线型dp

1 Codeforces 118D Caesar's Legions

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <vector>
#include <stack>
#include <map>
#include <set>
#include <cmath>
#include <cctype>
#include <ctime>

using namespace std;

#define REP(i, n) for (int i = 0; i < (n); ++i)
#define eps 1e-9
#define SZ(x) ((int)x.size())

typedef long long ll;
typedef pair<int, int> pii;
const int mod = 1e8;
int n1, n2, k1, k2;
int dp[105][105][15][15];

int main() {
#ifdef __AiR_H
    freopen("in.txt", "r", stdin);
//    freopen("out.txt", "w", stdout);
#endif // __AiR_H
    scanf("%d %d %d %d", &n1, &n2, &k1, &k2); int ans = 0;
    for (int i = 1; i <= min(n1, k1); ++i) { dp[i][0][i][0] = 1; }
    for (int i = 1; i <= min(n2, k2); ++i) { dp[0][i][0][i] = 1; }
    for (int i = 1 ; i <= n1; ++i) {
        for (int j = 1; j <= n2; ++j) {
            for (int k = 1; k <= min(j, k2); ++k) {
                dp[i][j][1][0] += dp[i - 1][j][0][k];
                dp[i][j][1][0] %= mod;
            }
            for (int k = 1; k <= min(i, k1); ++k) {
                dp[i][j][0][1] += dp[i][j - 1][k][0];
                dp[i][j][0][1] %= mod;
            }
            for (int k = 2; k <= min(k1, i); ++k) {
                dp[i][j][k][0] += dp[i - 1][j][k - 1][0];
                dp[i][j][k][0] %= mod;
            }
            for (int k = 2; k <= min(k2, j); ++k) {
                dp[i][j][0][k] += dp[i][j - 1][0][k - 1];
                dp[i][j][0][k] %= mod;
            }
        }
    }
    for (int i = 1; i <= min(n1, k1); ++i) {
        ans += dp[n1][n2][i][0]; ans %= mod;
    }
    for (int i = 1; i <= min(n2, k2); ++i) {
        ans += dp[n1][n2][0][i]; ans %= mod;
    }
    printf("%d
", ans);
#ifdef __AiR_H
    printf("Time used = %.2fs
", (double)clock() / CLOCKS_PER_SEC);
#endif // __AiR_H
    return 0;
}