DP! | 不要怂!

　　跟一个博客刷： http://blog.csdn.net/cc_again/article/details/25866971

一、简单基础dp

　　1.递推

　　　　HDU 2084

#include <bits/stdc++.h>
using namespace std;

const int MAXN = 111;
int dp[MAXN][MAXN];
int towel[MAXN][MAXN];

int main(){
    int t;
    scanf("%d", &t);
    while(t--){
        memset(towel, 0, sizeof(towel));
        int n;
        scanf("%d", &n);
        for(int i = 0; i < n; ++i)
            for(int j = 0; j <= i; ++j)
                scanf("%d", &towel[i][j]);
        for(int i = n-1; i > 0; --i)
            for(int j = 0; j < i; ++j)
                towel[i-1][j] += max(towel[i][j], towel[i][j+1]);
        printf("%d
", towel[0][0]);
/*　
*        memset(dp, 0, sizeof(dp));
*        dp[0][0] = towel[0][0];
*        for(int i = 0; i < n; ++i){
*            for(int j = 0; j <= i; ++j){
*                dp[i+1][j] = max(dp[i+1][j], dp[i][j]+towel[i+1][j]);
*                dp[i+1][j+1] = max(dp[i+1][j+1], dp[i][j]+towel[i+1][j+1]);
*            }
*        }
*        int ans = 0;
*        for(int i = 0; i < n; ++i)
*            ans = max(ans, dp[n-1][i]);
*        printf("%d
", ans);
*/
    }
    return 0;
}

　　　　HDU 2018

#include <bits/stdc++.h>
using namespace std;

const int MAXN = 66;
int cow[MAXN];

int main(){
    cow[1] = 1;
    for(int i = 2; i < MAXN; ++i)
        cow[i] = i > 4 ? cow[i-1] + cow[i-3] : cow[i-1] + 1;
    int n;
    while(scanf("%d", &n) == 1 && n)
        printf("%d
", cow[n]);
    return 0;
}

　　　　HDU 2044

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
const int MAXN = 55;
ll cell[MAXN];

int main(){
    int t;
    scanf("%d", &t);
    while(t--){
        int a, b;
        scanf("%d %d", &a, &b);
        cell[a] = 1; cell[a+1] = 1;
        for(int i = a+2; i <= b; ++i)
            cell[i] = cell[i-1] + cell[i-2];
        printf("%I64d
", cell[b]);
    }
    return 0;
}

　　　　HDU 2041

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
const int MAXN = 50;
ll step[MAXN] = {0, 0, 1, 2, 3};

int main(){
    for(int i = 4; i < MAXN; ++i) step[i] = step[i-1]+step[i-2];
    int t;
    scanf("%d", &t);
    while(t--){
        int n;
        scanf("%d", &n);
        printf("%d
", step[n]);
    }
    return 0;
}

　　　　HDU 2050..............

#include <bits/stdc++.h>
using namespace std;

int main(){
    int t;
    scanf("%d", &t);
    while(t--){
        int n;
        scanf("%d", &n);
        printf("%d
", 2*n*n-n+1);
    }
    return 0;
}

　　　　CF 429B

    

#include <bits/stdc++.h>
using namespace std;

const int MAXN = 1e3+7;
int gym[MAXN][MAXN];
int dp[4][MAXN][MAXN];

