[TOC]

动态规划

P8784 蓝桥杯 2022 省 B - 积木画 

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const int mod = 1000000007;

int f[6] = { 0,1,2,5 };

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    int n;
    cin >> n;

    for (int i = 4; i <= n; i++) {
        f[i] = (2 * f[i-1] % mod + f[i-3] % mod) % mod;
    }

    cout << f[n];

    return 0;
}

P8786 蓝桥杯 2022 省 B - 李白打酒加强版 

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const int mod = 1000000007;

int jiu[201][101][101];

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    int n, m;
    cin >> n >> m;

    jiu[0][0][2] = 1;
    //i 位置
    //j 花
    //k 酒
    for (int i = 0; i < n + m; i++) {
        for (int j = 0; j < m; j++) {
            for (int k = 0; k <= m; k++) {
                if (jiu[i][j][k]) {
                    if (k > 0) jiu[i + 1][j + 1][k - 1] = (jiu[i + 1][j + 1][k - 1] + jiu[i][j][k]) % mod;
                    if (k <= m/2) jiu[i + 1][j][k * 2] = (jiu[i + 1][j][k * 2] + jiu[i][j][k]) % mod;
                }
            }
        }
    }

    cout << jiu[n + m][m][0];

    return 0;
}

P2758 编辑距离 

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int n, m;
int ans;
//dp[i][j]

//A的前i位转换为 B前j位的最小步骤
int dp[2001][2001];
/*
Ⅰ：删除一个字符；
Ⅱ：插入一个字符；
Ⅲ：将一个字符改为另一个字符。
*/
signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    
    string str1, str2;
    cin >> str1 >> str2;
    n = str1.size();
    m = str2.size();
    for (int i = 1; i <= n; i++) {
        dp[i][0] = i;
    }
    for (int i = 1; i <= m; i++) {
        dp[0][i] = i;
    }

    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            if (str1[i - 1] == str2[j - 1]) {
                dp[i][j] = dp[i - 1][j - 1];
                continue;
            }
            
		//分别对应i情况：			Ⅰ			Ⅱ				Ⅲ
            dp[i][j] = min(min(dp[i - 1][j], dp[i][j - 1]), dp[i - 1][j - 1]) + 1;
        }
    }

    cout << dp[n][m];

    return 0;
}

P1077 NOIP2012 普及组 摆花

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int dp[101][101];
int n, m;
int a[101];

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    //m盆
    //n种花
    //第i种不能超ai盆
    //同一种放一起，标号从小到大排
    cin >> n >> m;
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
    }
    for (int i = 0; i <= n; i++) {
        dp[i][0] = 1;
    }

    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            for (int num = 0; num <= min(j,a[i]); num++) {
                //状态方程
                //i种j盆的方法数 = 自身 + i-1种j-a_i选择盆的方法数
                dp[i][j] = (dp[i][j] + dp[i - 1][j - num])%1000007;
            }
        }
    }

    cout << dp[n][m];
    return 0;
}

P4933 大师 - 洛谷 | 计算机科学教育新生态 (luogu.com.cn)

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#define mod 998244353

int n;
int h[1001];
int dp[1001][40001];

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    cin >> n;
    for (int i = 1; i <= n; i++) {
        cin >> h[i];
    }

    int ans = 0;
    for (int i = 1; i <= n; i++) {
        ans++;//每个数自身也是一个答案
        for (int j = i - 1; j; j--) {
            dp[i][h[i] - h[j] + 20000] += dp[j][h[i] - h[j] + 20000] + 1;
            dp[i][h[i] - h[j] + 20000] %= mod;
            ans += dp[j][h[i] - h[j] + 20000] + 1;
            ans %= mod;
        }
    }


    cout << ans;

    return 0;
}

[P1091 NOIP2004 提高组 合唱队形 

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signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    cin >> n;
    for (int i = 0; i < n; i++) {
        cin >> h[i];
    }
    
    for (int i = 0; i < n; i++) {
        dp[i][0] = 1;
        for (int j = 0; j < i; j++) {
            if (h[j] < h[i]) {
                dp[i][0] = max(dp[i][0], dp[j][0] + 1);
            }
        }
    }

    for (int i = 0; i < n; i++) {
        dp[i][1] = 1;
        for (int j = 0; j < i; j++) {
            if (h[j] > h[i]) {
                dp[i][1] = max(dp[i][1], max(dp[j][0], dp[j][1]) + 1);
            }
        }
    }

    int ans = 0;
    for (int i = 0; i < n; i++) {
        ans = max(ans, max(dp[i][0], dp[i][1]));
    }

    cout << n - ans;

    return 0;
}

树

前序后序，确定中序数量

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//子结点为1的节点数目为n
//2^n即为答案

string pre, post;
cin >> pre >> post;

int b = 0;
for (int i = 0; i < pre.size() - 1; i++) {
    for (int j = 1; j < post.size(); j++) {
        if (pre[i] == post[j] && pre[i + 1] == post[j - 1])
            b++;
    }
}

cout << (1 << b);

堆栈

小顶堆

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const int MAXN = 1314;
const int MINH = -1314;
int minS[MAXN], _size;

void Creat() {
	_size = 0;
	minS[0] = MINH;//设置岗哨
}

void Insert(int x) {
	int i;
    //岗哨的作用体现，岗哨是比插入数据都小的，不会导致越界
	for (i = ++_size; minS[i / 2] > x; i /= 2)
		minS[i] = minS[i / 2];
	minS[i] = x;
}



int main() {
	int n, m;
    //一个有n个数据的堆，m次查找
	cin >> n >> m;
	Creat();
	int x;
	for (int i = 0; i < n; i++) {
		cin >> x;
		Insert(x);
	}
	
    //m次查找，根据查找所给下标，返回其到根的路径
	for (int i = 0; i < m; i++) {
		cin >> x;
		cout << minS[x];
		while (x > 1) {
			x /= 2;
			cout << " " <<  minS[x];
		}
		cout << endl;
	}

	return 0;
}