最后打爆arr[R]的方案，先比较一下
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// int max = Math.max(arr[L - 1] * arr[L] * arr[R + 1] + process(arr, L + 1, R),
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// arr[L - 1] * arr[R] * arr[R + 1] + process(arr, L, R - 1));
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// // 尝试中间位置的气球最后被打爆的每一种方案
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// for (int i = L + 1; i < R; i++) {
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// max = Math.max(max, arr[L - 1] * arr[i] * arr[R + 1] + process(arr, L, i - 1) + process(arr, i + 1, R));
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// }
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// return max;
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// }
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//
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// public static int maxCoins2(int[] arr) {
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// if (arr == null || arr.length == 0) {
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// return 0;
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// }
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// if (arr.length == 1) {
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// return arr[0];
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// }
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// int N = arr.length;
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// int[] help = new int[N + 2];
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// help[0] = 1;
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// help[N + 1] = 1;
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// for (int i = 0; i < N; i++) {
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// help[i + 1] = arr[i];
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// }
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// int[][] dp = new int[N + 2][N + 2];
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// for (int i = 1; i <= N; i++) {
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// dp[i][i] = help[i - 1] * help[i] * help[i + 1];
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// }
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// for (int L = N; L >= 1; L--) {
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// for (int R = L + 1; R <= N; R++) {
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// int ans = help[L - 1] * help[L] * help[R + 1] + dp[L + 1][R];
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// ans = Math.max(ans, help[L - 1] * help[R] * help[R + 1] + dp[L][R - 1]);
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// for (int i = L + 1; i < R; i++) {
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// ans = Math.max(ans, help[L - 1] * help[i] * help[R + 1] + dp[L][i - 1] + dp[i + 1][R]);
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// }
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// dp[L][R] = ans;
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// }
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// }
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// return dp[1][N];
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// }
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}
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algorithmzuo
1 year ago