Go: package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

type Matrix struct {
	r int // num of row
	c int // num of column
}

type Range struct {
	start int // index, inclusive
	end   int // index, inclusive
}

func calcMultiplication(x, y Matrix) (Matrix, int) {
	if x.c != y.r {
		panic("cannnot calculate")
	}
	return Matrix{x.r, y.c}, x.r * y.c * x.c
}

func calcMinMatrixChainMultiplication(matrices []Matrix, r Range, memo map[Range]int) (Matrix, int) {
	if v, ok := memo[r]; ok {
		return Matrix{matrices[0].r, matrices[len(matrices)-1].c}, v
	}
	if len(matrices) == 0 {
		panic("must not be empty")
	} else if len(matrices) == 1 {
		return matrices[0], 0
	} else if len(matrices) == 2 {
		return calcMultiplication(matrices[0], matrices[1])
	}

	var minCount int = math.MaxInt32

	for i := 0; i < len(matrices)-1; i++ {
		formerMatrices := matrices[:i+1]
		latterMatrices := matrices[i+1:]
		matF, countF := calcMinMatrixChainMultiplication(formerMatrices, Range{0, i}, memo)
		matL, countL := calcMinMatrixChainMultiplication(latterMatrices, Range{i + 1, len(matrices) - 1}, memo)
		_, countFL := calcMultiplication(matF, matL)
		count := countF + countL + countFL
		if count < minCount {
			minCount = count
		}
	}
	return Matrix{matrices[0].r, matrices[len(matrices)-1].c}, minCount
}

func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	n, _ := nextInt(sc)
	matrices := make([]Matrix, n)
	for i := 0; i < n; i++ {
		r, _ := nextInt(sc)
		c, _ := nextInt(sc)
		matrices[i] = Matrix{r, c}
	}
	memo := make(map[Range]int)
	_, resultCount := calcMinMatrixChainMultiplication(matrices, Range{0, len(matrices) - 1}, memo)
	fmt.Println(resultCount)
}

func nextInt(sc *bufio.Scanner) (int, error) {
	sc.Scan()
	return strconv.Atoi(sc.Text())
}

Python: def memoize(f):  
    cache = {}  
    def helper(x):  
        if x not in cache:              
            cache[x] = f(x)  
        return cache[x]  
    return helper 

def split_rc(rc):
    for i in range(1, len(rc)):
        yield rc[:i], rc[i:]

@memoize
def cost(rc):
    if len(rc) == 1:
        return 0
    return min(calc_cost(first, second) for first, second in split_rc(rc))

def calc_cost(first, second):
    return cost(first) + cost(second) + first[0][0] * first[-1][1] * second[-1][1]

n = int(input())
rc = tuple(tuple(map(int, input().split())) for _ in range(n))
print(cost(rc))

Python: n = int(input())
data = []
for i in range(n):
    data.append(list(map(int, input().split())))

memo = []
for _ in range(n):
    memo.append([-1]*n)


def mul(i, j):
    if i == j:
        return 0
    if memo[i][j] >= 0:
        return memo[i][j]
    num = 100000
    for k in range(i, j):
        num = min(num, mul(i, k) + mul(k+1, j) + data[i][0] * data[k][1] * data[j][1])
    memo[i][j] = num
    return memo[i][j]

print(mul(0, n-1))

Python: import sys, copy

num = int(sys.stdin.readline())

if num==1:
    print(0)
    quit()
    
mm = list(map(int, sys.stdin.readline().split()))
for _ in range(num-1):
    mm.append(int(sys.stdin.readline().split()[1]))

used = [False] * num
seq = [0] * (num-2)
minv = 0
j=mm[1]
for i in mm[2:]:
    minv += i*j
    j=i
minv *= mm[0]    

print('min=',minv)
def sequence(n, k, m, t):
    global minv, used, seq
    if k==m:
        t += mm[0]*mm[used[1:].index(False)+1]*mm[num]
        if minv>t:    minv = t
    else:
        for i in range(1,n+1):
            if used[i]: continue
            seq[m] = i
            used[i]=True

            l=i-1
            while l>0 and used[l]:     l-=1
            u=i+1
            while u<num and used[u]:   u+=1
            v = mm[l]*mm[i]*mm[u]
            if minv>t+v: sequence(n, k, m+1, t+v)
            used[i]=False

sequence(num-1, num-2, 0, 0)

print(minv)

Python: #!/usr/bin/env python3
# -*- coding: utf-8 -*-

import sys
import re
import math
import collections
import itertools
import functools
import logging

logging.basicConfig(level=logging.DEBUG, format="DBG: %(message)s")

def dbg(msg, *args, **kwargs):
    logging.debug(msg, *args, **kwargs)

