Uva11040 Add bricks in the wall

题目：

This in not “another brick in the wall”, it’s just a matter of adding numbers. Suppose you have a wall with the shape of a triangle, like the one shown below. The wall has 9 rows and row i has exactly i bricks, considering that top row is the first one and bottom row is the ninth. Some bricks are labeled
with a number and other ones are blank. Notice that labeled bricks appear only on odd rows and they occupy odd positions within the row. The problem you must solve is finding a suitable number for each blank brick taking into account one simple rule: the number of a brick is obtained by adding the numbers of the two bricks below it. Obviously, this rule does not apply to the ninth row. Numbers are supposed to be integers.

Paste_Image.png

Input
The first line of the input contains an integer N, indicating the number of test cases. This line is followed by the lines corresponding to the test cases. Each test case is described in five lines. These five lines correspond to odd rows of the wall, from top to bottom, as described above. Line i contains
the numbers corresponding to odd bricks on row i of the wall (that is, non blank bricks), enumerated from left to right and separated with a single space. It is supposed that each test case is correct, that is, there exists a solution to the problem that the case describes.
Output
For each test case, the output should consist of nine lines describing the numbers of all bricks of the wall.
So, line i should contain the numbers corresponding to the i bricks on row i of the wall, enumerated
from left to right and separated by a single space.
Note: Here we have an example with two test cases. The first one corresponds to the wall depicted
above.
Sample Input
2
255
54 67
10 18 13
3 3 5 2
2 1 2 1 1
256
64 64
16 16 16
4 4 4 4
1 1 1 1 1
Sample Output
255
121 134
54 67 67
23 31 36 31
10 13 18 18 13
5 5 8 10 8 5
3 2 3 5 5 3 2
2 1 1 2 3 2 1 1
2 0 1 0 2 1 1 0 1
256
128 128
64 64 64
32 32 32 32
16 16 16 16 16
8 8 8 8 8 8
4 4 4 4 4 4 4
2 2 2 2 2 2 2 2
1 1 1 1 1 1 1 1 1

题意：
45块石头按照上述方式排列，每块石头上有一个整数。
除了最后一行外，每块石头上的整数等于支撑它的两块石头上的正数之和。目前只有奇数行的左数奇数个位置上的数已知，你的任务是求出其余所有整数。输入保证有唯一解（《算法竞赛入门经典（第2版）》）。

如图所示：
z
x+a y+a
x a y
则x+a+y+a=x+y+2*a=z，则a = (z-x-y) / 2.这样我们就可以以此计算出奇数行偶数个位置上的数。之后就可以通过题目中的条件计算出偶数行的数。

参考代码：

#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
const int N = 10+2;

int mp[N][N];

void init() {
    memset(mp, 0, sizeof(mp));
}

void input() {//奇数行的奇数列已知;
    for (int i = 1;i <= 9;i += 2) {
        for (int j = 1;j <= i;j += 2) {
            cin >> mp[i][j];
        }
    }
}

void bricks() {
    //cout << "xyz" << endl;
    for (int i = 3;i <= 9;i += 2) {//先将单行双列的数填满;
        for (int j = 2;j <= i;j += 2) {
            mp[i][j] = (mp[i-2][j-1] - mp[i][j-1] - mp[i][j+1]) / 2;
        }
    }
    //for (int i = 1;i <= 9;++i) {
    //  for (int j = 1;j <= i;++j) {
    //      cout << mp[i][j] << " ";
    //  }
    //  cout << endl;
    //}
    //cout << "xyz" << endl;
    for (int i = 2;i <= 8;i += 2) {//填满双行;
        for (int j = 1;j <= i;++j) {
            mp[i][j] = mp[i+1][j] + mp[i+1][j+1];
        }
    }
}

void print() {
    for (int i = 1;i <= 9;++i) {
        int cnt = 0;
        for (int j = 1;j <= i;++j) {
            if (cnt > 0) cout << " ";
            cout << mp[i][j];
            ++cnt;
        }
        cout << endl;
    }
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    int t;
    cin >> t;
    while (t--) {
        init();
        input();
        bricks();
        print();
    }
    return 0;
}