function numOfWays2(n) {
if (n < 0) return 0;
if (n == 0) return 1;
return numOfWays2(n-1) + numOfWays2(n-2);
}
numOfWays2(1)
numOfWays2(2)
numOfWays2(3)
numOfWays2(4)
numOfWays2(5)
function numOfWays3(n) {
if (n == 0) return 1;
let res = 0;
for (let i = 1; i <= 3; i++) {
if (n - i < 0) continue;
res = res + numOfWays3(n - i);
}
return res
}
numOfWays3(3)
numOfWays3(4)
numOfWays3(5)
function numOfWays(maxSteps, totalStairs) {
function climb(n) {
if (n == 0) return 1;
let res = 0;
for (let i = 1; i <= maxSteps; i++) {
if (n - i < 0) continue;
res = res + climb(n - i);
}
return res;
}
return climb(totalStairs);
}
numOfWays(2,3)
numOfWays(3,4)
function numOfWaysM(maxSteps, totalStairs) {
let mem = {};
function climb(n) {
if (n == 0) return 1;
if (n in mem) return mem[n];
let res = 0;
for (let i = 1; i <= maxSteps; i++) {
if (n - i < 0) continue;
res = res + climb(n - i);
}
mem[n] = res;
return res;
}
return climb(totalStairs);
}
numOfWaysM(2,40)
numOfWaysM(2,50)
numOfWaysM(3,40)
numOfWaysM(10,50)
function numOfWaysN(maxSteps, totalStairs) {
let mem = {};
function climb(n) {
if (n == 0) return 1n;
if (n in mem) return mem[n];
let sum = 0n;
for (let i = 1; i <= maxSteps; i++) {
if (n < i) continue;
sum += climb(n - i);
}
mem[n] = sum;
return sum;
}
return climb(totalStairs);
}
numOfWaysN(2,100)
numOfWaysN(3,100)
numOfWaysN(4,100)
function numOfWaysL(maxSteps, totalStairs) {
let climbs = [1n];
for (let n = 1; n <= totalStairs; n++) {
let res = 0n;
for (let i = 1; i <= maxSteps; i++) {
if (n - i < 0) continue;
res = res + climbs[n - i];
}
climbs.push(res);
}
return climbs.at(-1);
}
numOfWaysL(10,10000)
function numOfWaysP(maxSteps, totalStairs) {
let m = [1];
function climb(n) {
if (n == 0) return 1;
if (n in m) return m[n];
let res = 0;
for (let i = 1; i <= maxSteps; i++) {
if (n - i < 0) continue;
res = res + climb(n - i);
}
m[n] = res;
return res;
}
climb(totalStairs);
return m
}
numOfWaysP(2,40)
numOfWaysP(3,70)
numOfWaysP(4,60)
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