Interval DP learning from entry to the template

main idea

Interval DP, by definition, be an enumeration range DP. It represents the optimal solution with a range dp [i] [j], then the large interval from an inter combined, the final solution is obtained throughout a large interval.
Process enumeration algorithm is three, the first layer enumeration interval length, a second enumeration starting interval, the third layer enumeration division point intervals.
So that when the enumeration second layer, third layer ensures that the interval has passed enumeration.

State transition:

	dp[i][j] = max(dp[i][j],dp[i][k]+dp[k+1][j]+w[i][j]);

template

Simple enumeration: the n- ³

memset(dp,0,sizeof(dp))			 //初始dp数组
for(int len=1;len<=n;len++){ 	 //第一层枚举区间长度
    for(int i=0;i+len <= n;++i){ //枚举区间的起点
        int j=i+len-1;			 //根据起点和长度得出终点
        for(int k=i;k<=j;++k)	 //枚举分割点
            dp[i][j]=min(dp[i][j],dp[i][k]+dp[k+1][j]+w[i][j]);//状态转移方程
    }
}          

Quadrilateral optimized code: n- ²

for(int len=2;len<=n;len++){
    for(int i = 1;i<=n;i++){
	int j = i+len-1;
	if(j>n) break;
	for(int k = s[i][j-1];k<=s[i+1][j];k++){
	    if(dp[i][j]>dp[i][k]+dp[k+1][j]+w[i][j]){
		dp[i][j]=dp[i][k]+dp[k+1][j]+w[i][j];
		s[i][j]=k;
	    }
	}
    }
}

A few classic examples

Getting template question: stone merge

Simple question: poj1651-- optimal chain matrix multiplication , poj2955-- bracket matching interval dp + Classic title

Thinking: hdu2476-- classic range dp , hdu4283-- classic range dp ,