// void print(int x, int n, int m){
//     for(int i = 1; i <= n; ++i){
//         for(int j = 1; j <= m; ++j)
//             printf("%d ", dp[x][i][j]);
//         puts("");
//     }
//     puts("");
// }
int main(){
    //while(true){
        int n, m;
        scanf("%d %d", &n, &m);
        for(int i = 1; i <= n; ++i)
            for(int j = 1; j <= m; ++j)
                scanf("%d", &gym[i][j]);
        memset(dp, 0, sizeof(dp));
        for(int i = n; i >= 1; --i)
            for(int j = m; j >= 1; --j)
                dp[0][i][j] = max(dp[0][i][j+1], dp[0][i+1][j]) + gym[i][j];
        for(int i = 1; i <= n; ++i)
            for(int j = 1; j <= m; ++j)
                dp[1][i][j] = max(dp[1][i][j-1], dp[1][i-1][j]) + gym[i][j];
        for(int i = n; i >= 1; --i)
            for(int j = 1; j <= m; ++j)
                dp[2][i][j] = max(dp[2][i][j-1], dp[2][i+1][j]) + gym[i][j];
        for(int i = 1; i <= n; ++i)
            for(int j = m; j >= 1; --j)
                dp[3][i][j] = max(dp[3][i-1][j], dp[3][i][j+1]) + gym[i][j];
        // for(int i = 0; i < 4; ++i)
        //     print(i, n, m);
        int ans = 0;
        for(int i = 2; i < n; ++i)
            for(int j = 2; j < m; ++j){
                ans = max(ans, dp[0][i+1][j] + dp[1][i-1][j] + dp[2][i][j-1] + dp[3][i][j+1]);
                ans = max(ans, dp[0][i][j+1] + dp[1][i][j-1] + dp[2][i+1][j] + dp[3][i-1][j]);
            }
        printf("%d
", ans);
    //}
    return 0;
}

　　　　ZOJ 3747

 http://blog.csdn.net/cc_again/article/details/24841249

 http://blog.csdn.net/wust_zjx/article/details/46809951

　　　 ans = ((ans - calc(m-1, k)) % MOD + MOD) % MOD; 能减出负数？

#include <bits/stdc++.h>
//#pragma comment(linker, "/STACK:1024000000,1024000000")
using namespace std;

typedef long long ll;
const int MOD = 1e9+7;
const int MAXN = 1e6+7;
ll dp[MAXN][5];
ll n, m, k;

ll calc(int u, int v){

    dp[0][2] = 1;
    dp[0][0] = dp[0][1] = 0;

    for(int i = 1; i <= n; ++i){
        ll sum = (dp[i-1][0] + dp[i-1][1] + dp[i-1][2]) % MOD;

        dp[i][2] = sum;

        if(i <= u) dp[i][0] = sum;
        else if(i == u+1) dp[i][0] = sum - 1;
        else dp[i][0] = sum - dp[i-u-1][1] - dp[i-u-1][2];

        if(i <= v) dp[i][1] = sum;
        else if(i == v+1) dp[i][1] = sum - 1;
        else dp[i][1] = sum - dp[i-v-1][0] - dp[i-v-1][2];
    }

    return (dp[n][0] + dp[n][1] + dp[n][2]) % MOD;
}
int main(){
    ios::sync_with_stdio(false);
    //printf("%d %d
", MAXN, MOD);
    while(cin >> n >> m >> k){
        ll ans = calc(n, k);
        ans = ((ans - calc(m-1, k)) % MOD + MOD) % MOD;
        cout << ans << endl;
    }
    return 0;
}

　　　　uva 10328

　　　怂了不敢撸高精度直接上python    UVA是python3啊.........

while True:
    try:
        a = [int(i) for i in input().split()]
    except:
        break

    n = a[0]
    k = a[1]

    k -= 1;
    dp = [([0]*2) for i in range(111)]

    dp[0][0] = 1
    for i in range(1, n+2):
        sum = dp[i-1][0] + dp[i-1][1]
        dp[i][1] = sum
        #print sum
        if i < k+1: dp[i][0] = sum
        if i == k+1: dp[i][0] = sum - 1
        if i > k+1: dp[i][0] = sum - dp[i-k-1][1]
        # print i
        # print dp

    ans = 1<<n
    ans -= dp[n+1][1]
    print(ans)

　　　　HDU 4747

　　看不懂

　　http://www.cnblogs.com/xin-hua/p/3325154.html

　　http://blog.csdn.net/cc_again/article/details/11856847

　　　　HDU 4489

　　　　HDU 4055

 　　2.背包