Mat = collections.namedtuple("Mat", "r c")

def mat_mul(ms):
    return Mat(ms[0].r, ms[-1].c)

def cost(m1, m2):
    return m1.r * m1.c * m2.c

def solve(n, ms):
    if n == 1: return 0

    dp = {}
    for i in range(n):
        dp[(i,i)] = 0

    for l in range(2, n+1):
        for i in range(n-l+1):
            #cost_min = math.inf
            cost_min = float("inf")
            for j in range(l-1):
                #dbg("l, i, j: %d %d %d", l, i, j)
                m_lhs = mat_mul(ms[i:i+j+1])
                m_rhs = mat_mul(ms[i+j+1:i+l])
                #dbg("m_lhs, m_rhs: %r %r", m_lhs, m_rhs)
                cost_lhs = dp[(i,i+j)]
                cost_rhs = dp[(i+j+1,i+l-1)]
                #dbg("cost_lhs, cost_rhs: %d %d", cost_lhs, cost_rhs)
                cost_mul = cost(m_lhs, m_rhs)
                #dbg("cost_mul: %d", cost_mul)
                cost_now = cost_mul + cost_lhs + cost_rhs
                #dbg("cost_now: %d", cost_now)
                if cost_min > cost_now:
                    cost_min = cost_now
            dp[(i,i+l-1)] = cost_min

    #dbg(dp)
    return dp[(0,n-1)]

def main():
    n = int(input())

    ms = []
    for _ in range(n):
        r,c = map(int, input().split())
        ms.append(Mat(r,c))

    print(solve(n, ms))

if __name__ == "__main__": main()

Python: n = int(input())
r=[0]*(n+1)
c=[0]*(n+1)
for i in range(n):
    r[i+1], c[i+1] = map(int, input().split())

dp = [[float('inf') for i in range(n+1)] for j in range(n+1)]

for i in range(n+1):
    dp[i][i] = 0

# print("")
for l in range(2, n+1):
    for i in range(1, n-l+2):
        # print("l=", l, "i=", i)
        tmp_list = [r[i] * c[i+l-1] * r[j+1] + dp[i][j] + dp[j+1][i+l-1] for j in range(i, i+l-1)]
        dp[i][i+l-1] = min(tmp_list)

print(dp[1][n])

Python: n=int(input())+1
e=[input().split()for _  in[0]*~-n]
p=[int(e[0][0])]+list(int(x[1])for x in e)
m=[[0]*n for _ in[0]*n]
for l in range(2,n):
 for i in range(1,n-l+1):
  j=i+l-1;m[i][j]=1e6
  for k in range(i,j):m[i][j]=min(m[i][j],m[i][k]+m[k+1][j]+p[i-1]*p[k]*p[j])
print(m[1][n-1])

Python: n = int(input())
p = [0] * (n + 1)
m = [[0 for _ in range(100)] for _ in range(100)]

for i in range(n):
    p[i], p[i + 1] = map(int, input().split())

for l in range(2, n + 1):
    for i in range(1, n - l + 2):
        j = i + l - 1
        m[i][j] = float('inf')
        for k in range(i, j):
            m[i][j] = min(m[i][j], m[i][k] + m[k+1][j] + p[i-1] * p[k] * p[j])
print(m[1][n])

Python: def s():
 n=int(input())+1
 e=[input().split()for _  in[0]*~-n]
 p=[int(e[0][0])]+list(int(x[1])for x in e)
 m=[[0]*n for _ in[0]*n]
 for i in range(n):
  for r in range(n-i-1):
   c=r+i+1
   for j in range(r+1,c):
    x=m[r][j]+m[j][c]+p[r]*p[j]*p[c]
    if not 0<m[r][c]<=x:m[r][c]=x
 print(m[r][c])
if'__main__'==__name__:s()

Python: def s():
 n=int(input())+1
 e=[input().split()for _  in[0]*~-n]
 p=[int(e[0][0])]+list(int(x[1])for x in e)
 m=[[0]*n for _ in[0]*n]
 for i in range(n):
  for r in range(n-i-1):
   c=r+i+1
   for j in range(r+1,c):
    x=m[r][j]+m[j][c]+p[r]*p[j]*p[c]
    if 1>m[r][c]or m[r][c]>x:m[r][c]=x
 print(m[r][c])
if'__main__'==__name__:s()

Python: N = int(input())
P = []
for i in range(N):
    r, c = map(int, input().split())
    if i == 0:
        P.append(r)
    P.append(c)


def matrix_chain():
    dp = [[None for j in range(N+1)] for i in range(N+1)]
    for i in range(1, N+1):
        dp[i][i] = 0

    for l in range(2, N+1):
        for i in range(1, N-l+2):
            j = i + l - 1
            dp[i][j] = 1000000000000000
            for k in range(i, j):
                dp[i][j] = min(dp[i][j], dp[i][k]+dp[k+1][j]+P[i-1]*P[k]*P[j])

    return dp[1][N]


def main():
    print(matrix_chain())


if __name__ == '__main__':
    main()