经典DP水题D

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本文介绍了一种算法挑战，即通过给定的一系列参数构建最高的堆叠游戏块。使用二维数组来记录每种可能的堆叠组合，并采用动态规划的方法来找出可以达到的最大高度。

Description

Michael The Kid receives an interesting game set from his grandparent as his birthday gift. Inside the game set box, there are n tiling blocks and each block has a form as follows:

Each tiling block is associated with two parameters (l,m), meaning that the upper face of the block is packed with l protruding knobs on the left and m protruding knobs on the middle. Correspondingly, the bottom face of an (l,m)-block is carved with l caving dens on the left and m dens on the middle.
It is easily seen that an (l,m)-block can be tiled upon another (l,m)-block. However,this is not the only way for us to tile up the blocks. Actually, an (l,m)-block can be tiled upon another (l',m')-block if and only if l >= l' and m >= m'.
Now the puzzle that Michael wants to solve is to decide what is the tallest tiling blocks he can make out of the given n blocks within his game box. In other words, you are given a collection of n blocks B = {b1, b2, . . . , bn} and each block bi is associated with two parameters (li,mi). The objective of the problem is to decide the number of tallest tiling blocks made from B.

Input

Several sets of tiling blocks. The inputs are just a list of integers.For each set of tiling blocks, the first integer n represents the number of blocks within the game box. Following n, there will be n lines specifying parameters of blocks in B; each line contains exactly two integers, representing left and middle parameters of the i-th block, namely, li and mi. In other words, a game box is just a collection of n blocks B = {b1, b2, . . . , bn} and each block bi is associated with two parameters (li,mi).
Note that n can be as large as 10000 and li and mi are in the range from 1 to 100.
An integer n = 0 (zero) signifies the end of input.

Output

For each set of tiling blocks B, output the number of the tallest tiling blocks can be made out of B. Output a single star '*' to signify the end of
outputs.

Sample Input

Sample Output

2
3
*

题意：两串序列同时要最长上升子序列。

思路：一开始直接排序一个然后DP另一个。。。果断WA。。。

new一个a[][]和dp[][]，a[i][j]++，画个表出来就懂了。

关键代码：dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]) + a[i][j];（参考网上。。为啥自己就想不出来嘞。。）

AC java 代码：

import java.util.Scanner;

public class sdupractice0724DPD {
//5324 KB 360 ms
public static void main(String[] args) {
Scanner scan = new Scanner(System.in);
int n = scan.nextInt();
while (n != 0) {
int[][] a = new int[105][105];
int[][] dp = new int[105][105];
for (int i = 1; i <= n; i++) {
int c = scan.nextInt();
int b = scan.nextInt();
a[c][b]++;
}
for (int i = 1; i <= 100; i++) {
for (int j = 1; j <= 100; j++) {
dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]) + a[i][j];
}
}
System.out.println(dp[100][100]);
n = scan.nextInt();
}
System.out.println("*");
}
}