Topic link

【 The valley gate 】

Answer key

\(f[i][j][k]\) It means to eliminate \((i,j)\), Add... To the back \(k\) The total number of beads per bead .
Consider three kinds of decisions :( The title gives \(k\) It is expressed as \(K\))

Decision making 1

When \(k<K-1\) when , Consider adding a bead , That is the state \(f[i][j][k+1]\) Transfer to get \(f[i][j][k]\). Because with a bead , So the equation is \(f[i][j][k]=min(f[i][j][k+1]+1)\)

Decision making 2

If \(k=K+1\), It shows that this can be eliminated , That is from \(f[i][j][k]=f[i+1][j][0]\).

Decision making 3

If \(i\) The color and \(i+1\) It's the same color , So you can take \(i\) Add to \(i+1\) in , So the equation is \(f[i][j][k]=f[i+1][j][k+1]\).

The answer is obviously \(f[1][n][0]\).

In view of this problem, the equation and the state transfer between the equations are relatively scattered , So it's easy to use memory search .


#include <bits/stdc++.h>
#define inf 0x3f3f3f3f
#define N 105
using namespace std;
int f[N][N][N], a[N];
int n, K;
int DP(int l, int r, int k) {
if (f[l][r][k] != -1) return f[l][r][k];
if (l > r) return 0;
f[l][r][k] = inf;
if (k < K - 1) f[l][r][k] = min(f[l][r][k], DP(l, r, k + 1) + 1);
if (k == K - 1) f[l][r][k] = DP(l + 1, r, 0);
for (int i = l + 1; i <= r; i ++)
if (a[i] == a[l]) f[l][r][k] = min(f[l][r][k], DP(l + 1, i - 1, 0) + DP(i, r, min(K - 1, k + 1)));
return f[l][r][k];
int main() {
cin >> n >> K;
for (int i = 1; i <= n; i ++) cin >> a[i];
memset(f, -1, sizeof(f));
DP(1, n, 0);
cout<< f[1][n][0] << endl;
return 0;

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